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Since the beginning of the COVID-19 pandemic in early 2020 until the time of finishing this dissertation in July 2022, the World Health Organization has registered almost 560 Million cases and well over 6 Million deaths from COVID-19. Although a number of effective vaccines have been developed and large-scale vaccination campaigns have been implemented globally, only 58 of 194 WHO member states have met the 70\% vaccine coverage goal. Thus, mathematical models of disease spread remain one of the most important tools to understand the spread of such dynamics and can thus support public health policymaking. Network models of disease spread, the type of model addressed in this dissertation, have the advantage of accounting for social structure. However, they typically neglect the changes in our social relationships, despite the evidence that people avoid public places or infectious others during times of increased risk of infection. This dissertation presents, to our knowledge, the first model for the co-evolution of social networks and infectious diseases considering theory from social sciences, health psychology and epidemiology. The Networking during Infectious Diseases Model (NIDM) describes networking decisions as a trade-off between the benefits, costs, and potential harms of infections that a social relation creates. Agent-based simulations suggest that disease avoidance may reduce infection numbers significantly, depending on risk perceptions and network structure. A large-scale networking experiment, however, suggests that when disease avoidance is prioritized over maintaining social relationships, the cost might be a loss of social cohesion.

Many human and natural systems are highly complex, because they consist of many interacting parts. Such systems are known as complex adaptive systems (CAS). Understanding CAS is possible only by studying the interactions between constituent parts, rather than focussing only on the properties of the parts in isolation. Often, the possibilities for systematically studying these interactions in real-life systems are limited. Simulation models can then be an important tool for testing what properties may emerge, given various assumptions on the interactions in the system. Agent-based models (ABMs) are particularly useful for studying CAS, because ABMs explicitly model interactions between autonomous agents and their environment. Currently, the utility of ABMs is limited by a lack of available methodologies for analysing their results. The main tool for analysing CAS models is sensitivity analysis. Yet, standard methods of sensitivity analysis are not well-suited to deal with the complexity of ABMs. Thus, there is a need for sensitivity analysis methodologies that are specifically developed for analysing ABMs. The objective of this thesis is to contribute such methodologies. Specifically, we propose methodologies for (1) detecting tipping points, (2) analysing the effects of agent adaptation, and (3) analysing resilience of ABMs. Chapter 2 introduces traditional methods of sensitivity analysis. These methods are demonstrated by applying them to rank the most influential parameters of an ODE model of predator-prey interaction. Furthermore, the role of sensitivity analysis in model validation is discussed. In Chapter 3 we investigate the use of sensitivity analysis for detecting tipping points. Whereas bifurcation analysis methods are available for detecting tipping points in ODE models, these methods are not applicable to ABMs. Therefore, we use an ODE model to verify the results from sensitivity analysis against those of bifurcation analysis. We conclude that one-factor-at-a-time sensitivity analysis (OFAT) is a helpful method for detecting tipping points. However, OFAT is a local method that considers only changes in individual parameters. It is therefore recommended to supplement OFAT with a global method to investigate interaction effects. For this purpose, we recommend all-but-one-at-a-time sensitivity analysis (ABOS) as a graphical sensitivity analysis method that takes into account parameter interactions and can help with the detection of tipping points. In Chapter 4 we introduce a basic ABM model of agents competing in a spatial environment for a renewable resource. This basic model will be extended in the subsequent chapters, and will serve as a testing case for various sensitivity analysis methods. In Chapter 4, it is used to assess the utility of existing sensitivity analysis methods for ABMs. The results show that traditional methods of sensitivity are not sufficient to analyse the ABM, due to the presence of tipping points and other strong non-linearities in the model output. In contrast, OFAT is found to be helpful for detecting tipping points, as was suggested in Chapter 3. Based on these outcomes, OFAT is recommended as a starting point for sensitivity analysis of ABMs, preferably supplemented by a global method to investigate interaction effects. In Chapter 5 we extend the ABM of Chapter 4 by adding agent adaptation in the form of a mechanism of natural selection. On short time-scales, the model behaviour appears to be similar to the non-adaptive model version. On longer time-scales, the agent adaptation causes the state of the model to gradually change as agents continue to adapt to their surroundings. We propose a sensitivity analysis method to measure the effects of this adaptation. This method is based on a quantification of the difference between probability density functions of model version with and without adaptation. Using this method, we show that this adaptation increases the resilience of the system by giving it the flexibility needed to respond to pressures. In Chapter 6 we further extend the test-case by giving agents the option to harvest either cooperatively or individually. Cooperation increases the potential yields, but introduces the risk of defection of the interaction partner. It is shown that ecological factors, which are usually not considered in models on cooperation, strongly affect the level of cooperation in the system. For example, low levels of cooperation lead to a decreased population size, and causes the formation of small groups of agents with a higher level of cooperation. As a result, cooperation persists even without any mechanisms to promote it. Nevertheless, the inclusion of such mechanisms in the form of indirect reciprocity does further increase the level of cooperation. Furthermore, we show that the resulting high levels of cooperation, depending on the circumstances, can increase the resilience of the agent population against shocks. To conclude, in this thesis several methodologies have been proposed to help with ABM analysis. Specifically, OFAT and ABOS are recommended for detecting tipping points in ABMs, and in Chapter 5 a protocol is introduced for quantifying the effects of adaptation. By suggesting these methodologies, this thesis aims to contribute to the utility of ABMs, especially for studying CAS.

Modern biological research is accumulating an ever-increasing amount of information on genes and their functions. It is apparent that biological functions can very rarely be attributed to a single genes, but rather arise from complex interaction within networks that comprise many genes. A fundamentally important challenge in contemporary biology is to extract mechanistic understanding about the complex behavior of genetic networks from the available data. The interactions within a genetic network are often exceedingly complex and no-linear in nature, and thus are not open to intuitive understanding. This situation has given rise to a host of mathematical and computational approaches aimed at in-depth analysis of genetic network topologies and dynamics. In particular these approaches focus on system level proprieties of these networks, not directly derivable from their constituent components. To a large extent the power of these theoretical approaches rely on meaningful reduction in complexity by utilizing justified simplifications and abstractions. The underlying principle is that in order to comprehend a mechanism, it is not necessary to take into account all the available information about the mechanism. Given this, Computational models that follow this approach focus on incorporating core components that are essential in answering a specific biological question, while simplifying/omitting the less relevant processes. A fundamental question is this regard is what simplifying concept should be employed when developing a theoretical model of a genetic network. A successful approach to address this question is the notion of network motif analysis. This approach is based on the core idea that most genetic networks are not arbitrary nor unique, instead they can be categorized into common network dynamics and topologies that perform core functions. Analogous to components of an electric circuit (resistors, capacitor, etc.) these network motifs have distinct properties that are independent of the network that they are embedded in. Therefore analysis of genetic networks in terms of their constituent motifs can potentially be an effective mean in obtaining mechanistic understanding about them. In this thesis the network motif approach is utilized to study two instances of pattern formation in plant tissues. The first study focuses on organization of stem cells within the shoot apical meristem of the model plant, Arabidopsis thaliana. The results demonstrate that three interconnected network motifs can account for a range of experimental observations regarding this system. Furthermore through an exhaustive exploration of the available data, candidate genes and interactions corresponding to these motifs are outlined, thus paving the way for future interdisciplinary investigations. The second study explores the development of vasculature during arabidopsis embryogenesis. In contrast to shoot apical mersitem in mature plant, the cell number and arrangement of vasculature in highly dynamic during its embryonic development. To account for this feature, a computational framework was utilized that is capable of capturing the interplay between genes and cell growth and division. The outcome revealed that two interlocking networks motifs dynamically control both patterning and growth of the vascular tissue. The study revealed novel spatial features of a motif previously studies exclusively in non-spatial settings. Furthermore the study resulted in a compelling example of model-driven discovery, where theoretical analysis predicted a specific cellular arrangement to be crucial for the correct development of vasculature. Subsequent analysis of experimental data confirmed the existence of this cellular arrangement in the embryo. The projects presented in this thesis exemplify successful applications of the network motif approach in studying spatial genetic network. In both cases the networks were successfully examined in terms of their constituent motifs, which subsequently lead to increased mechanistic understanding of them. Ultimately the work presented in this thesis demonstrates the effectiveness of studying genetic networks by a combination of careful examination of available biological data and a reductionist modeling approach guided by the concept of network motifs.

Keywords: Control, cost-benefit, economic impact, epidemiology, Ethiopia, Foot and mouth disease, intention, modelling, production system. Bioeconomic Modelling of Foot and Mouth Disease and Its control in Ethiopia Foot and mouth disease (FMD) is a highly contagious viral disease which affects cloven hoofed animals. FMD is endemic in Ethiopia with potential impact both on national and household economies because of its effect on production and trade. The general objective of this PhD research was to provide insight into the epidemiology and economics of FMD and its control in Ethiopia to support decision making in the control of the disease. A study of the national incidence of FMD outbreak revealed that the disease is endemic in all regional states affecting more than a quarter of the country every year, with the highest frequency of outbreaks occurring in the central, southern and southeastern parts of the country. The type of production system, presence of a major livestock market and/or route, and adjacency to a national parks or wildlife sanctuary were associated with the risk of outbreaks in the districts. Field outbreak study indicated that FMD morbidity rates of 85% and 95 % at herd level; and 74% and 61% at animal level in the affected herds in the crop–livestock mixed system (CLM) and pastoral system, respectively. The herd level economic loss estimates were on average USD 76 per affected herd in CLM and USD 174 per affected herd in the pastoral production system. Study of motivation of farmers to implement FMD control, through the Health Belief Model (HBM) framework, revealed that almost all farmers had high intention to implement FMD vaccination free of charge, which decreases, especially in CLM system, if the vaccine is charged. Farmers in the pastoral and crop-livestock mixed production systems had low intention to implement herd isolation and animal movement restriction control measure. Among the HBM perception constructs perceived barrier was found to be the most important predictor of the intention to implement FMD control measures. A modelling study on the national economic impact and cost-benefit analysis FMD control strategies showed that the annual cost of the disease is about 1,354 million birr. A stochastic cost-benefit analysis of three potential FMD control strategies indicated that all the strategies on average have a positive economic return but with variable degree of uncertainty including possibility of loss. Targeted vaccination strategy gives relatively the best economic return with relatively less risk of loss.

Keywords: Control, cost-benefit, economic impact, epidemiology, Ethiopia, Foot and mouth disease, intention, modelling, production system. Bioeconomic Modelling of Foot and Mouth Disease and Its control in Ethiopia Foot and mouth disease (FMD) is a highly contagious viral disease which affects cloven hoofed animals. FMD is endemic in Ethiopia with potential impact both on national and household economies because of its effect on production and trade. The general objective of this PhD research was to provide insight into the epidemiology and economics of FMD and its control in Ethiopia to support decision making in the control of the disease. A study of the national incidence of FMD outbreak revealed that the disease is endemic in all regional states affecting more than a quarter of the country every year, with the highest frequency of outbreaks occurring in the central, southern and southeastern parts of the country. The type of production system, presence of a major livestock market and/or route, and adjacency to a national parks or wildlife sanctuary were associated with the risk of outbreaks in the districts. Field outbreak study indicated that FMD morbidity rates of 85% and 95 % at herd level; and 74% and 61% at animal level in the affected herds in the crop–livestock mixed system (CLM) and pastoral system, respectively. The herd level economic loss estimates were on average USD 76 per affected herd in CLM and USD 174 per affected herd in the pastoral production system. Study of motivation of farmers to implement FMD control, through the Health Belief Model (HBM) framework, revealed that almost all farmers had high intention to implement FMD vaccination free of charge, which decreases, especially in CLM system, if the vaccine is charged. Farmers in the pastoral and crop-livestock mixed production systems had low intention to implement herd isolation and animal movement restriction control measure. Among the HBM perception constructs perceived barrier was found to be the most important predictor of the intention to implement FMD control measures. A modelling study on the national economic impact and cost-benefit analysis FMD control strategies showed that the annual cost of the disease is about 1,354 million birr. A stochastic cost-benefit analysis of three potential FMD control strategies indicated that all the strategies on average have a positive economic return but with variable degree of uncertainty including possibility of loss. Targeted vaccination strategy gives relatively the best economic return with relatively less risk of loss.

De auteurs van dit artikel vinden dat een platform als de Commissie voor Hydrologisch Onderzoek (CHO) nuttig kan zijn om kennis uit te wisselen. Daarbij moet worden nagedacht hoe deze kennis voor langere tijd kan worden vastgehouden. Een belangrijk deel van de kennis die indertijd via de technische bijeenkomsten van de CHO is uitgewisseld en is vastgelegd in haar verslagen, is momenteel wellicht niet meer paraat. Er wordt een oproep gedaan om de in het H2O-artikel "Omgekeerde hydrologie" (2008) gepresenteerde casus te modelleren. De auteurs stellen voor om over enige tijd de bevindingen onderling te delen in een workshop

Het artikel beschrijft de voornaamste ontwikkelingen in gewasgroeimodellen (WOFOST), hun gebruik in CGMS en geïntegreerde modellering

Op welke manier kunnen wiskundige modellen worden ingezet bij het ontwerpen van mengsels, en hoe kan dat op een robuuste manier worden gedaan?

Biogas, synthesis and natural gas streams often require treatment because of the presence of gaseous hydrogen sulphide (H2S). About 25 years ago, a biotechnological gas treatment process was developed as an alternative to the conventionally applied technologies. This process is known as the Thiopaq process and offers a number of advantages compared to the existing physical-chemical processes. Depending on the process conditions, H2S is oxidized to elemental bio-sulfur (90-94 mol%) and sulphate (6-10 mol%). In order to enable cost effective large scale applications, the selectivity for sulfur production should be increased to more than 97 mol%. Hence, a better understanding of the combined effect of abiotic and biological reaction kinetics and the relation to hydrodynamic characteristics is required. The first part of this PhD study focuses on biological reaction kinetics and biological pathways for sulphide oxidation that occur in the process at haloalkaline conditions. It was found that two different sulfide oxidizing enzyme systems are present in haloalkaline sulfide oxidizing bacteria. It has been hypothesized that the different enzymatic routes are determined by the process conditions. Both enzyme systems were taken into account to propose and validate a new physiological mathematical model that can handle multi-substrates and multi-products. In the second part of the thesis, this model was evaluated via a normalized sensitivity method and it was demonstrated that certain key parameters affect the activity of the biomass at different substrate levels. Furthermore, from CSTR simulations it has been demonstrated that non-linear effects are of importance when scaling up from lab-scale to full-scale industrial units. Finally, the developed kinetic models have been incorporated in a full-scale biodesulfurization model that includes the effects of turbulent flow regimes and mass transfer of oxygen. This enables us to better understand the overall process. Moreover, the model can also be used as a tool to design model-based control strategies which will lead to better overall process performance, i.e. maximize sulfur production and minimize chemical consumption rates.

(R.Kiwamoto ISBN 978-94-6257-284-3) Various α,β-unsaturated aldehydes are present in fruits, vegetables, spices, or processed products containing these items as natural constituents or as added food flavouring agents. Because of the α,β-unsaturated aldehyde moiety the β carbon in the molecule becomes electron deficient and the aldehydes react with electron rich molecules including DNA via Michael addition. The formation of DNA adducts raises a concern for genotoxicity, although formation of DNA adducts may not be significant at low doses relevant for dietary exposure in vivo because of adequate detoxification. This thesis therefore aimed at determining dose-dependent detoxification and DNA adduct formation of food-borne α,β-unsaturated aldehydes by using a physiologically based in silico modelling approach in order to contribute to the safety assessment of these aldehydes used as food flavourings instead of performing animal experiments. Physiologically based in silico models were developed for 18 α,β-unsaturated aldehydes. The model outcomes indicated that the DNA adduct formation by the 18 α,β-unsaturated aldehydes as food flavourings is negligible and does not raise a safety concern at their levels of intake resulting from their use as food flavourings. The application of QSAR models strongly accelerated the development process of the PBK/D models of the group of 18 compounds. Also, it was illustrated that physiologically based in silico models provide a very useful and powerful tool to facilitate a group evaluation and read-across for food-borne DNA reactive agents. PBK/D models developed for the group of compounds supported read-across from cinnamaldehyde which is known not to be genotoxic or carcinogenic in vivo to other aldehydes, by allowing comparison of dose-dependent DNA adduct formations. Altogether this thesis presented physiologically based in silico modelling as an approach to test relevance of positive in vitro genotoxicity results by DNA reactive compounds in vivo without using animal experiments.

(R.Kiwamoto ISBN 978-94-6257-284-3) Various α,β-unsaturated aldehydes are present in fruits, vegetables, spices, or processed products containing these items as natural constituents or as added food flavouring agents. Because of the α,β-unsaturated aldehyde moiety the β carbon in the molecule becomes electron deficient and the aldehydes react with electron rich molecules including DNA via Michael addition. The formation of DNA adducts raises a concern for genotoxicity, although formation of DNA adducts may not be significant at low doses relevant for dietary exposure in vivo because of adequate detoxification. This thesis therefore aimed at determining dose-dependent detoxification and DNA adduct formation of food-borne α,β-unsaturated aldehydes by using a physiologically based in silico modelling approach in order to contribute to the safety assessment of these aldehydes used as food flavourings instead of performing animal experiments. Physiologically based in silico models were developed for 18 α,β-unsaturated aldehydes. The model outcomes indicated that the DNA adduct formation by the 18 α,β-unsaturated aldehydes as food flavourings is negligible and does not raise a safety concern at their levels of intake resulting from their use as food flavourings. The application of QSAR models strongly accelerated the development process of the PBK/D models of the group of 18 compounds. Also, it was illustrated that physiologically based in silico models provide a very useful and powerful tool to facilitate a group evaluation and read-across for food-borne DNA reactive agents. PBK/D models developed for the group of compounds supported read-across from cinnamaldehyde which is known not to be genotoxic or carcinogenic in vivo to other aldehydes, by allowing comparison of dose-dependent DNA adduct formations. Altogether this thesis presented physiologically based in silico modelling as an approach to test relevance of positive in vitro genotoxicity results by DNA reactive compounds in vivo without using animal experiments.

Biogas, synthesis and natural gas streams often require treatment because of the presence of gaseous hydrogen sulphide (H2S). About 25 years ago, a biotechnological gas treatment process was developed as an alternative to the conventionally applied technologies. This process is known as the Thiopaq process and offers a number of advantages compared to the existing physical-chemical processes. Depending on the process conditions, H2S is oxidized to elemental bio-sulfur (90-94 mol%) and sulphate (6-10 mol%). In order to enable cost effective large scale applications, the selectivity for sulfur production should be increased to more than 97 mol%. Hence, a better understanding of the combined effect of abiotic and biological reaction kinetics and the relation to hydrodynamic characteristics is required. The first part of this PhD study focuses on biological reaction kinetics and biological pathways for sulphide oxidation that occur in the process at haloalkaline conditions. It was found that two different sulfide oxidizing enzyme systems are present in haloalkaline sulfide oxidizing bacteria. It has been hypothesized that the different enzymatic routes are determined by the process conditions. Both enzyme systems were taken into account to propose and validate a new physiological mathematical model that can handle multi-substrates and multi-products. In the second part of the thesis, this model was evaluated via a normalized sensitivity method and it was demonstrated that certain key parameters affect the activity of the biomass at different substrate levels. Furthermore, from CSTR simulations it has been demonstrated that non-linear effects are of importance when scaling up from lab-scale to full-scale industrial units. Finally, the developed kinetic models have been incorporated in a full-scale biodesulfurization model that includes the effects of turbulent flow regimes and mass transfer of oxygen. This enables us to better understand the overall process. Moreover, the model can also be used as a tool to design model-based control strategies which will lead to better overall process performance, i.e. maximize sulfur production and minimize chemical consumption rates.

The use of DNA markers to evaluate genetic diversity is an important component of the management of animal genetic resources. The Food and Agriculture Organisation of the United Nations (FAO) has published a list of recommended microsatellite markers for such studies; however, other markers are potential alternatives. This paper describes results obtained with a set of amplified fragment length polymorphism (AFLP) markers as part of a genetic diversity study of European pig breeds that also utilized microsatellite markers. Data from 148 AFLP markers genotyped across samples from 58 European and one Chinese breed were analysed. The results were compared with previous analyses of data from 50 microsatellite markers genotyped on the same animals. The AFLP markers had an average within-breed heterozygosity of 0.124 but there was wide variation, with individual markers being monomorphic in 3¿98% of the populations. The biallelic and dominant nature of AFLP markers creates a challenge for their use in genetic diversity studies as each individual marker contains limited information and AFLPs only provide indirect estimates of the allelic frequencies that are needed to estimate genetic distances. Nonetheless, AFLP marker-based characterization of genetic distances was consistent with expectations based on breed and regional distributions and produced a similar pattern to that obtained with microsatellites. Thus, data from AFLP markers can be combined with microsatellite data for measuring genetic diversity.

This paper aims to explain results of respirometry experiments using Activated Sludge Model No. 1. In cases of insufficient fit of ASM No. 1, further modifications to the model were carried out and the so-called “Enzymatic model” was developed. The best-fit method was used to determine the effect of the proposed modifications. Increased agreement was found between simulated data and respirometry results, particularly for repeated respirometric tests with acetate as the sole substrate. Additionally, the influence of different biomass pre-conditioning methods was examined. Results from repeated respirometric tests suggest that presence of residual products in an activated sludge sample before respiration testing may decrease the sample's activity and significantly affect results from respirometric tests. An innovative approach to recover original activity is suggested by washing activated sludge samples with tap water or “mineral medium”. As allylthiourea (ATU) was used in most experiments to suppress endogenous nitrification, its influence on kinetic parameters was reviewed. Respirometric tests confirmed that ATU addition has a significant effect on activity and respiration rate of activated sludge samples and could affect results of respirometric analyses.

Scenarios are a way of creating alternative pictures of possible and desirable futures in the field of public health and health care. In preparing scenarios use can be made of models, especially mathematical models. Firstly, a review of the use of mathematical models in disease epidemiology studies by the STG is given. The STG is the Steering committee on Future health scenarios in the Netherlands. Secondly, an introduction in modelling, especially mathematical modelling, is given. The following topics are to be discussed: a system, a model, the cycle of building models, markov models and the validation of models. Thirdly, a review of models currently used in describing demography, disease epidemiology, risk and health care is presented. Finally, the link between mathematical modelling and the methodological aspects of scenarios is to be discussed.

Mathematical models play an important role in support of the preparation of policies and decision-making in health and environment. A major objective for the near future is to pay more attention to modelling quality assurance (MODQUA). Within the framework of the research project MODQUA the need of guidelines to the process of development and application of models has been investigated. This study revealed four main topics, which ask for the formulation of specific quality control criteria. Firstly, a software quality assurance plan is required. Secondly, the ease of use of the software package needs to be guaranteed. The administrative quality control of model calculations including input scenarios is another important item. Undoubtedly, the quality of the mathematical model itself is a key factor and makes the availability of methods, such as validation tools, for a systematic model analysis indispensable. It is recommended to start a pilot-study aimed at the integration and elaboration of criteria for these topics in practice.

Due to limited water resources available in the world and the ever growing world population, there is an increasing need for water recycling, recovery and multi-sourcing strategies. One of the new physical process technologies being investigated for water purification and/or constituent recycling is ultrasonic particle separation. This technology is especially interesting for harvesting particles with an almost neutral buoyancy. An ultrasonic particle filter does not use a filter medium, like sand or a membrane, but filters on a basis of acoustic forces in ultrasonic standing waves, which are able to immobilise particles in flowing water. The objective of this study was to develop an ultrasonic separation device for particle recovery and water purification. This separator should be fit for industrial applications treating cubic meters of water per hour. In order to reach this objective, a combined numerical-experimental approach was proposed to develop a model-based design of an ultrasonic separator. Each individual component of this separator was modelled using a finite element (FE) approach. The numerical simulations were continuously cross-checked with experiments in order to find the best solution possible. In this thesis, the source of the acoustic wave is a piezoelectric transducer attached to a glass matching layer of the acoustic cavity, which couples the transducer to the fluid inside the cavity, forming an acoustic resonator/separator. In order to obtain a valid FE transducer model, a limited set of material parameters for the piezoelectric transducer were obtained from the manufacturer, thus preserving prior physical knowledge to a large extent. The remaining unknown parameters were estimated from impedance (admittance) analysis combined with a numerical optimisation routine using 2D and 3D FE models. Thus, a full set of physically interpretable material parameters was obtained. The approach provided adequate accuracy of the estimates of the material parameters, near 1%. A similar approach as used for the transducer was applied to an existing ultrasonic separator, again preserving known physical parameters and estimating the remaining unknown or less certain parameters. The results showed that the approach led to a fully calibrated 2D model of the emptyseparator, which was subsequently validated with experiments on a filledseparator chamber. The large sensitivity of the separator to small variations indicated that either such system should be made and operated within tight specifications to obtain the required performance. Alternatively, the operation of the system should be adaptable to cope with a slightly off-spec system, requiring a feedback controller. Starting from a fully characterised existing separator with all material parameters found so far, the subsequent step was the actual design of, or extrapolation to, a new separator. A basic design for an industrial scale acoustic separator was obtained based on simulated flow characteristics inside the separation chamber, on acoustic analysis within the chamber and simulated particle trajectories combining these two analyses. Results showed that positioning the piezoelectric transducer surfaces perpendicular to the flow direction and introducing chamber partitioning with multiple flow lanes to enforce laminar flow, resulted in high particle retention. The average particle displacement was found to be related to acoustic pressure in the fluid, showing large retention at peak pressures above 1 MPa or average pressures above 0.5 MPa for small (10 µm), near buoyant (1100 kg/m3) particles at a flow speed of 3.5 cm/s, thus providing comprehensible criteria for subsequent optimisation. This basic ultrasonic standing wave separator design was optimised with respect to separation efficiency, throughput and energy consumption. The methodology, using a design of experiments (DOE) approach, showed that it was possible to improve system performance based on acoustic pressure profiles, separation efficiency and flow robustness. Compromising the energy consumption and aiming for maximum separation efficiency with a laminar stable flow up to 5 ml/s resulted in a separator with inner dimensions of 70 mm length, 20 mm width and 28.5 mm height using two transducers perpendicular to the direction of flow and three parallel flow lanes with 9.5 mm height each. The lowest power consumption (with an average of 30 W) with adequate pressure to trap the particles was obtained when it was not operated at the main eigenfrequency. Finally, this new ultrasonic particle filter was built and evaluated experimentally. The particle filter was a three channel device, manufactured from glass with four in/outlet ports made of ABS. It was operated in sequenced batch mode and the separation efficiency was determined at three flow rates ranging from 1 to 3 ml/s, using a stock suspension of insoluble potato starch of 1 g/l (1000 ppm). Concentrations of stock, filtrate and concentrate were measured using a turbidity meter and significant effects of acoustic particle concentration were measured at both outlets of the process. The maximum filtration efficiency and concentration efficiency were 54% and 76%, respectively. The performance found was lower than the 100% that was expected for 10 µm particles from the model based design study. The deviation in performance is mainly a result of (i) the pulsation of the feed pump, (ii) differences between the model and the actual prototype, (iii) the limited power supply of only 10 W used and (iv) (too) small particles, below 10 µm, occurring in the starch suspension. The best dimensions for an acoustic separator were obtained, but thus far operational characteristics were not yet studied. Operational characterisation and optimisation is the last step in the process of obtaining the best possible solution for operation. With the aim to achieve a high separation efficiency with minimal energy consumption, a model-based open-loop switching control strategy was designed for the commercially available BioSep, using a numerical-experimental approach. Firstly, a dynamic BioSep model structure was derived from mass balances and its system properties were studied. Then, the unknown system parameters were estimated from steady state and dynamic experimental data and subsequently, the switching times of the control input were determined. The model with switching control outputs was then validated by experiments. Finally, the control strategy was implemented in an experimental setup and tested using suspended potato starch. Results showed that the optimal control strategy reached a mass separation efficiency of 96%, which was an improvement of 4% with respect to the initial settings, while using less energy. Concluding, a stepwise numerical-experimental approach to acoustic separator design was presented in this study. The minimum power required was estimated to be 22-34 W, resulting in an average electric energy consumption of 1-1.5 kWh/m3. The practical concentration efficiency obtained was 76% at a flow rate of 2 ml/s and a filtration efficiency of 54% at 1 ml/s with a real power input of 8.8 W. An optimal open loop control strategy showed that it is possible to operate an acoustic separator with high separation efficiency using the least power possible. Parallelisation, instead of enlarging the separator, is recommended to scale this system up to larger, industrial flows.

Summary Optimization-based decision support systems for planning problems in processing industries Nowadays, efficient planning of material flows within and between supply chains is of vital importance and has become one of the most challenging problems for decision support in practice. The tremendous progress in hard- and software of the past decades was an important gateway for developing computerized systems that are able to support decision making on different levels within enterprises. The history of such systems started in 1971 when the concept of Decision Support Systems (DSS) emerged. Over the years, the field of DSS has evolved into a broad variety of directions. The described research in this thesis limits to the category of model-driven or optimization-based DSS. Simultaneously with the emergence of DSS, software vendors recognized the high potentials of available data and developed Enterprise Systems to standardize planning problems. Meanwhile, information oriented systems like MRP and its successors are extended by the basic concepts of optimization based decision support. These systems are called Advanced Planning Systems (APS). The main focus of APS is to support decision making at different stages or phases in the material flow, i.e. from procurement, production, distribution to sales (horizontal-axis), on different hierarchical aggregation levels (vertical-axis) ranging from strategic (long-term) to operational (short- term) planning. This framework of building blocks decomposes planning tasks hierarchically into partial planning problems. This basic architecture of the planning processes in APS is known as the Supply Chain Planning Matrix (SCPM). Compared to, for instance, discrete parts manufacturing, planning tasks are much more complicated in processing industries due to a natural variation in the composition of raw materials, the impact of processing operations on properties of material flows, sequence dependent change-over times, the inevitable decline in quality of product flows and relatively low margins. These specific characteristics gave rise to focus on optimization-based decision support in the domain of processing industries. The problems to be addressed in this field call for (inter-related) decisions with respect to the required raw materials, the production quantities to be manufactured, the efficient use of available resources, and the times at which raw materials must be available. Although different APS modules can interact directly, coordination and integration is often restricted to the exchange of data flows between different modules. Given the need for specific integrated decision support, the research presented in this thesis focusses particularly on medium to short term decision support at production stage in processing industry, including the vertical and horizontal integration and coordination with adjacent building blocks in the SCPM. Extensive reviews from literature show that the gap between research and practice of DSS is widening. As the field of DSS was initiated as an application oriented discipline, the strategy of what is referred to as “application-driven theory” was taken as the preferred approach for this thesis. “Application-driven” refers to a bottom-up approach which means that the relevance of the research should both be initiated and obtained from practice. The intended successful use of the proposed approaches should, where possible, be represented by tests of adequacy. Simultaneously, the contribution to “theory” aims to be a recognizable part of the research effort, i.e. obtained understanding and insights from problems in practice should provide the basis for new approaches. Based on the preceding considerations we defined the following general research objective: General research objective To support medium- to short term planning problems by optimization-based models and solution techniques such that: i) The applicability and added value of (prototype) systems is recognized and carried by decision makers in practice ii) The proposed approaches contribute to knowledge, understanding and insights from a model building and – solving point of view. In order to link the general objective with the different studies in the thesis, we defined five, recurring research premises, i.e. Professional relevance and applicability (P1), Aggregation (P2), Decomposition and reformulation (P3), Vertical integration at production level (P4), and Horizontal coordination and integration (P5). The overarching premise P1 refers to the first part of the research objective. All other premises refer to the second part of the research objective, i.e. model building and/or – solving. Several planning issues are studied to give substance to the research objective and each study is connected to at least two research premises. Study 1: Planning and scheduling in food processing industry The main question in Chapter 2 was:” How to apply aggregation, decomposition and reformulation in model-based DSS at planning and scheduling level such that the aspect of decision support is recognized and appreciated by decision makers in practice, and which level of aggregation is needed to integrate production planning (i.e. lot-sizing) and scheduling problems in a single model? The study consists of two parts. The first part of the study refers to a case study for the bottleneck packaging facilities of a large dairy company. The goal was to develop, implement and test a pilot DSS which was able to deliver solutions recognized and carried by decision makers at lower decision levels. The latter aim implied that a straight-forward aggregation on time, product type, resources or product stage, was not preferred. The key to develop an approach for regular use was to identify and take advantage of specific problem characteristics. Clustering of numerous jobs, while retaining information at order level, could be exploited in a reformulation approach. The inclusion of (combined) generalized- and variable upper bound constraints gave very tight lower bounds and sparse search trees. An extensive test phase in daily practice showed that the main benefit of the DSS was the initial quality of the generated plans including the time needed to generate these schedules. Hence, decision makers could i) postpone their planning tasks, ii) conveniently cope with rush orders or planned maintenance and iii) easily generate alternatives or revised plans when unforeseen disturbances occur. Moreover, the graphical presentation and overview of the (future) working schedule enabled order acceptance to make use of remaining capacity. The study also showed that planning problems in practice cannot be captured exhaustively by a (simplified) model. Decision makers need the opportunity to modify automatically generated plans manually and use human judgement and experience such that the solution is tuned to the actual situation. Hence, the DSS should not be considered as an optimizer but rather as a tool for generating high quality plans to be used for further analysis. Within this context the various options of a user-friendly, graphical, and fully interactive user interface, were of major importance. Although the case study clearly demonstrates the validity of earlier case based DSS research for current days APS, the proposed approach is hardly a generic solution for a complete vertical integration between lot-sizing and scheduling. If lot-size decisions are strongly affected by the sequence of jobs, production planning and scheduling should be performed simultaneously. As the described case refers to an earlier study and today’s APS do not provide modules for integrated lot-sizing and scheduling, the second part of the study gives an overview of developments in literature regarding lot-sizing and scheduling models and assess their suitability for addressing sequence-dependent setups, non-triangular setups and product decay. The review shows a tendency in which so-called Big Bucket (BB) models are currently proposed for short term time horizons too. However, we argue that segmentation of the planning horizon is a key issue for simultaneous lot-sizing and scheduling. The advantage of BB models may become a major obstacle for i) the effectiveness of simultaneous lot-sizing and scheduling, and ii) addressing specific characteristics in food processing industry. Study 2: Vertical integration of lot-sizing and scheduling in food processing industry Chapter 3 focused on a complete integration of lot-sizing and scheduling decisions in a single model. The main question was:” How to integrate production planning (i.e. lot- sizing) and scheduling problems in a single model, such that common assumptions regarding the triangular setup conditions are relaxed and issues of product decay and limited shelf lives are taken into account?” The literature research in Chapter 2 revealed that the computational advantage of time oriented aggregation in BB models may become a major obstacle in addressing the identified characteristics in FPI. In addition, product decay is primarily associated with the “age” of products and consequently relates to the segmentation of the time- horizon. Therefore, two SB models are developed to demonstrate the impact of non- triangular setups and product decay on the generated solutions. Small scale examples were used to demonstrate how a small change in the balance between inventory - and changeover costs may generate significantly different solutions, especially when the triangular setup conditions do not hold. The developed models are potentially very large formulations and, as expected, hard to solve. Exploratory research was conducted with a Relax-and-Fix (R&F) heuristic. The heuristic is based on a decomposition of the time horizon. Numerical results of small to medium sized problem instances are promising. However, solving real-size problem instances is not possible yet. Study 3: Integrated planning between procurement and production The case study in Chapter 4 focussed on the need for horizontal coordination and integration between the phases procurement and production, which is of particular importance in inter-organizational supply chains. The main question was:” How to model and solve an integrated planning problem between procurement and production, both on a mid-term and short-term planning level, in an inter-organizational supply chain? The research question was projected on an illustrative milk collection problem in practice. The aim was to develop a pilot DSS that lifted decision support for a “weaker” partner in a food supply chain to a higher level, and to illustrate the importance of horizontal integration between the phases procurement and production in an APS framework. Problem analysis revealed that the problem can be classified as an extension of the Periodic Vehicle Routing Problem (PVRP). The problem was decomposed into more tractable sub problems on different hierarchical levels, i.e. the daily (vehicle) routing problem was separated from a medium-term planning problem. On the higher planning level, numerous suppliers were aggregated such that total supply within a cluster met (multiple) vehicle loading capacities. The continuous supply of relatively small amounts from many suppliers had to be balanced with strict delivery conditions at processing level. A model was developed to assign a single (stable) collection rhythm to each cluster such that the total, weighted deviation of desired processing levels on various days in the planning horizon was minimized. The applied aggregation on the higher planning level turned out to be very beneficial for the required disaggregation at the lower planning level. Once supplier farms were geographically grouped into clusters and the aggregated supply within a cluster was assigned to a single collection rhythm with fixed collection days, the (initial) daily routing problem was considerably easier to solve for vehicle schedulers. The computational complexity of the problem was reduced by exploiting application-based properties algorithmically in a specific branch-and-bound scheme, i.e. a customized approach of Special Ordered Sets type 1 (SOS1) This approach made it possible to solve the generated problems exactly for real-size problem instances. The various facilities of a user-friendly and interactive man-machine interface (i.e. an input, planning, simulation and analysing module) turned out to be essential. Decision makers could easily change the data, and the generated plans, in a separate simulation module. However, the impact of any modification was immediately visualised by several (conflicting) indicators in the output screens, both on supply and demand level. Study 4: Mixed Integer (0-1) Fractional Programming in Paper Production Industry The study in Chapter 5 focussed on the impact of technical settings of production units on material flows. The main question was:” How to support decision-makers in practice if crucial properties of end products simultaneously depend on (endogenous) types of raw materials with different chemical or physical properties and (endogenous) technical settings of processing units? The goal of the study was to revise and upgrade an existing, locally used DSS, to a tailored and flexible tool for decision support within the enterprise. The study revealed that the aimed extension towards multi-objective decision support, together with new physical insight for calculating properties of end products due to process operations, had a substantial impact on the optimization module. The proposed solution procedure takes advantage of the problem characteristics and gives rise i) to apply and extend a classical reformulation approach for continuous linear fractional programming (FP) problems to a more general class of mixed integer (binary) FP problems and ii) to exploit the special structure between the original non- linear mixed integer model and the continuous, linear reformulation by applying the concept of Special Ordered Sets type 1 (SOS1). Although Chapter 5 focusses in particular on the reformulation and solution approach, the DSS consists of four main building blocks, i.e. the user interface, a scenario manager, a simulation- and optimization routine. The optimization module provides a powerful tool to find feasible solutions and the best (unexpected) recipes for any available set of raw materials. Moreover, it provides an innovative way of decision support for purchasing (new) pulps on the market, for assigning available pulps to different paper grades, and for attuning available stock levels of raw materials to (changing) production targets for different paper grades. The results of the optimization routine are mainly used to obtain alternative recipes for different paper grades. Usually, these recipes are stored as base scenarios and adapted to daily practice in the simulation module. Main conclusions and future research Based on the studies in the Chapters 2 and 3 we conclude that no generically applicable models and/or solution approaches exist for simultaneous planning and scheduling in processing industries. More industry-specific solutions are needed incorporating specificities of different production environments into those models. The key to develop solvable approaches for contemporary practice may be i) to use knowledge and experience from practice and take advantage of specific characteristics in different problem domains during model construction, and/or ii) to identify and exploit special problem structures for solving the related models. We conclude that surprisingly little research has been devoted to issues of coordination and integration between “procurement” and “production”. The studies in the chapters 4 and 5 confirm that sourcing of (raw) materials flows needs more attention in processing industries, particularly in push-oriented, inter-organizational networks. The valorisation of raw materials can be improved even more if the composition of raw materials is considered too in future planning problems at production level. In the second part of this thesis we focused on extensions for the applicability of Special Ordered Sets type 1 (SOS1), both from an algorithmic (Chapter 4) and modelling (Chapter 5) point of view. We conclude that the concept of SOS1 can extend a classical reformulation approach for continuous fractional programming (FP) problems, to a specific class of mixed integer (0-1) FP problems. Moreover, we conclude that a natural ordering of the variables within the sets is not necessary to make their use worthwhile. A separate (user defined) reference row or weights associated to the variables in the sets might be omitted for an efficient use of SOS1 in commercially available mathematical programming packages. However, this requires further research and extensive computational tests.

This thesis explores the applicability of the resilience perspective on agro-ecosystems dynamics. It start out by using the five heuristics of the resilience perspective on intensive agricultural systems. Simulations with a dynamic farm model suggest that conventional farming short cuts the adaptive cycle leading to an ‘incremental adaptation’ trap. Panarchy is therefore claimed as a leading heuristic to understand long-term dynamics and current management characteristics. This interaction of long-term dynamics with current management leads to an asymmetry in the landscape. This asymmetry leads to windows of opportunities for farmers. However, disregarding the cross-scale nature of the asymmetry might also lead to a cascade of events that undermine the resilience of the landscape as whole. The cross-scale interactions of landscape dynamics and farm management suggest a co-evolution of production intensity and landscape pattern. Moreover trajectories of intensification might even be linked to certain tipping points of combinations of landscape characteristics and management. Therefore the landscape asymmetry might yield insight in agro-ecosystem functioning. The landscape asymmetry potentially provides a level of self-organisation above the farm. However, identifying the asymmetry appeared to be problematic. Next to scale issues, the current pattern does not necessary result from current management, leading to a de-coupling of pattern and process. A re-coupling of management and landscape asymmetry can exploit positive feedbacks. I suggest the use of identity to locate asymmetries and to use space-time substitutions to experiment with the typical slow variables that shape the asymmetry. The theory developed in this thesis is grounded on empirical farm management data and dynamical model simulation of intensive dairy farming in the Netherlands and small-holder systems in Zimbabwe.

This thesis explores the applicability of the resilience perspective on agro-ecosystems dynamics. It start out by using the five heuristics of the resilience perspective on intensive agricultural systems. Simulations with a dynamic farm model suggest that conventional farming short cuts the adaptive cycle leading to an ‘incremental adaptation’ trap. Panarchy is therefore claimed as a leading heuristic to understand long-term dynamics and current management characteristics. This interaction of long-term dynamics with current management leads to an asymmetry in the landscape. This asymmetry leads to windows of opportunities for farmers. However, disregarding the cross-scale nature of the asymmetry might also lead to a cascade of events that undermine the resilience of the landscape as whole. The cross-scale interactions of landscape dynamics and farm management suggest a co-evolution of production intensity and landscape pattern. Moreover trajectories of intensification might even be linked to certain tipping points of combinations of landscape characteristics and management. Therefore the landscape asymmetry might yield insight in agro-ecosystem functioning. The landscape asymmetry potentially provides a level of self-organisation above the farm. However, identifying the asymmetry appeared to be problematic. Next to scale issues, the current pattern does not necessary result from current management, leading to a de-coupling of pattern and process. A re-coupling of management and landscape asymmetry can exploit positive feedbacks. I suggest the use of identity to locate asymmetries and to use space-time substitutions to experiment with the typical slow variables that shape the asymmetry. The theory developed in this thesis is grounded on empirical farm management data and dynamical model simulation of intensive dairy farming in the Netherlands and small-holder systems in Zimbabwe.

Summary Optimization-based decision support systems for planning problems in processing industries Nowadays, efficient planning of material flows within and between supply chains is of vital importance and has become one of the most challenging problems for decision support in practice. The tremendous progress in hard- and software of the past decades was an important gateway for developing computerized systems that are able to support decision making on different levels within enterprises. The history of such systems started in 1971 when the concept of Decision Support Systems (DSS) emerged. Over the years, the field of DSS has evolved into a broad variety of directions. The described research in this thesis limits to the category of model-driven or optimization-based DSS. Simultaneously with the emergence of DSS, software vendors recognized the high potentials of available data and developed Enterprise Systems to standardize planning problems. Meanwhile, information oriented systems like MRP and its successors are extended by the basic concepts of optimization based decision support. These systems are called Advanced Planning Systems (APS). The main focus of APS is to support decision making at different stages or phases in the material flow, i.e. from procurement, production, distribution to sales (horizontal-axis), on different hierarchical aggregation levels (vertical-axis) ranging from strategic (long-term) to operational (short- term) planning. This framework of building blocks decomposes planning tasks hierarchically into partial planning problems. This basic architecture of the planning processes in APS is known as the Supply Chain Planning Matrix (SCPM). Compared to, for instance, discrete parts manufacturing, planning tasks are much more complicated in processing industries due to a natural variation in the composition of raw materials, the impact of processing operations on properties of material flows, sequence dependent change-over times, the inevitable decline in quality of product flows and relatively low margins. These specific characteristics gave rise to focus on optimization-based decision support in the domain of processing industries. The problems to be addressed in this field call for (inter-related) decisions with respect to the required raw materials, the production quantities to be manufactured, the efficient use of available resources, and the times at which raw materials must be available. Although different APS modules can interact directly, coordination and integration is often restricted to the exchange of data flows between different modules. Given the need for specific integrated decision support, the research presented in this thesis focusses particularly on medium to short term decision support at production stage in processing industry, including the vertical and horizontal integration and coordination with adjacent building blocks in the SCPM. Extensive reviews from literature show that the gap between research and practice of DSS is widening. As the field of DSS was initiated as an application oriented discipline, the strategy of what is referred to as “application-driven theory” was taken as the preferred approach for this thesis. “Application-driven” refers to a bottom-up approach which means that the relevance of the research should both be initiated and obtained from practice. The intended successful use of the proposed approaches should, where possible, be represented by tests of adequacy. Simultaneously, the contribution to “theory” aims to be a recognizable part of the research effort, i.e. obtained understanding and insights from problems in practice should provide the basis for new approaches. Based on the preceding considerations we defined the following general research objective: General research objective To support medium- to short term planning problems by optimization-based models and solution techniques such that: i) The applicability and added value of (prototype) systems is recognized and carried by decision makers in practice ii) The proposed approaches contribute to knowledge, understanding and insights from a model building and – solving point of view. In order to link the general objective with the different studies in the thesis, we defined five, recurring research premises, i.e. Professional relevance and applicability (P1), Aggregation (P2), Decomposition and reformulation (P3), Vertical integration at production level (P4), and Horizontal coordination and integration (P5). The overarching premise P1 refers to the first part of the research objective. All other premises refer to the second part of the research objective, i.e. model building and/or – solving. Several planning issues are studied to give substance to the research objective and each study is connected to at least two research premises. Study 1: Planning and scheduling in food processing industry The main question in Chapter 2 was:” How to apply aggregation, decomposition and reformulation in model-based DSS at planning and scheduling level such that the aspect of decision support is recognized and appreciated by decision makers in practice, and which level of aggregation is needed to integrate production planning (i.e. lot-sizing) and scheduling problems in a single model? The study consists of two parts. The first part of the study refers to a case study for the bottleneck packaging facilities of a large dairy company. The goal was to develop, implement and test a pilot DSS which was able to deliver solutions recognized and carried by decision makers at lower decision levels. The latter aim implied that a straight-forward aggregation on time, product type, resources or product stage, was not preferred. The key to develop an approach for regular use was to identify and take advantage of specific problem characteristics. Clustering of numerous jobs, while retaining information at order level, could be exploited in a reformulation approach. The inclusion of (combined) generalized- and variable upper bound constraints gave very tight lower bounds and sparse search trees. An extensive test phase in daily practice showed that the main benefit of the DSS was the initial quality of the generated plans including the time needed to generate these schedules. Hence, decision makers could i) postpone their planning tasks, ii) conveniently cope with rush orders or planned maintenance and iii) easily generate alternatives or revised plans when unforeseen disturbances occur. Moreover, the graphical presentation and overview of the (future) working schedule enabled order acceptance to make use of remaining capacity. The study also showed that planning problems in practice cannot be captured exhaustively by a (simplified) model. Decision makers need the opportunity to modify automatically generated plans manually and use human judgement and experience such that the solution is tuned to the actual situation. Hence, the DSS should not be considered as an optimizer but rather as a tool for generating high quality plans to be used for further analysis. Within this context the various options of a user-friendly, graphical, and fully interactive user interface, were of major importance. Although the case study clearly demonstrates the validity of earlier case based DSS research for current days APS, the proposed approach is hardly a generic solution for a complete vertical integration between lot-sizing and scheduling. If lot-size decisions are strongly affected by the sequence of jobs, production planning and scheduling should be performed simultaneously. As the described case refers to an earlier study and today’s APS do not provide modules for integrated lot-sizing and scheduling, the second part of the study gives an overview of developments in literature regarding lot-sizing and scheduling models and assess their suitability for addressing sequence-dependent setups, non-triangular setups and product decay. The review shows a tendency in which so-called Big Bucket (BB) models are currently proposed for short term time horizons too. However, we argue that segmentation of the planning horizon is a key issue for simultaneous lot-sizing and scheduling. The advantage of BB models may become a major obstacle for i) the effectiveness of simultaneous lot-sizing and scheduling, and ii) addressing specific characteristics in food processing industry. Study 2: Vertical integration of lot-sizing and scheduling in food processing industry Chapter 3 focused on a complete integration of lot-sizing and scheduling decisions in a single model. The main question was:” How to integrate production planning (i.e. lot- sizing) and scheduling problems in a single model, such that common assumptions regarding the triangular setup conditions are relaxed and issues of product decay and limited shelf lives are taken into account?” The literature research in Chapter 2 revealed that the computational advantage of time oriented aggregation in BB models may become a major obstacle in addressing the identified characteristics in FPI. In addition, product decay is primarily associated with the “age” of products and consequently relates to the segmentation of the time- horizon. Therefore, two SB models are developed to demonstrate the impact of non- triangular setups and product decay on the generated solutions. Small scale examples were used to demonstrate how a small change in the balance between inventory - and changeover costs may generate significantly different solutions, especially when the triangular setup conditions do not hold. The developed models are potentially very large formulations and, as expected, hard to solve. Exploratory research was conducted with a Relax-and-Fix (R&F) heuristic. The heuristic is based on a decomposition of the time horizon. Numerical results of small to medium sized problem instances are promising. However, solving real-size problem instances is not possible yet. Study 3: Integrated planning between procurement and production The case study in Chapter 4 focussed on the need for horizontal coordination and integration between the phases procurement and production, which is of particular importance in inter-organizational supply chains. The main question was:” How to model and solve an integrated planning problem between procurement and production, both on a mid-term and short-term planning level, in an inter-organizational supply chain? The research question was projected on an illustrative milk collection problem in practice. The aim was to develop a pilot DSS that lifted decision support for a “weaker” partner in a food supply chain to a higher level, and to illustrate the importance of horizontal integration between the phases procurement and production in an APS framework. Problem analysis revealed that the problem can be classified as an extension of the Periodic Vehicle Routing Problem (PVRP). The problem was decomposed into more tractable sub problems on different hierarchical levels, i.e. the daily (vehicle) routing problem was separated from a medium-term planning problem. On the higher planning level, numerous suppliers were aggregated such that total supply within a cluster met (multiple) vehicle loading capacities. The continuous supply of relatively small amounts from many suppliers had to be balanced with strict delivery conditions at processing level. A model was developed to assign a single (stable) collection rhythm to each cluster such that the total, weighted deviation of desired processing levels on various days in the planning horizon was minimized. The applied aggregation on the higher planning level turned out to be very beneficial for the required disaggregation at the lower planning level. Once supplier farms were geographically grouped into clusters and the aggregated supply within a cluster was assigned to a single collection rhythm with fixed collection days, the (initial) daily routing problem was considerably easier to solve for vehicle schedulers. The computational complexity of the problem was reduced by exploiting application-based properties algorithmically in a specific branch-and-bound scheme, i.e. a customized approach of Special Ordered Sets type 1 (SOS1) This approach made it possible to solve the generated problems exactly for real-size problem instances. The various facilities of a user-friendly and interactive man-machine interface (i.e. an input, planning, simulation and analysing module) turned out to be essential. Decision makers could easily change the data, and the generated plans, in a separate simulation module. However, the impact of any modification was immediately visualised by several (conflicting) indicators in the output screens, both on supply and demand level. Study 4: Mixed Integer (0-1) Fractional Programming in Paper Production Industry The study in Chapter 5 focussed on the impact of technical settings of production units on material flows. The main question was:” How to support decision-makers in practice if crucial properties of end products simultaneously depend on (endogenous) types of raw materials with different chemical or physical properties and (endogenous) technical settings of processing units? The goal of the study was to revise and upgrade an existing, locally used DSS, to a tailored and flexible tool for decision support within the enterprise. The study revealed that the aimed extension towards multi-objective decision support, together with new physical insight for calculating properties of end products due to process operations, had a substantial impact on the optimization module. The proposed solution procedure takes advantage of the problem characteristics and gives rise i) to apply and extend a classical reformulation approach for continuous linear fractional programming (FP) problems to a more general class of mixed integer (binary) FP problems and ii) to exploit the special structure between the original non- linear mixed integer model and the continuous, linear reformulation by applying the concept of Special Ordered Sets type 1 (SOS1). Although Chapter 5 focusses in particular on the reformulation and solution approach, the DSS consists of four main building blocks, i.e. the user interface, a scenario manager, a simulation- and optimization routine. The optimization module provides a powerful tool to find feasible solutions and the best (unexpected) recipes for any available set of raw materials. Moreover, it provides an innovative way of decision support for purchasing (new) pulps on the market, for assigning available pulps to different paper grades, and for attuning available stock levels of raw materials to (changing) production targets for different paper grades. The results of the optimization routine are mainly used to obtain alternative recipes for different paper grades. Usually, these recipes are stored as base scenarios and adapted to daily practice in the simulation module. Main conclusions and future research Based on the studies in the Chapters 2 and 3 we conclude that no generically applicable models and/or solution approaches exist for simultaneous planning and scheduling in processing industries. More industry-specific solutions are needed incorporating specificities of different production environments into those models. The key to develop solvable approaches for contemporary practice may be i) to use knowledge and experience from practice and take advantage of specific characteristics in different problem domains during model construction, and/or ii) to identify and exploit special problem structures for solving the related models. We conclude that surprisingly little research has been devoted to issues of coordination and integration between “procurement” and “production”. The studies in the chapters 4 and 5 confirm that sourcing of (raw) materials flows needs more attention in processing industries, particularly in push-oriented, inter-organizational networks. The valorisation of raw materials can be improved even more if the composition of raw materials is considered too in future planning problems at production level. In the second part of this thesis we focused on extensions for the applicability of Special Ordered Sets type 1 (SOS1), both from an algorithmic (Chapter 4) and modelling (Chapter 5) point of view. We conclude that the concept of SOS1 can extend a classical reformulation approach for continuous fractional programming (FP) problems, to a specific class of mixed integer (0-1) FP problems. Moreover, we conclude that a natural ordering of the variables within the sets is not necessary to make their use worthwhile. A separate (user defined) reference row or weights associated to the variables in the sets might be omitted for an efficient use of SOS1 in commercially available mathematical programming packages. However, this requires further research and extensive computational tests.

Due to limited water resources available in the world and the ever growing world population, there is an increasing need for water recycling, recovery and multi-sourcing strategies. One of the new physical process technologies being investigated for water purification and/or constituent recycling is ultrasonic particle separation. This technology is especially interesting for harvesting particles with an almost neutral buoyancy. An ultrasonic particle filter does not use a filter medium, like sand or a membrane, but filters on a basis of acoustic forces in ultrasonic standing waves, which are able to immobilise particles in flowing water. The objective of this study was to develop an ultrasonic separation device for particle recovery and water purification. This separator should be fit for industrial applications treating cubic meters of water per hour. In order to reach this objective, a combined numerical-experimental approach was proposed to develop a model-based design of an ultrasonic separator. Each individual component of this separator was modelled using a finite element (FE) approach. The numerical simulations were continuously cross-checked with experiments in order to find the best solution possible. In this thesis, the source of the acoustic wave is a piezoelectric transducer attached to a glass matching layer of the acoustic cavity, which couples the transducer to the fluid inside the cavity, forming an acoustic resonator/separator. In order to obtain a valid FE transducer model, a limited set of material parameters for the piezoelectric transducer were obtained from the manufacturer, thus preserving prior physical knowledge to a large extent. The remaining unknown parameters were estimated from impedance (admittance) analysis combined with a numerical optimisation routine using 2D and 3D FE models. Thus, a full set of physically interpretable material parameters was obtained. The approach provided adequate accuracy of the estimates of the material parameters, near 1%. A similar approach as used for the transducer was applied to an existing ultrasonic separator, again preserving known physical parameters and estimating the remaining unknown or less certain parameters. The results showed that the approach led to a fully calibrated 2D model of the emptyseparator, which was subsequently validated with experiments on a filledseparator chamber. The large sensitivity of the separator to small variations indicated that either such system should be made and operated within tight specifications to obtain the required performance. Alternatively, the operation of the system should be adaptable to cope with a slightly off-spec system, requiring a feedback controller. Starting from a fully characterised existing separator with all material parameters found so far, the subsequent step was the actual design of, or extrapolation to, a new separator. A basic design for an industrial scale acoustic separator was obtained based on simulated flow characteristics inside the separation chamber, on acoustic analysis within the chamber and simulated particle trajectories combining these two analyses. Results showed that positioning the piezoelectric transducer surfaces perpendicular to the flow direction and introducing chamber partitioning with multiple flow lanes to enforce laminar flow, resulted in high particle retention. The average particle displacement was found to be related to acoustic pressure in the fluid, showing large retention at peak pressures above 1 MPa or average pressures above 0.5 MPa for small (10 µm), near buoyant (1100 kg/m3) particles at a flow speed of 3.5 cm/s, thus providing comprehensible criteria for subsequent optimisation. This basic ultrasonic standing wave separator design was optimised with respect to separation efficiency, throughput and energy consumption. The methodology, using a design of experiments (DOE) approach, showed that it was possible to improve system performance based on acoustic pressure profiles, separation efficiency and flow robustness. Compromising the energy consumption and aiming for maximum separation efficiency with a laminar stable flow up to 5 ml/s resulted in a separator with inner dimensions of 70 mm length, 20 mm width and 28.5 mm height using two transducers perpendicular to the direction of flow and three parallel flow lanes with 9.5 mm height each. The lowest power consumption (with an average of 30 W) with adequate pressure to trap the particles was obtained when it was not operated at the main eigenfrequency. Finally, this new ultrasonic particle filter was built and evaluated experimentally. The particle filter was a three channel device, manufactured from glass with four in/outlet ports made of ABS. It was operated in sequenced batch mode and the separation efficiency was determined at three flow rates ranging from 1 to 3 ml/s, using a stock suspension of insoluble potato starch of 1 g/l (1000 ppm). Concentrations of stock, filtrate and concentrate were measured using a turbidity meter and significant effects of acoustic particle concentration were measured at both outlets of the process. The maximum filtration efficiency and concentration efficiency were 54% and 76%, respectively. The performance found was lower than the 100% that was expected for 10 µm particles from the model based design study. The deviation in performance is mainly a result of (i) the pulsation of the feed pump, (ii) differences between the model and the actual prototype, (iii) the limited power supply of only 10 W used and (iv) (too) small particles, below 10 µm, occurring in the starch suspension. The best dimensions for an acoustic separator were obtained, but thus far operational characteristics were not yet studied. Operational characterisation and optimisation is the last step in the process of obtaining the best possible solution for operation. With the aim to achieve a high separation efficiency with minimal energy consumption, a model-based open-loop switching control strategy was designed for the commercially available BioSep, using a numerical-experimental approach. Firstly, a dynamic BioSep model structure was derived from mass balances and its system properties were studied. Then, the unknown system parameters were estimated from steady state and dynamic experimental data and subsequently, the switching times of the control input were determined. The model with switching control outputs was then validated by experiments. Finally, the control strategy was implemented in an experimental setup and tested using suspended potato starch. Results showed that the optimal control strategy reached a mass separation efficiency of 96%, which was an improvement of 4% with respect to the initial settings, while using less energy. Concluding, a stepwise numerical-experimental approach to acoustic separator design was presented in this study. The minimum power required was estimated to be 22-34 W, resulting in an average electric energy consumption of 1-1.5 kWh/m3. The practical concentration efficiency obtained was 76% at a flow rate of 2 ml/s and a filtration efficiency of 54% at 1 ml/s with a real power input of 8.8 W. An optimal open loop control strategy showed that it is possible to operate an acoustic separator with high separation efficiency using the least power possible. Parallelisation, instead of enlarging the separator, is recommended to scale this system up to larger, industrial flows.

Transmission of infections between spatially separated hosts is a common problem, not only during major outbreaks of livestock diseases, but also in many other settings such as the transmission of infectious diseases between plants and crops or in healthcare settings. During the last major epidemics of livestock diseases in the Netherlands and abroad, disease transmission events occurred despite movement bans and other (bio-)security measures, implying that indirect transmission plays a major role. A better understanding of indirect transmission is necessary to put in place evidence based bio-security measures against neighbourhood (indirect) transmission. To gain more insight in the mechanisms underlying indirect transmission a series of experimental studies combined with mathematical modelling were conducted of which the results are presented in this thesis. First the effect of acidification of drinking water on the transmission parameters of direct and indirect transmission of Campylobacter jejuni (C. jejuni) between broilers was studied. It was shown that acidified drinking water has an effect on indirect transmission but not on direct transmission of C. jejuni between broilers. The sender and receiver sub-process of indirect transmission was then studied in more detail and it was shown that a significant negative interaction effect between acidification of the sender and receiver sub-processes exists, indicating that there is no additional effect of acidification of the drinking water on both sides of the transmission process compared to acidified drinking water only on one side. To study the transport of the pathogen in the environment in more detail, a series of indirect transmission experiments was carried out and a model framework was developed to study indirect transmission between spatially separated hosts. These studies showed that indirect transmission of C. jejuni between broilers is best described by a multistage environmental route from sending to receiving animal, suggesting that indirect transmission occurs through progressive (but slow) contamination of the environment surrounding the source. Indirect transmission experiments where repeated with both C. jejuni and Escherichia coli and the results showed that for C. jejuni it takes much longer for the first effective (viable) bacterium to cross the small distance of approximately 75 cm than it does for Escherichia coli. A new modelling approach to study indirect transmission was developed guided by these indirect transmission experiments. This model is capable of accurately describing the pathogen dispersal process by a diffusive transport mechanism which includes pathogen mortality. Lastly, a range of dose-response models were compared and tested how well these fitted to the data from a dose-response experiment. Here it was shown that for interpolation purposes two relatively simple models are best capable of describing the data from the dose-response experiment. For extrapolation purposes, however, it was shown that from the models that were studied a model that abides by the independent action hypothesis is best.

Transmission of infections between spatially separated hosts is a common problem, not only during major outbreaks of livestock diseases, but also in many other settings such as the transmission of infectious diseases between plants and crops or in healthcare settings. During the last major epidemics of livestock diseases in the Netherlands and abroad, disease transmission events occurred despite movement bans and other (bio-)security measures, implying that indirect transmission plays a major role. A better understanding of indirect transmission is necessary to put in place evidence based bio-security measures against neighbourhood (indirect) transmission. To gain more insight in the mechanisms underlying indirect transmission a series of experimental studies combined with mathematical modelling were conducted of which the results are presented in this thesis. First the effect of acidification of drinking water on the transmission parameters of direct and indirect transmission of Campylobacter jejuni (C. jejuni) between broilers was studied. It was shown that acidified drinking water has an effect on indirect transmission but not on direct transmission of C. jejuni between broilers. The sender and receiver sub-process of indirect transmission was then studied in more detail and it was shown that a significant negative interaction effect between acidification of the sender and receiver sub-processes exists, indicating that there is no additional effect of acidification of the drinking water on both sides of the transmission process compared to acidified drinking water only on one side. To study the transport of the pathogen in the environment in more detail, a series of indirect transmission experiments was carried out and a model framework was developed to study indirect transmission between spatially separated hosts. These studies showed that indirect transmission of C. jejuni between broilers is best described by a multistage environmental route from sending to receiving animal, suggesting that indirect transmission occurs through progressive (but slow) contamination of the environment surrounding the source. Indirect transmission experiments where repeated with both C. jejuni and Escherichia coli and the results showed that for C. jejuni it takes much longer for the first effective (viable) bacterium to cross the small distance of approximately 75 cm than it does for Escherichia coli. A new modelling approach to study indirect transmission was developed guided by these indirect transmission experiments. This model is capable of accurately describing the pathogen dispersal process by a diffusive transport mechanism which includes pathogen mortality. Lastly, a range of dose-response models were compared and tested how well these fitted to the data from a dose-response experiment. Here it was shown that for interpolation purposes two relatively simple models are best capable of describing the data from the dose-response experiment. For extrapolation purposes, however, it was shown that from the models that were studied a model that abides by the independent action hypothesis is best.

Na een theoretisch kader voor winstfunctiemodellen en voor huishoudproductiemodellen worden met behulp van gegevens uit het Bedrijven-Informatienet beide modellen toegepast teneinde beleid beter op de korte en op de lange termijn op agrarische gezinsbedrijven af te stemmen

Water repellent soils are known to inhibit water infiltration, ultimately forcing water to flow via preferential paths through the vadose zone. To study water flow and transport in a water repellent sandy soil, a bromide tracer experiment was carried out, which started in the fall, after winter wheat had been sown. Field average soil water content and bromide profiles were determined seven times during a 474 d period. A one-dimensional convection–dispersion model was used to simulate observed flow and transport. It was found that water content and bromide profiles could be successfully simulated. The main reason was that despite water repellency no distinct preferential flow occurred within this particular experimental field. Only wavy wetting fronts were observed. This was due to a uniform vegetation cover and a relatively thick A-horizon (30 cm), which contrasts with known water repellent sandy soils with thin (10 cm) top layers in which typical fingered flow patterns had previously been found.

De invloed van technologische vooruitgang op de winstfunctie van landbouwbedrijven heeft men getracht in een econometisch model te gieten, met gebruikmaking van gegevens uit de Nederlandse landbouwsector

Being sessile by nature plants are continuously challenged by biotic and abiotic stress factors. At the cellular level, different stimuli are perceived and translated to the desired response. In order to achieve this, signal transduction cascades have to be interlinked. Complex networks of downstream targets as well as positive and negative regulatory elements are essential for proper signal transduction. This often complicates analysis of signal transduction cascades via genetic approaches as a mutation in one gene results in a pleiotropic phenotype. Pathway components can be placed in the signal transduction cascade based on genetics as well as biochemical interactions between proteins. This results in a signal transduction network which is based on Boolean logics; either the gene is there and is functional (on) or it’s mutated and not functional (off). In such a genetic scheme, intermediate conditions and the effect of concentration on pathway components is not taken into account. Also, the effect of intermediate or transient activation states on signal transduction pathways is rarely included. In principle all proteins in a signal transduction network obey mass action laws suggesting that reaction rate and as a consequence the output of the signal depends on the concentration of the reactants. In addition, signals can be subjected to negative feedback thereby resulting in a signal that attenuates itself to maintain cellular homeostasis, or only responds to a stimulus temporarily and only when required. At the cellular level, the cell has to decipher all stimuli to enable the desired integrated cellular response. In this respect, concentration or amplitudes matter very much as the plant must not respond to background noise. Hence a cellular response will only be induced when a signal is above a certain threshold resulting in “switch like” behaviour of the system. Mathematical modelling can help to visualise and explain the temporal and concentration effects of pathway components on the output of signal transduction cascades. In order to do so, the signal transduction cascade needs to be well described with a clear and measurable response. Obviously, to know how receptor concentration affects the signalling output one has to know its numbers, and this was the starting point of the work described in this thesis. The final challenge was to describe the modulatory effect of SERK co-receptors on BR signalling. For this, SERK mediated BRI1 signalling was incorporated in a mathematical model that describes root growth and hypocotyl elongation based on the BRI1 receptor activity. In Chapter 1 the brassinosteroid signalling pathway as well as the role of SERK co-receptors on BRI1 mediated signalling is described. BRs are perceived by the plasma membrane localised Brassinosteroid insensitive 1 (BRI1) receptor. For its signalling, BRI1 completely depends on the presence of non-ligand binding co-receptors of the somatic embryogenesis receptor like kinase (SERK) co-receptor family. An added complexity is that SERK co-receptors associate with different main ligand perceiving receptors thereby affecting multiple signalling pathways simultaneously. Therefore, it is important to know how SERK co-receptors modulate the output of the main ligand perceiving receptor and how SERK co-receptors are distributed between the signal transduction cascades. The BRI1 signal transduction pathway is one of the best understood signal transduction cascades in Arabidopsis with clearly described ligands and associated phenotypes. For this reason, the focus of this study was on how SERK co-receptors affect BRI1 mediated signalling quantitatively using a mathematical modelling approach. This requires knowledge on the concentration of the main ligand perceiving receptor, SERK co-receptor and ligand levels. Since the BRI1 and SERK co-receptor concentration was unknown we set out to quantify the number of receptors in a cell. In Chapter 2 a confocal microscopy based method is described that enables quantification of BRI1, SERK1 and SERK3 in planta. The number of BRI1 receptor molecules in root epidermal cells ranges from 22,000 in the meristem to 80,000 in the maturation zone. However, when taking into account differences in cell size, the root meristem cells have the same receptor density which reduces significantly in the maturation zone. The root meristem cells are thought to be most active in BR signalling, suggesting that receptor density rather than total number of BRI1 receptors affects the sensitivity of a cell for BRs. The next question is, how the physiological response of the cell depends on both ligand stimulation of the receptor and on ligand concentration. To address this, a mathematical modelling approach was employed where the receptor - ligand concentrations were coupled to root growth and hypocotyl elongation as a downstream physiological readout for BR signalling (Chapter 3). Based on the BRI1 receptor activity the model faithfully predicts root growth as observed in bri1 loss-of-function mutants. The model also predicts that a rather low number of receptor molecules are needed to initiate a physiological response. Interestingly, the “switch” between activation and inhibition of root growth depends on the BRI1 occupancy level. This suggests that BRI1 may be a core regulator based on activating different targets based on its occupancy level. Root growth is robust against reduction in the BRI1 receptor level but not to variation in the BR concentration. This indicates that BR signalling is mainly regulated via ligand availability and biochemical activity. Since BRI1 signalling is highly dependent on the presence of SERK co-receptors, it is important to determine how these co-receptors affect the signalling output. Therefore, in Chapter 4, the BRI1 receptor model was extended with two co-receptors, SERK1 and SERK3. The model also takes into account BRI1 signalling independent of SERK1 and SERK3. This may occur due the activity of BRI1 alone, or due to interaction of BRI1 with another co-receptor, for example SERK4. It appears that roots of the serk1serk3 double mutant are almost completely irresponsive for BRs while the hypocotyl is not, suggesting either a difference in co-receptor usage or a higher activity of BRI1 alone in the hypocotyl. The usage of different co-receptors may reflect a mechanism by which the sensitivity of a cell for BRs is regulated. It appears that co-receptors mainly act by increasing the magnitude of the response. In addition, in silico simulations confirm that BRI1 signalling is not impaired when the majority of SERK co-receptors operate in other signalling pathways. The presented model provides a starting point to incorporate the effect of other modulators of the BRI1 signal transduction cascade on a complex physiological response. Current models for BRI1 mediated signalling postulate that SERK3 is recruited upon ligand binding. However, Fluorescence Recovery After Photo bleaching (FRAP) measurements described in Chapter 5, indicate that BRI1 receptors located in root meristem cells have a relatively low mobility. This suggests that BRI1 and SERK already form complexes in the absence of ligand. It has been repeatedly reported that SERK co-receptors are involved in various biological processes and signal transduction networks. In Chapter 6, the changes in gene expression in absence of functional SERK1 and SERK3 are studied using transcriptional analysis. Microarrays were performed on RNA isolated from roots of 4-day-old seedlings of serk1, serk3 and serk1serk3 mutants. Hierarchical cluster analysis indicated that serk3 mutant roots have the same transcriptional pattern when compared to roots of the serk1serk3 double mutant but to a lower magnitude. More than half of the genes differentially regulated in the serk1serk3 double mutant relate to BRI1 mediated signalling. In addition, a number of BR dependent and independent metabolic processes are affected in absence of SERK3 indicating that this co-receptor may have an additional function in metabolic control. Performing microarray analysis on receptor mutants is complicated as effects on gene transcripts may be indirect and due to differential regulation of downstream transcriptional regulators. This complexity is further enhanced in the SERK co-receptor mutants as multiple signalling pathways are affected. This raises the question if it is truly possible to correlate alterations in gene expression due to the absence of functional SERK co-receptors to one particular signal transduction pathway. In Chapter 7, the general discussion, it is described how modelling of BRI1 signalling in this thesis has contributed to new insights into the brassinosteroid signalling. Microscopy has been an important tool to quantify the number of receptors in a cell or the number of cells in a tissue. What is still needed is a clear link between a signalling activity, and, therefore, the physiological response of the cell, to local and intracellular protein-protein interactions and protein concentrations. Further expanding the available microscopic techniques and mathematical models to the cellular level is one of the next challenges. The research described in this thesis is a starting point for such an approach to study signal transduction in Arabidopsis.

Being sessile by nature plants are continuously challenged by biotic and abiotic stress factors. At the cellular level, different stimuli are perceived and translated to the desired response. In order to achieve this, signal transduction cascades have to be interlinked. Complex networks of downstream targets as well as positive and negative regulatory elements are essential for proper signal transduction. This often complicates analysis of signal transduction cascades via genetic approaches as a mutation in one gene results in a pleiotropic phenotype. Pathway components can be placed in the signal transduction cascade based on genetics as well as biochemical interactions between proteins. This results in a signal transduction network which is based on Boolean logics; either the gene is there and is functional (on) or it’s mutated and not functional (off). In such a genetic scheme, intermediate conditions and the effect of concentration on pathway components is not taken into account. Also, the effect of intermediate or transient activation states on signal transduction pathways is rarely included. In principle all proteins in a signal transduction network obey mass action laws suggesting that reaction rate and as a consequence the output of the signal depends on the concentration of the reactants. In addition, signals can be subjected to negative feedback thereby resulting in a signal that attenuates itself to maintain cellular homeostasis, or only responds to a stimulus temporarily and only when required. At the cellular level, the cell has to decipher all stimuli to enable the desired integrated cellular response. In this respect, concentration or amplitudes matter very much as the plant must not respond to background noise. Hence a cellular response will only be induced when a signal is above a certain threshold resulting in “switch like” behaviour of the system. Mathematical modelling can help to visualise and explain the temporal and concentration effects of pathway components on the output of signal transduction cascades. In order to do so, the signal transduction cascade needs to be well described with a clear and measurable response. Obviously, to know how receptor concentration affects the signalling output one has to know its numbers, and this was the starting point of the work described in this thesis. The final challenge was to describe the modulatory effect of SERK co-receptors on BR signalling. For this, SERK mediated BRI1 signalling was incorporated in a mathematical model that describes root growth and hypocotyl elongation based on the BRI1 receptor activity. In Chapter 1 the brassinosteroid signalling pathway as well as the role of SERK co-receptors on BRI1 mediated signalling is described. BRs are perceived by the plasma membrane localised Brassinosteroid insensitive 1 (BRI1) receptor. For its signalling, BRI1 completely depends on the presence of non-ligand binding co-receptors of the somatic embryogenesis receptor like kinase (SERK) co-receptor family. An added complexity is that SERK co-receptors associate with different main ligand perceiving receptors thereby affecting multiple signalling pathways simultaneously. Therefore, it is important to know how SERK co-receptors modulate the output of the main ligand perceiving receptor and how SERK co-receptors are distributed between the signal transduction cascades. The BRI1 signal transduction pathway is one of the best understood signal transduction cascades in Arabidopsis with clearly described ligands and associated phenotypes. For this reason, the focus of this study was on how SERK co-receptors affect BRI1 mediated signalling quantitatively using a mathematical modelling approach. This requires knowledge on the concentration of the main ligand perceiving receptor, SERK co-receptor and ligand levels. Since the BRI1 and SERK co-receptor concentration was unknown we set out to quantify the number of receptors in a cell. In Chapter 2 a confocal microscopy based method is described that enables quantification of BRI1, SERK1 and SERK3 in planta. The number of BRI1 receptor molecules in root epidermal cells ranges from 22,000 in the meristem to 80,000 in the maturation zone. However, when taking into account differences in cell size, the root meristem cells have the same receptor density which reduces significantly in the maturation zone. The root meristem cells are thought to be most active in BR signalling, suggesting that receptor density rather than total number of BRI1 receptors affects the sensitivity of a cell for BRs. The next question is, how the physiological response of the cell depends on both ligand stimulation of the receptor and on ligand concentration. To address this, a mathematical modelling approach was employed where the receptor - ligand concentrations were coupled to root growth and hypocotyl elongation as a downstream physiological readout for BR signalling (Chapter 3). Based on the BRI1 receptor activity the model faithfully predicts root growth as observed in bri1 loss-of-function mutants. The model also predicts that a rather low number of receptor molecules are needed to initiate a physiological response. Interestingly, the “switch” between activation and inhibition of root growth depends on the BRI1 occupancy level. This suggests that BRI1 may be a core regulator based on activating different targets based on its occupancy level. Root growth is robust against reduction in the BRI1 receptor level but not to variation in the BR concentration. This indicates that BR signalling is mainly regulated via ligand availability and biochemical activity. Since BRI1 signalling is highly dependent on the presence of SERK co-receptors, it is important to determine how these co-receptors affect the signalling output. Therefore, in Chapter 4, the BRI1 receptor model was extended with two co-receptors, SERK1 and SERK3. The model also takes into account BRI1 signalling independent of SERK1 and SERK3. This may occur due the activity of BRI1 alone, or due to interaction of BRI1 with another co-receptor, for example SERK4. It appears that roots of the serk1serk3 double mutant are almost completely irresponsive for BRs while the hypocotyl is not, suggesting either a difference in co-receptor usage or a higher activity of BRI1 alone in the hypocotyl. The usage of different co-receptors may reflect a mechanism by which the sensitivity of a cell for BRs is regulated. It appears that co-receptors mainly act by increasing the magnitude of the response. In addition, in silico simulations confirm that BRI1 signalling is not impaired when the majority of SERK co-receptors operate in other signalling pathways. The presented model provides a starting point to incorporate the effect of other modulators of the BRI1 signal transduction cascade on a complex physiological response. Current models for BRI1 mediated signalling postulate that SERK3 is recruited upon ligand binding. However, Fluorescence Recovery After Photo bleaching (FRAP) measurements described in Chapter 5, indicate that BRI1 receptors located in root meristem cells have a relatively low mobility. This suggests that BRI1 and SERK already form complexes in the absence of ligand. It has been repeatedly reported that SERK co-receptors are involved in various biological processes and signal transduction networks. In Chapter 6, the changes in gene expression in absence of functional SERK1 and SERK3 are studied using transcriptional analysis. Microarrays were performed on RNA isolated from roots of 4-day-old seedlings of serk1, serk3 and serk1serk3 mutants. Hierarchical cluster analysis indicated that serk3 mutant roots have the same transcriptional pattern when compared to roots of the serk1serk3 double mutant but to a lower magnitude. More than half of the genes differentially regulated in the serk1serk3 double mutant relate to BRI1 mediated signalling. In addition, a number of BR dependent and independent metabolic processes are affected in absence of SERK3 indicating that this co-receptor may have an additional function in metabolic control. Performing microarray analysis on receptor mutants is complicated as effects on gene transcripts may be indirect and due to differential regulation of downstream transcriptional regulators. This complexity is further enhanced in the SERK co-receptor mutants as multiple signalling pathways are affected. This raises the question if it is truly possible to correlate alterations in gene expression due to the absence of functional SERK co-receptors to one particular signal transduction pathway. In Chapter 7, the general discussion, it is described how modelling of BRI1 signalling in this thesis has contributed to new insights into the brassinosteroid signalling. Microscopy has been an important tool to quantify the number of receptors in a cell or the number of cells in a tissue. What is still needed is a clear link between a signalling activity, and, therefore, the physiological response of the cell, to local and intracellular protein-protein interactions and protein concentrations. Further expanding the available microscopic techniques and mathematical models to the cellular level is one of the next challenges. The research described in this thesis is a starting point for such an approach to study signal transduction in Arabidopsis.

One of the main obstacles in systems biology is complexity, a feature that is inherent to living systems. This complexity stems both from the large number of components involved and from the intricate interactions between these components. When the system is described by a mathematical model, we frequently end up with a large nonlinear set of mathematical equation that contains many parameters. Such a large model usually has a number of undesirable properties, e.g., its dynamical behavior is hard to understand, its parameters are difficult to identify, and its simulation requires a very long computing time. In this thesis, we present several strategies that may help to overcome these problems. On the level of method development, we focus on two issues: a) method development to analyze robustness, and b) method development to reduce model complexity. On the level of practical systems biology, we develop and analyze a model for the cell cycle in tomato fruit pericarp. Robustness, that is the ability of a system to preserve biological functionality in spite of internal and external perturbations, is an essential feature of a biological system. Any mathematical model that describes this system should reflect this property. This implies the needs of a mathematical method to evaluate the robustness of mathematical models for biological processes. However, assessing robustness of a complex non-linear model that contains many parameters is not straightforward. In this thesis, we present a novel method to evaluate the robustness of mathematical models efficiently. This method enables us to find which parameter combinations in a model are responsible for its robustness. In this way, we get more insight into the underlying mechanisms that govern the robustness of the biological system. The advantage of our method is that the effort to apply the method scales linearly with the number of parameters. It is therefore very efficient when it is applied on mathematical models that contain a large number of parameters. The complexity in a model can be brought down by simplifying the model. In this thesis, we also present a novel reduction method to simplify mathematical representations of biological models. In this method, biological components and parameters that do not contribute to the observed dynamics are considered redundant and hence are removed from the model. This results in a simpler model with less components and parameters, without losing predictive capabilities for any testable experimental condition. Since the reduced model contains less parameters, parameter identification can be carried out more efficaciously. In the last part of this thesis we show how modeling can help us in understanding the cell cycle in tomato fruit pericarp. The cell cycle in this system is quite unique since the classical cell cycle, in which the cell division takes place, after some periods turns into a partial cycle where the cell keeps replicating its DNA but skips the division. Several mechanisms that are putatively responsible for this transition have been proposed. With modeling, we show that although each of these putative mechanisms could lead on its own the cell cycle to this transition, also their combination could lead to the same result. We also show that the mechanisms that yield the transition are very robust.

Keywords: safrole, PBBK model, DNA adduct, mace Safrole has been demonstrated to be carcinogenic in rodent studies at high doses of the pure compound. The use of pure safrole in foodshas already been prohibited. As a result, the main exposure to safrole occurs through the use of herbs and spices containing low levels of safrole, such as nutmeg, mace, star anise, pimento, cinnamon, and black pepper, and food products containing these herbs and spices or their essential oils. The Scientific Committee on Food of the European Union concluded in their evaluation that safrole is genotoxic and carcinogenic and that reductions in the exposure and restriction in the use levels are indicated. This opinion is based on carcinogenicity data from rodent studies as adequate human data were not available. Therefore, translation from animal bioassays at high dose levels of the pure compound to the risk for the human population exposed to safrole at relatively low levels via dietary intake within the complex food matrix is obviously needed. The aim of this thesis was to obtain insight into the dose-, species-, interindividual- and matrix dependent effects on the bioactivation and detoxification of safrole using physiologically based biokinetic (PBBK) modeling. PBBK models for safrole in male rats and humans were developed based on in vitro metabolic parameters determined, in silico derived partition coefficients, and physiological parameter values taken from literature. The performance of the PBBK model for rats was evaluated by comparison of predicted levels of 1,2-dihydroxy-4-allylbenzene, 1′-hydroxysafrole glucuronide and total urinary safrole metabolites to the reported levels of these metabolites in urine of rats exposed to safrole. This evaluation revealed that the predictions adequately matched observed experimental values. The PBBK model for humans was evaluated by comparison of the PBBK predicted and the reported experimental data on the level of total safrole metabolites detected in the urine of human volunteers exposed to safrole whichshowed an adequately match. The comparison of the PBBK model for rats and humans revealed that the predicted level of formation of 1ʹ-hydroxysafrole in human liver is fourfold higher than that for rat liver and the predicted formation of 1ʹ-sulfooxysafrole is about fivefold higher than that for rat liver. This indicates that the interspecies differences in toxicokinetics for bioactivation of safrole between rat an human are in line with the uncertainty factor normally taken into account for interspecies differences in toxicokinetics of 4. Species differences between humans and rats in the nature of the detoxification pathways of 1ʹ-hydroxysafrole were larger, with the formation of 1ʹ-oxosafrole being the main detoxification pathway in humans but a minor pathway in rats and glucuronidation of 1ʹ-hydroxysafrole being less important in humans than in rats. Monte Carlo simulations revealed that the formation of 1′-sulfooxysafrole was predicted to vary 4- to 17-fold in the population (fold-difference between the 95th and median, and 95th and 5th percentile, respectively). Risk assessment of safrole resulting from consumption of herbs and spices containing safrole should be performed taking into account the possible modulating effect of other compounds present in these herbs or spices. In this study, mace was chosen as the model spice of interest because it contains significant levels of safrole. Mace fraction with the highest SULT inhibiting activity was identified as malabaricone C. Studies using human HepG2 cells exposed to 1ʹ-hydroxysafrole and in the presence of mace extract showed that formation of the DNA adduct N2-(trans-isosafrol-3′-yl)-2′-deoxyguanosine was inhibited. To investigate the possible effects on safrole bioactivation to 1′-sulfooxysafrole by malabaricone C-containing mace extract could also be expected in vivo, the SULT inhibition was integrated into the PBBK model. The PBBK models predicted that at a dose of 50 mg/kg bw safrole and a ratio of malabaricone C-containing mace extract to safrole similar to the level of these constituents in mace, inhibition of 1′-sulfooxysafrole formation by malabaricone C-containing mace extract for rats and humans amounts to 90 and 100%, respectively. To see whether the inhibition of safrole DNA adduct formation by malabaricone C-containing mace extract is also observed in in vivo, to the end, Sprague-Dawley rats were orally exposed to mace extract and safrole. The results demonstrated that safrole DNA adduct formation in the liver of Sprague-Dawley rats by the mace extract was reduced by 55%. The results of the in vitro and in vivo studies that demonstrated inhibition of the formation of safrole DNA adducts by mace extract, support that combination effects should be taken into account in the risk assessment when safrole is tested in the presence of a relevant food matrix. To integrate thefood matrix dependent modulation of safrole bioactivation in the risk assessment of safrole, the so-called Margin of Exposure (MOE) approach can be used. This revealed that when safrole would be tested in rodent bioassays in the presence of a matrix containing SULT inhibitors the MOE values would be higher and the need for risk management actions would be lower.

Food science problems are complex. Scientists may be able to capture more of the complexity of an investigated theme if they were able to integrate related studies. Unfortunately, individual studies are usually not designed to allow such integration, and the common statistical methods cannot be used for analyzing integrated data. The modeling technique of Bayesian networks has gained popularity in many fields of application due to its ability to deal with complexity, but has emerged only recently in food science. This thesis used data from experiments on sensory satiation as case studies. The objective was to explore the use of Bayesian networks to combine raw data of independently performed but related experiments to build a quantitative model of sensory satiation. Methods This thesis started with introducing the theoretical background of Bayesian networks to food science. The available data from various independent experiments on sensory satiation were then examined for their potential to be combined. Finally, the outcomes obtained using Bayesian networks on a single dataset were compared with the published outcomes of the respective study, in which classical statistical procedures were used to analyze the data. Results Two hurdles were identified when combining the data of related studies that were performed independently and without the intention of combining their data. The first hurdle was a lack of essential information for reliable estimations of parameters of the combined model network. This information could be obtained by deriving it from existing information in the individual studies or by performing extra experiments; these practices are, however, not always possible. The second hurdle was a possible conflict in causal relationships underlying the individual experimental designs, which can cause misleading analyses of the combined dataset. This was the case for some experiments that involved the control of secondary explanatory variables. As such, an approach termed as Global Experimental Design was proposed in this thesis as a solution to overcome these hurdles. This approach emphasizes the building of an overall network prior to designing individual studies. In comparison to using the classical statistical procedures, more information can be extracted using Bayesian networks. This technique could make use of the domain knowledge in a transparent manner as well as empirical data with missing values. Conclusions It is possible to combine raw data from related studies for a meaningful analysis if effort is made in the phase of experimental design. The approach of Global Experimental Design outlines this phase with the building of an overall network. By using Bayesian networks as a tool for exploratory analysis, scientists are able to gain more insights into a research domain.

Keywords: safrole, PBBK model, DNA adduct, mace Safrole has been demonstrated to be carcinogenic in rodent studies at high doses of the pure compound. The use of pure safrole in foodshas already been prohibited. As a result, the main exposure to safrole occurs through the use of herbs and spices containing low levels of safrole, such as nutmeg, mace, star anise, pimento, cinnamon, and black pepper, and food products containing these herbs and spices or their essential oils. The Scientific Committee on Food of the European Union concluded in their evaluation that safrole is genotoxic and carcinogenic and that reductions in the exposure and restriction in the use levels are indicated. This opinion is based on carcinogenicity data from rodent studies as adequate human data were not available. Therefore, translation from animal bioassays at high dose levels of the pure compound to the risk for the human population exposed to safrole at relatively low levels via dietary intake within the complex food matrix is obviously needed. The aim of this thesis was to obtain insight into the dose-, species-, interindividual- and matrix dependent effects on the bioactivation and detoxification of safrole using physiologically based biokinetic (PBBK) modeling. PBBK models for safrole in male rats and humans were developed based on in vitro metabolic parameters determined, in silico derived partition coefficients, and physiological parameter values taken from literature. The performance of the PBBK model for rats was evaluated by comparison of predicted levels of 1,2-dihydroxy-4-allylbenzene, 1′-hydroxysafrole glucuronide and total urinary safrole metabolites to the reported levels of these metabolites in urine of rats exposed to safrole. This evaluation revealed that the predictions adequately matched observed experimental values. The PBBK model for humans was evaluated by comparison of the PBBK predicted and the reported experimental data on the level of total safrole metabolites detected in the urine of human volunteers exposed to safrole whichshowed an adequately match. The comparison of the PBBK model for rats and humans revealed that the predicted level of formation of 1ʹ-hydroxysafrole in human liver is fourfold higher than that for rat liver and the predicted formation of 1ʹ-sulfooxysafrole is about fivefold higher than that for rat liver. This indicates that the interspecies differences in toxicokinetics for bioactivation of safrole between rat an human are in line with the uncertainty factor normally taken into account for interspecies differences in toxicokinetics of 4. Species differences between humans and rats in the nature of the detoxification pathways of 1ʹ-hydroxysafrole were larger, with the formation of 1ʹ-oxosafrole being the main detoxification pathway in humans but a minor pathway in rats and glucuronidation of 1ʹ-hydroxysafrole being less important in humans than in rats. Monte Carlo simulations revealed that the formation of 1′-sulfooxysafrole was predicted to vary 4- to 17-fold in the population (fold-difference between the 95th and median, and 95th and 5th percentile, respectively). Risk assessment of safrole resulting from consumption of herbs and spices containing safrole should be performed taking into account the possible modulating effect of other compounds present in these herbs or spices. In this study, mace was chosen as the model spice of interest because it contains significant levels of safrole. Mace fraction with the highest SULT inhibiting activity was identified as malabaricone C. Studies using human HepG2 cells exposed to 1ʹ-hydroxysafrole and in the presence of mace extract showed that formation of the DNA adduct N2-(trans-isosafrol-3′-yl)-2′-deoxyguanosine was inhibited. To investigate the possible effects on safrole bioactivation to 1′-sulfooxysafrole by malabaricone C-containing mace extract could also be expected in vivo, the SULT inhibition was integrated into the PBBK model. The PBBK models predicted that at a dose of 50 mg/kg bw safrole and a ratio of malabaricone C-containing mace extract to safrole similar to the level of these constituents in mace, inhibition of 1′-sulfooxysafrole formation by malabaricone C-containing mace extract for rats and humans amounts to 90 and 100%, respectively. To see whether the inhibition of safrole DNA adduct formation by malabaricone C-containing mace extract is also observed in in vivo, to the end, Sprague-Dawley rats were orally exposed to mace extract and safrole. The results demonstrated that safrole DNA adduct formation in the liver of Sprague-Dawley rats by the mace extract was reduced by 55%. The results of the in vitro and in vivo studies that demonstrated inhibition of the formation of safrole DNA adducts by mace extract, support that combination effects should be taken into account in the risk assessment when safrole is tested in the presence of a relevant food matrix. To integrate thefood matrix dependent modulation of safrole bioactivation in the risk assessment of safrole, the so-called Margin of Exposure (MOE) approach can be used. This revealed that when safrole would be tested in rodent bioassays in the presence of a matrix containing SULT inhibitors the MOE values would be higher and the need for risk management actions would be lower.

One of the main obstacles in systems biology is complexity, a feature that is inherent to living systems. This complexity stems both from the large number of components involved and from the intricate interactions between these components. When the system is described by a mathematical model, we frequently end up with a large nonlinear set of mathematical equation that contains many parameters. Such a large model usually has a number of undesirable properties, e.g., its dynamical behavior is hard to understand, its parameters are difficult to identify, and its simulation requires a very long computing time. In this thesis, we present several strategies that may help to overcome these problems. On the level of method development, we focus on two issues: a) method development to analyze robustness, and b) method development to reduce model complexity. On the level of practical systems biology, we develop and analyze a model for the cell cycle in tomato fruit pericarp. Robustness, that is the ability of a system to preserve biological functionality in spite of internal and external perturbations, is an essential feature of a biological system. Any mathematical model that describes this system should reflect this property. This implies the needs of a mathematical method to evaluate the robustness of mathematical models for biological processes. However, assessing robustness of a complex non-linear model that contains many parameters is not straightforward. In this thesis, we present a novel method to evaluate the robustness of mathematical models efficiently. This method enables us to find which parameter combinations in a model are responsible for its robustness. In this way, we get more insight into the underlying mechanisms that govern the robustness of the biological system. The advantage of our method is that the effort to apply the method scales linearly with the number of parameters. It is therefore very efficient when it is applied on mathematical models that contain a large number of parameters. The complexity in a model can be brought down by simplifying the model. In this thesis, we also present a novel reduction method to simplify mathematical representations of biological models. In this method, biological components and parameters that do not contribute to the observed dynamics are considered redundant and hence are removed from the model. This results in a simpler model with less components and parameters, without losing predictive capabilities for any testable experimental condition. Since the reduced model contains less parameters, parameter identification can be carried out more efficaciously. In the last part of this thesis we show how modeling can help us in understanding the cell cycle in tomato fruit pericarp. The cell cycle in this system is quite unique since the classical cell cycle, in which the cell division takes place, after some periods turns into a partial cycle where the cell keeps replicating its DNA but skips the division. Several mechanisms that are putatively responsible for this transition have been proposed. With modeling, we show that although each of these putative mechanisms could lead on its own the cell cycle to this transition, also their combination could lead to the same result. We also show that the mechanisms that yield the transition are very robust.

Food science problems are complex. Scientists may be able to capture more of the complexity of an investigated theme if they were able to integrate related studies. Unfortunately, individual studies are usually not designed to allow such integration, and the common statistical methods cannot be used for analyzing integrated data. The modeling technique of Bayesian networks has gained popularity in many fields of application due to its ability to deal with complexity, but has emerged only recently in food science. This thesis used data from experiments on sensory satiation as case studies. The objective was to explore the use of Bayesian networks to combine raw data of independently performed but related experiments to build a quantitative model of sensory satiation. Methods This thesis started with introducing the theoretical background of Bayesian networks to food science. The available data from various independent experiments on sensory satiation were then examined for their potential to be combined. Finally, the outcomes obtained using Bayesian networks on a single dataset were compared with the published outcomes of the respective study, in which classical statistical procedures were used to analyze the data. Results Two hurdles were identified when combining the data of related studies that were performed independently and without the intention of combining their data. The first hurdle was a lack of essential information for reliable estimations of parameters of the combined model network. This information could be obtained by deriving it from existing information in the individual studies or by performing extra experiments; these practices are, however, not always possible. The second hurdle was a possible conflict in causal relationships underlying the individual experimental designs, which can cause misleading analyses of the combined dataset. This was the case for some experiments that involved the control of secondary explanatory variables. As such, an approach termed as Global Experimental Design was proposed in this thesis as a solution to overcome these hurdles. This approach emphasizes the building of an overall network prior to designing individual studies. In comparison to using the classical statistical procedures, more information can be extracted using Bayesian networks. This technique could make use of the domain knowledge in a transparent manner as well as empirical data with missing values. Conclusions It is possible to combine raw data from related studies for a meaningful analysis if effort is made in the phase of experimental design. The approach of Global Experimental Design outlines this phase with the building of an overall network. By using Bayesian networks as a tool for exploratory analysis, scientists are able to gain more insights into a research domain.

The lack of sufficient knowledge on the mechanisms of between-farm spread of livestock diseases hampers the development of much needed effective and fast control strategies. Some of the mechanisms responsible for pathogen spread can be deduced from epidemic tracing reports and literature while others can only be hypothesized from findings of studies on daily farm practices throughout the production round. For outbreaks without known/traced transmission routes, the concept of ‘neighbourhood’ infection is often adopted. This concept was founded based on the distance-dependence of the transmission risk with geographical proximity to an infectious farm being the key determinant of risk. Mathematical modelling plays an important role in obtaining quantitative insights into the contributions of the different mechanisms to disease spread. This can be by ranking the contributions of the individual transmission routes and/or obtaining a generic distance-dependent transmission risk. The models can guide the design of control strategies by providing a means to assess the efficacy of intervention strategies. In this thesis, modelling was used to assess the contributions of the wind-borne route and the other (traced) between-farm contacts to the transmission of highly pathogenic avian influenza during an epidemic in the Netherlands in 2003. It was found that these two routes together could only explain approximately 31% of the infections/cases. Visits by epidemic control teams were the least risky indicating the effectiveness of their biosecurity protocols in preventing transmission. New data on day-to-day farm practices and farmer opinion was collected in an attempt to generate hypotheses on transmission pathways and mechanisms that were yet to be appreciated. Indeed relevant unappreciated practices were found. They include irregularities in compliance to biosecurity as well as a broad category of neighbourhood-related risks. A new modelling approach to study neighbourhood transmission was developed guided by indirect transmission experiments. It involves the approximation of the pathogen dispersal process by a diffusive transport mechanism. Applying this diffusion model to the outbreak data of 2003, it was found that assuming delayed transmission, as opposed to instantaneous transmission, is an important phenomenon to be considered when modelling disease spread between locations. This modelling approach has the added advantage of availing an opportunity to assess the performance of intervention strategies without detailed mechanism-specific information.

The lack of sufficient knowledge on the mechanisms of between-farm spread of livestock diseases hampers the development of much needed effective and fast control strategies. Some of the mechanisms responsible for pathogen spread can be deduced from epidemic tracing reports and literature while others can only be hypothesized from findings of studies on daily farm practices throughout the production round. For outbreaks without known/traced transmission routes, the concept of ‘neighbourhood’ infection is often adopted. This concept was founded based on the distance-dependence of the transmission risk with geographical proximity to an infectious farm being the key determinant of risk. Mathematical modelling plays an important role in obtaining quantitative insights into the contributions of the different mechanisms to disease spread. This can be by ranking the contributions of the individual transmission routes and/or obtaining a generic distance-dependent transmission risk. The models can guide the design of control strategies by providing a means to assess the efficacy of intervention strategies. In this thesis, modelling was used to assess the contributions of the wind-borne route and the other (traced) between-farm contacts to the transmission of highly pathogenic avian influenza during an epidemic in the Netherlands in 2003. It was found that these two routes together could only explain approximately 31% of the infections/cases. Visits by epidemic control teams were the least risky indicating the effectiveness of their biosecurity protocols in preventing transmission. New data on day-to-day farm practices and farmer opinion was collected in an attempt to generate hypotheses on transmission pathways and mechanisms that were yet to be appreciated. Indeed relevant unappreciated practices were found. They include irregularities in compliance to biosecurity as well as a broad category of neighbourhood-related risks. A new modelling approach to study neighbourhood transmission was developed guided by indirect transmission experiments. It involves the approximation of the pathogen dispersal process by a diffusive transport mechanism. Applying this diffusion model to the outbreak data of 2003, it was found that assuming delayed transmission, as opposed to instantaneous transmission, is an important phenomenon to be considered when modelling disease spread between locations. This modelling approach has the added advantage of availing an opportunity to assess the performance of intervention strategies without detailed mechanism-specific information.

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