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Treating bone-cartilage defects is a fundamental clinical problem. The ability of damaged cartilage to self-repair is limited due to its avascularity. Left untreated, these defects can lead to osteoarthritis. Details of osteochondral defect repair are elusive, but animal models indicate healing occurs via an endochondral ossification-like process, similar to that in the growth plate. In the growth plate, the signalling molecules parathyroid hormone-related protein (PTHrP) and Indian Hedgehog (Ihh) form a feedback loop regulating chondrocyte hypertrophy, with Ihh inducing and PTHrP suppressing hypertrophy. To better understand this repair process and to explore the regulatory role of signalling molecules on the regeneration process, we formulate a reaction–diffusion mathematical model of osteochondral defect regeneration after chondrocyte implantation. The drivers of healing are assumed to be chondrocytes and osteoblasts, and their interaction via signalling molecules. We model cell proliferation, migration and chondrocyte hypertrophy, and matrix production and conversion, spatially and temporally. We further model nutrient and signalling molecule diffusion and their interaction with the cells. We consider the PTHrP-Ihh feedback loop as the backbone mechanisms but the model is flexible to incorporate extra signalling mechanisms if needed. Our mathematical model is able to represent repair of osteochondral defects, starting with cartilage formation throughout the defect. This is followed by chondrocyte hypertrophy, matrix calcification and bone formation deep inside the defect, while cartilage at the surface is maintained and eventually separated from the deeper bone by a thin layer of calcified cartilage. The complete process requires around 48 months. A key highlight of the model demonstrates that the PTHrP-Ihh loop alone is insufficient and an extra mechanism is required to initiate chondrocyte hypertrophy, represented by a critical cartilage density. A parameter sensitivity study reveals that the timing of the repair process crucially depends on parameters, such as the critical cartilage density, and those describing the actions of PTHrP to suppress hypertrophy, such as its diffusion coefficient, threshold concentration and degradation rate. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for modelling cell migration and aggregation due to chemotaxis where the cell is attracted towards the direction in which the concentration of a chemical signal is increasing. In the model presented here, each cell is represented by a system of springs connected together at node points on the cell's membrane and on the boundary of the cell's nucleus. The nodes located on a cell's membrane are subject to a force which is proportional to the gradient of the concentration of the chemical signal which mimics the behaviour of the chemical receptors in the cell's membrane. In particular, the model developed here will consider what happens when two (or more) cells collide and how their membranes connect to each other to form clusters of cells. The methods described in this paper will be illustrated with a number of typical examples simulating cells moving in response to a chemical signal and how they combine to form clusters. • Motion of cells in response to a diffusing chemical signal. • Cells emitting the chemical signal rather that it being in the environment. • Formation of clusters after the cells have collided. • Numerical examples which simulate the behaviour of real cells. [ABSTRACT FROM AUTHOR]

Abstract Current methods to optimize vaccine dose are purely empirically based, whereas in the drug development field, dosing determinations use far more advanced quantitative methodology to accelerate decision-making. Applying these established methods in the field of vaccine development may reduce the currently large clinical trial sample sizes, long time frames, high costs, and ultimately have a better potential to save lives. We propose the field of immunostimulation/immunodynamic (IS/ID) modelling, which aims to translate mathematical frameworks used for drug dosing towards optimizing vaccine dose decision-making. Analogous to Pharmacokinetic/Pharmacodynamic (PK/PD) modelling, the mathematical description of drug distribution (PK) and effect (PD) in host, IS/ID modelling approaches apply mathematical models to describe the underlying mechanisms by which the immune response is stimulated by vaccination (IS) and the resulting measured immune response dynamics (ID). To move IS/ID modelling forward, existing datasets and further data on vaccine allometry and dose-dependent dynamics need to be generated and collate, requiring a collaborative environment with input from academia, industry, regulators, governmental and non-governmental agencies to share modelling expertise, and connect modellers to vaccine data. [ABSTRACT FROM AUTHOR]

Highlights • An optimal control-ordinary differential equation model is constructed for basic fibroblast growth factor and binding agent interactions. • Theoretical predictions for optimal bFGF delivery are proposed for chronic wounds. • Insight is provided into the priority of minimising bFGF delivery and optimising bound bFGF distribution. Abstract In this paper, we present an ordinary differential equation model depicting the interactions of basic fibroblast growth factor (bFGF) and its binding agents in a chronic wound. The delivery of bFGF was treated as a control variable and is coupled to an objective functional. By optimising the objective functional with respect to the control, predictions for optimal delivery rates of bFGF are proposed. The optimal control is then validated by comparing the cost of the objective functional for the optimal delivery rate and several alternative delivery rates. This paper addresses two objectives of effective drug delivery to chronic wounds. The first is to provide insight for the priority of delivering bFGF: to minimise the quantity of bFGF, or to optimise the distribution of bound bFGF. For effective concentrations of bound bFGF, the optimisation of bound bFGF must be prioritised over the minimisation of bFGF delivered. The second objective is to comment on the effect of the proteolytic environment within the wound, with the concentration of bound bFGF starting to decrease late in the treatment period for highly proteolytic environments. This will lead to long term complications with wound closure after the treatment has been completed. Also, it was found that for highly proteolytic environments, the cost of delivering bFGF increased. The need for optimal drug delivery is made apparent by the burden of chronic wounds on the medical industry across the developed world. [ABSTRACT FROM AUTHOR]

Highlights • Extended model of Chong (2015) and Zhang (2009) for p53 activation of apoptosis. • Incorporation of the apoptosis initiation module involving Puma, Bcl2 and Bax. • Activation of Bax with an all-or-none response as an indicator for apoptosis. • The p53 apoptosis model shows ATM's auto-activation dictates cell fate decisions. • Prediction of Puma gene therapy in cancer cells overexpressing Bcl2. Abstract The p53 protein, a tumour suppressor, is a key player in the DNA damage response. The activation of apoptosis by p53 involves the intrinsic apoptotic pathway to eliminate stressed cells that contain DNA lesions. Recent experiments have found that apoptosis happen in an all-or-none switch like manner (Albeck et al., 2008; Rehm et al., 2002). We focus on modelling the mechanism of p53 activation of apoptosis in response to sustained high DNA double-strand breaks. The aim of the research is to investigate the design principles behind the regulation of p53 activation of apoptotic switch. Building on previous models (Chong et al., 2015; Zhang et al., 2009a), we developed a mathematical model that incorporated the molecular interactions in the core regulation of p53 and the apoptosis initiation module involving Puma, Bcl2 and Bax. Activation of Bax was assumed to be an indicator of apoptosis initiation. Chen et al. (2013) suggested that one of the components in the p53 pathway may control a threshold activation of apoptosis. We hypothesized that ATM auto-activation is the component that controls p53 threshold activation of apoptosis with ATM's multi-site autophosphorylation depending on damage intensity. The constructed model demonstrated how molecular interactions and stress signalling molecule ATM's auto-activation of the p53 network dictate cell fate decisions. Our simulation results are qualitatively consistent with the experimental findings of all-or-none activation of apoptosis and predicted overexpression of Bcl2 as a factor in causing malfunction of the apoptotic switch. We present a simplified yet plausible model of molecular mechanism that controls p53 activation of apoptotic switch. [ABSTRACT FROM AUTHOR]

Highlights • A continuum model of macrophages releasing an oncolytic virus within a tumour spheroid. • Predictive modelling of this treatment given in combination with radiotherapy. • Investigation into how radiotherapy and oncolytic virotherapy should be scheduled. Abstract Tumour hypoxia has long presented a challenge for cancer therapy: Poor vascularisation in hypoxic regions hinders both the delivery of chemotherapeutic agents and the response to radiotherapy, and hypoxic cancer cells that survive treatment can trigger tumour regrowth after treatment has ended. Tumour-associated macrophages are attractive vehicles for drug delivery because they localise in hypoxic areas of the tumour. In this paper, we derive a mathematical model for the infiltration of an in vitro tumour spheroid by macrophages that have been engineered to release an oncolytic adenovirus under hypoxic conditions. We use this model to predict the efficacy of treatment schedules in which radiotherapy and the engineered macrophages are given in combination. Our work suggests that engineered macrophages should be introduced immediately after radiotherapy for maximum treatment efficacy. Our model provides a framework that may guide future experiments to determine how multiple rounds of radiotherapy and macrophage virotherapy should be coordinated to maximise therapeutic responses. [ABSTRACT FROM AUTHOR]

Highlights • The paper examines four possible mathematical models for the effect of fusion inhibitor treatment of respiratory syncytial virus infections. • The models are fit to data from a treatment study of RSV in African green monkeys. • We find that the data are insufficient to discriminate between the different drug models. • We find dose and treatment delay combinations that could discriminate between the different models. Abstract Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, ε max , the maximum efficacy of the drug, and EC 50 , the drug concentration needed to achieve half the maximum effect. We find that if TMC353121 is having multiple effects on viral kinetics, more detailed data, using different treatment delays, is needed to detect this effect. [ABSTRACT FROM AUTHOR]

The use of viruses as a cancer treatment is becoming increasingly more robust; however, there is still a long way to go before a completely successful treatment is formulated. One major challenge in the field is to select which virus, out of a burgeoning number of oncolytic viruses and engineered derivatives, can maximise both treatment spread and anticancer cytotoxicity. To assist in solving this problem, an in-depth understanding of the virus-tumour interaction is crucial. In this article, we present a novel integro-differential system with distributed delays embodying the dynamics of an oncolytic adenovirus with a fixed population of tumour cells in vitro , allowing for heterogeneity to exist in the virus and cell populations. The parameters of the model are optimised in a hierarchical manner, the purpose of which is not to obtain a perfect representation of the data. Instead, we place our parameter values in the correct region of the parameter space. Due to the sparse nature of the data it is not possible to obtain the parameter values with any certainty, but rather we demonstrate the suitability of the model. Using our model we quantify how modifications to the viral genome alter the viral characteristics, specifically how the attenuation of the E1B 19 and E1B 55 gene affect the system performance, and identify the dominant processes altered by the mutations. From our analysis, we conclude that the deletion of the E1B 55 gene significantly reduces the replication rate of the virus in comparison to the deletion of the E1B 19 gene. We also found that the deletion of both the E1B 19 and E1B 55 genes resulted in a long delay in the average replication start time of the virus. This leads us to propose the use of E1B 19 gene-attenuated adenovirus for cancer therapy, as opposed to E1B 55 gene-attenuated adenoviruses. [ABSTRACT FROM AUTHOR]

Japanese encephalitis virus (JEV) is a zoonotic mosquito-borne virus, persisting in pigs, Ardeid birds and Culex mosquitoes. It is endemic to China and Southeastern Asia. The case-fatality ratio (CFR) or the rate of permanent psychiatric sequelae is 30% among symptomatic patients. There were no reported local JEV human cases between 2006 and 2010 in Hong Kong, but it was followed by a resurgence of cases from 2011 to 2017. The mechanism behind this “skip-and-resurgence” patterns is unclear. This work aims to reveal the mechanism behind the “skip-and-resurgence” patterns using mathematical modelling and likelihood-based inference techniques. We found that pig-to-pig transmission increases the size of JEV epidemics but is unlikely to maintain the same level of transmission among pigs. The disappearance of JEV human cases in 2006–2010 could be explained by a sudden reduction of the population of farm pigs as a result of the implementation of the voluntary “pig-rearing licence surrendering” policy. The resurgence could be explained by of a new strain in 2011, which increased the transmissibility of the virus or the spill-over ratio from reservoir to host or both. [ABSTRACT FROM AUTHOR]

Cross-immunity, as an evolutionary driver, can contribute to pathogen evolution, particularly pathogen diversity. Healthcare interventions aimed at reducing disease severity or transmission are commonly used to control diseases and can also induce pathogen evolution. Understanding pathogen evolution in the context of cross-immunity and healthcare interventions is crucial for infection control. This study starts by modelling cross-immunity, the extent of which is determined by strain traits and host characteristics. Given that all hosts have the same characteristics, full cross-immunity between residents and mutants occurs when mutation step sizes are small enough. Cross-immunity can be partial when the step size is large. The presence of partial cross-immunity reduces pathogen load and shortens the infectious period inside hosts, reducing transmission between hosts and improving host population survival and recovery. This study focuses on how pathogens evolve through small and large mutational steps and how healthcare interventions affect pathogen evolution. Using the theory of adaptive dynamics, we found that when mutational steps are small (only full cross-immunity is present), pathogen diversity cannot occur because it maximises the basic reproduction number. This results in intermediate values for both pathogen growth and clearance rates. However, when large mutational steps are allowed (with full and partial cross-immunity present), pathogens can evolve into multiple strains and induce pathogen diversity. The study also shows that different healthcare interventions can have varying effects on pathogen evolution. Generally, low levels of intervention are more likely to induce strain diversity, while high levels are more likely to result in strain reduction. • Cross-immunity is modelled at the host-individual level. • The extent of cross-immunity is determined by both strain traits and host characteristics. • Pathogen diversity arises because of the large mutation step size. • Low intervention levels are likely to result in strain diversity. • High intervention levels are likely to reduce strains. [ABSTRACT FROM AUTHOR]

• A mathematical model to analyse SARS-CoV-2 Omicron variant entry into cells. • Omicron variant's preference for different entry routes appears to be altered. • TMPRSS2 and Cathepsin inhibitors would synergistically block Omicron variant entry. • Drugs levels yielding maximum synergy would be different for the Omicron variant. The SARS-CoV-2 Omicron variant harbours many mutations in its spike protein compared to the original SARS-CoV-2 strain, which may alter its ability to enter cells, cell tropism, and response to interventions blocking virus entry. To elucidate these effects, we developed a mathematical model of SARS-CoV-2 entry into target cells and applied it to analyse recent in vitro data. SARS-CoV-2 can enter cells via two pathways, one using the host proteases Cathepsin B/L and the other using the host protease TMPRSS2. We found enhanced entry efficiency of the Omicron variant in cells where the original strain preferentially used Cathepsin B/L and reduced efficiency where it used TMPRSS2. The Omicron variant thus appears to have evolved to use the Cathepsin B/L pathway better but at the expense of its ability to use the TMPRSS2 pathway compared to the original strain. We estimated >4-fold enhanced efficiency of the Omicron variant in entry via the Cathepsin B/L pathway and >3-fold reduced efficiency via the TMPRSS2 pathway compared to the original or other strains in a cell type-dependent manner. Our model predicted that Cathepsin B/L inhibitors would be more efficacious and TMPRSS2 inhibitors less efficacious in blocking Omicron variant entry into cells than the original strain. Furthermore, model predictions suggested that drugs simultaneously targeting the two pathways would exhibit synergy. The maximum synergy and drug concentrations yielding it would differ for the Omicron variant compared to the original strain. Our findings provide insights into the cell entry mechanisms of the Omicron variant and have implications for intervention targeting these mechanisms. [ABSTRACT FROM AUTHOR]

An acute HIV infection in young children differs markedly from that in adults: Children have higher viral loads (VL), and a poor contraction to a setpoint VL that is not much lower than the peak VL. As a result, children progress faster towards AIDS in the absence of treatment. We used a classical ordinary differential equation model for viral infection dynamics to study why children have a lower viral contraction ratio than adults. We performed parameter sweeps to identify factors explaining the observed difference between children and adults. We grouped parameters associated with the host, the infection, or the immune response. Based on paediatric data available from datasets within the EPIICAL project (https://www.epiical.org/), we refuted that viral replication rates differ between young children and adults, and therefore these cannot be responsible for the low VL contraction ratios seen in children. The major differences in lowering VL contraction ratio resulted from sweeping the parameters linked to the immune response. Thus, we postulate that an "ineffective" (late and/or weak) immune response is the most parsimonious explanation for the higher setpoint VL in young children, and hence the reason for their fast disease progression. • Peak over setpoint viral load ratio is small in children with untreated HIV infection. • Paediatric viral replication rate is comparable to that in adults. • Simultaneous changes in source and death rate of target cells results in lower viral load contraction ratio. • Non-cytopathic virus can damp the viral load contraction ratio. • Immune response is the most parsimonious explanation for poor viral contraction. [ABSTRACT FROM AUTHOR]

We develop and analyse two population-based models of the transmission dynamics of the worm parasite Opisthorchis viverrini . The life cycle of O. viverrini includes humans, cats and dogs as definitive hosts; and snails and fish as intermediate hosts. The first model has only one definitive host (humans) while the second model has two additional hosts: the reservoir hosts, cats and dogs. We define reproduction numbers and endemic equilibrium points for the two models. We use prevalence data for the five hosts from two islands in Lao People’s Democratic Republic to estimate distributions of parameter values. We use these distributions to compute the sensitivity index and the partial rank correlation coefficient of the basic reproduction number and the endemic equilibrium point to the parameters. We calculate distributions of the host-specific type-reproduction number to show that humans are necessary to maintain transmission and can sustain transmission without additional reservoir hosts. Therefore interventions targeting humans could be sufficient to interrupt transmission of O. viverrini . [ABSTRACT FROM AUTHOR]

Falciparum malaria is a major parasitic disease causing widespread morbidity and mortality globally. Artemisinin derivatives—the most effective and widely-used antimalarials that have helped reduce the burden of malaria by 60% in some areas over the past decade—have recently been found to induce growth retardation of blood-stage Plasmodium falciparum when applied at clinically relevant concentrations. To date, no model has been designed to quantify the growth retardation effect and to predict the influence of this property on in vivo parasite killing. Here we introduce a mechanistic model of parasite growth from the ring to trophozoite stage of the parasite’s life cycle, and by modelling the level of staining with an RNA-binding dye, we demonstrate that the model is able to reproduce fluorescence distribution data from in vitro experiments using the laboratory 3D7 strain. We quantify the dependence of growth retardation on drug concentration and identify the concentration threshold above which growth retardation is evident. We estimate that the parasite life cycle is prolonged by up to 10 hours. We illustrate that even such a relatively short delay in growth may significantly influence in vivo parasite dynamics, demonstrating the importance of considering growth retardation in the design of optimal artemisinin-based dosing regimens. [ABSTRACT FROM AUTHOR]

We consider a hierarchy of ordinary differential equation models that describe the within-host viral kinetics of influenza infections: the IR model explicitly accounts for an immune response to the virus, while the simpler, target-cell limited TEIV and TV models do not. We show that when the IR model is fitted to pooled experimental murine data of the viral load, fraction of dead cells, and immune response levels, its parameters values can be determined. However, if, as is common, only viral load data are available, we can estimate parameters of the TEIV and TV models but not the IR model. These results are substantiated by a structural and practical identifiability analysis. We then use the IR model to generate synthetic data representing infections in hosts whose immune responses differ. We fit the TV model to these synthetic datasets and show that it can reproduce the characteristic exponential increase and decay of viral load generated by the IR model. Furthermore, the values of the fitted parameters of the TV model can be mapped from the immune response parameters in the IR model. We conclude that, if only viral load data are available, a simple target-cell limited model can reproduce influenza infection dynamics and distinguish between hosts with differing immune responses. • Target-cell limited model parameters can be estimated from viral load data. • Immune response data are needed to estimate parameters of immune response model. • The target-cell model can describe viral load in immunologically different hosts. • The target-cell limited model may be preferred when making viral load forecasts. [ABSTRACT FROM AUTHOR]

• It is crucial to assess the outbreak risk when a pathogen arrives in a new population. • We review two methods for estimating outbreak risks and their applications. • We show how these methods can be extended for complex outbreak models. • Estimates can be used to guide pathogen surveillance and control. • Development of these approaches is important for outbreak preparedness. Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". [ABSTRACT FROM AUTHOR]

Genetic insect control, such as self-limiting RIDL 2 2 RIDL ® is a registered trademark of Oxitec Limited, UK. (Release of Insects Carrying a Dominant Lethal) technology, is a development of the sterile insect technique which is proposed to suppress wild populations of a number of major agricultural and public health insect pests. This is achieved by mass rearing and releasing male insects that are homozygous for a repressible dominant lethal genetic construct, which causes death in progeny when inherited. The released genetically engineered (‘GE’) insects compete for mates with wild individuals, resulting in population suppression. A previous study modelled the evolution of a hypothetical resistance to the lethal construct using a frequency-dependent population genetic and population dynamic approach. This found that proliferation of resistance is possible but can be diluted by the introgression of susceptible alleles from the released homozygous-susceptible GE males. We develop this approach within a spatial context by modelling the spread of a lethal construct and resistance trait, and the effect on population control, in a two deme metapopulation, with GE release in one deme. Results show that spatial effects can drive an increased or decreased evolution of resistance in both the target and non-target demes, depending on the effectiveness and associated costs of the resistant trait, and on the rate of dispersal. A recurrent theme is the potential for the non-target deme to act as a source of resistant or susceptible alleles for the target deme through dispersal. This can in turn have a major impact on the effectiveness of insect population control. [ABSTRACT FROM AUTHOR]

Oncolytic viruses are a promising new treatment for cancer, whereby viruses are engineered to selectively destroy cancer cells. Mathematical modelling of the dynamics of the virus-tumour system can be modelled to provide insight into the system outcomes under different treatment protocols. In this study key metrics of treatment efficacy were identified and the mathematical model used to develop a decision framework to assess different treatment protocols. The optimal treatment outcome is the interplay between the virus application protocol and the uncertainty about the tumour characteristics. The uncertainty in the model parameters decreases as more data is available for their inference — however to obtain more data more time is required and the tumour then grows in size. Thus, there is an inherent tension whether it is better to wait to know the characteristics of the tumour system better or immediately initiating treatment. It is shown that, for small tumours, parameter inference with limited data does not constrain the choice of treatment protocol and rather only influences longer term decisions. • Parameter inference with limited data does not constrain the choice of treatment protocol for small tumours. • Modelling indicates delaying treatment for small tumours beneficial if tumour parameters are well known. • Increase in tumour size while gathering measurements negates benefits of optimising treatment protocol. • Adaptive treatment planning necessary to optimise treatment to individual tumours. [ABSTRACT FROM AUTHOR]

• Coordination of scientific research communities supported mathematical modelling of COVID-19. • Pre-existing research collaborations contributed to the success of coordination initiatives. • National infrastructure is key to support nationwide research networks. • Evidence synthesis important in supporting scientists providing advice to government. In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". [ABSTRACT FROM AUTHOR]

Eradication of malaria from the world in the latter part of the twentieth century proved an elusive, albeit desirable, objective. Unfortunately, resurgence of malarial incidence is currently underway. Key to understanding effective control schemes such as indoor residual spraying (spraying insecticide inside houses to kill the malarial vector mosquitoes) is the impact of spatial distributions for communities exposed to the malarial vector mosquito populations. Densities of human dwellings in small communities vary considerably in regions exposed to larval breeding sites. We extend prior modelling work to explore the spatial impact and diffusive transport of mosquito population densities on various distributions of human populations on relatively small landscape representations. Bistable dynamics of our reaction-diffusion model, which excludes advective transport, suggest two temporal phases for infection. An initial rapid phase occurs during transitions from initial homogeneous or spatially confined infections to peak levels over the course of days, and a relaxation phase develops to a steady state over weeks or months, suggesting successful intervention methods likely require recognising the phase of infection. We further observe a strong dependence of human infection and recovery on distributions of susceptible human populations with some degree of independence from mosquito distributions given an adequate supply of mosquito vectors to sustain infections. A subtle and complex interplay between human dwelling densities, mosquito diffusion and infection rates also emerges. With a sufficiently fast diffusive transport of mosquitoes, our model indicates that relative timescales for infection rates are slower, leading to lower rates of infection. This suggests that, although we here only include diffusive transport, if mosquitoes are subject to rapid enough movement (e.g., wind), communities situated in windy areas are exposed to less infectious risk than those in non-windy areas. This should help to guide intervention strategies with geographical considerations in mind. Our implementation of a reaction-diffusion model here further reveals some issues regarding continuum methods for population and infectious disease models that suggest consideration of discrete spatial methods (e.g., agent-based) for future work. [ABSTRACT FROM AUTHOR]

Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon- γ (IFN- γ ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13 months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013) . The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model. [ABSTRACT FROM AUTHOR]

Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator–inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns. [ABSTRACT FROM AUTHOR]

Nitric oxide (NO) is a neurotransmitter known to act as a potent cerebral vasodilator. Its role in neurovascular coupling (NVC) is discussed controversially and one of the main unanswered questions is which cell type provides the governing source of NO for the regulation of vasodynamics. Mathematical modelling can be an appropriate tool to investigate the contribution of NO towards the key components of NVC and analyse underlying mechanisms. The lumped parameter model of a neurovascular unit, including neurons (NE), astrocytes (AC), smooth muscle cells (SMC) and endothelial cells (EC), was extended to model the NO signalling pathway. Results show that NO leads to a general shift of the resting regional blood flow by dilating the arteriolar radius. Furthermore, dilation during neuronal activation is enhanced. Simulations show that potassium release is responsible for the fast onset of vascular response, whereas NO-modulated mechanisms maintain dilation. Wall shear stress-activated NO release from the EC leads to a delayed return to the basal state of the arteriolar radius. The governing source of vasodilating NO that diffuses into the SMC, which determine the arteriolar radius, depends on neuronal activation. In the resting state the EC provides the major contribution towards vasorelaxation, whereas during neuronal stimulation NO produced by the NE dominates. [ABSTRACT FROM AUTHOR]

Hepatitis B virus (HBV) dynamics in treated patients can be complex and differ considerably from other viral infections. We analyse dynamics of liver and serum levels of HBV DNA in 24 chronically HBV-infected individuals undergoing 1 year of combination therapy with pegylated interferon alpha and adefovir dipivoxil (ADV), followed by 2 years of ADV monotherapy. Serum viral dynamics differentiated the patients into four response groups dependent on how quickly viremia became undetectable: quickly suppressed (HBV DNA <100 copies/ml within 8 weeks and staying suppressed, GRP1); quickly suppressed but some rebound (<10,000 copies/ml, GRP2); slow decay (GRP3); virological failures (>10,000 copies/ml, GRP4). These groups did not differ before start of therapy by serum HBV DNA ( p =0.2), HBsAg ( p =0.1), ALT ( p =0.4), total HBV DNA within the liver ( p =0.08), or cccDNA ( p =0.3). Despite very different serum HBV DNA levels after 3 years, there was no statistical difference in total HBV DNA within the liver ( p =0.08), nor in cccDNA levels ( p =0.1), but HBsAg levels in serum were significantly lower for GRP1 compared to GRP4 ( p =0.02). Efficacy in terms of reduction over the 3 years of serum HBV DNA, liver HBV DNA, cccDNA, and ratios of liver HBV DNA to cccDNA were 99.98%, 99.5%, 98.4%, and 83.2% respectively, exhibiting larger antiviral effects in serum than in liver. Over the course of therapy, HBV DNA viremia exhibited large oscillations for some individuals. Mathematical modelling reproduced the dynamics of these diverse groups by assuming a number of viral clones arose that experienced delayed recognition by the antibody response. Large viremia oscillations under therapy suggest sequential outgrowth of viral clones with delayed recognition by the humoral response. [ABSTRACT FROM AUTHOR]

In Multiple Myeloma Bone Disease healthy bone remodelling is affected by tumour cells by means of paracrine cytokinetic signalling in such a way that osteoclast formation is enhanced and the growth of osteoblast cells inhibited. The participating cytokines are described in the literature. Osteoclast-induced myeloma cell growth is also reported. Based on existing mathematical models for healthy bone remodelling a three-way equilibrium model is presented for osteoclasts, osteoblasts and myeloma cell populations to describe the progress of the illness in a scenario in which there is a secular increase in the cytokinetic interactive effectiveness of paracrine processes. The equilibrium state for the system is obtained. The paracrine interactive effectiveness is explored by parameter variation and the stable region in the parameter space is identified. Then recently-discovered joint myeloma–osteoclast cells are added to the model to describe the populations inside lytic lesions. It transpires that their presence expands the available parameter space for stable equilibrium, thus permitting a detrimental, larger population of osteoclasts and myeloma cells. A possible relapse mechanism for the illness is explored by letting joint cells dissociate. The mathematics then permits the evaluation of the evolution of the cell populations as a function of time during relapse. [ABSTRACT FROM AUTHOR]

The theory of population genetics and evolutionary computation have been evolving separately for nearly 30 years. Many results have been independently obtained in both fields and many others are unique to its respective field. We aim to bridge this gap by developing a unifying framework for evolutionary processes that allows both evolutionary algorithms and population genetics models to be cast in the same formal framework. The framework we present here decomposes the evolutionary process into its several components in order to facilitate the identification of similarities between different models. In particular, we propose a classification of evolutionary operators based on the defining properties of the different components. We cast several commonly used operators from both fields into this common framework. Using this, we map different evolutionary and genetic algorithms to different evolutionary regimes and identify candidates with the most potential for the translation of results between the fields. This provides a unified description of evolutionary processes and represents a stepping stone towards new tools and results to both fields. [ABSTRACT FROM AUTHOR]

• We compare two metrics for assessing seasonal infectious disease epidemic risks. • The Instantaneous Epidemic Risk depends only on conditions at the outbreak start. • The Case Epidemic Risk accounts for changes in transmission after the outbreak start. • The Instantaneous Epidemic Risk is only accurate when the outbreak speed is fast. • We provide adaptable methods for computing epidemic risks with existing software. Seasonal variations in environmental conditions lead to changing infectious disease epidemic risks at different times of year. The probability that early cases initiate a major epidemic depends on the season in which the pathogen enters the population. The instantaneous epidemic risk (IER) can be tracked. This quantity is straightforward to calculate, and corresponds to the probability of a major epidemic starting from a single case introduced at time t = t 0 , assuming that environmental conditions remain identical from that time onwards (i.e. for all t ≥ t 0). However, the threat when a pathogen enters the population in fact depends on changes in environmental conditions occurring within the timescale of the initial phase of the outbreak. For that reason, we compare the IER with a different metric: the case epidemic risk (CER). The CER corresponds to the probability of a major epidemic starting from a single case entering the population at time t = t 0 , accounting for changes in environmental conditions after that time. We show how the IER and CER can be calculated using different epidemiological models (the stochastic Susceptible-Infectious-Removed model and a stochastic host-vector model that is parameterised using temperature data for Miami) in which transmission parameter values vary temporally. While the IER is always easy to calculate numerically, the adaptable method we provide for calculating the CER for the host-vector model can also be applied easily and solved using widely available software tools. In line with previous research, we demonstrate that, if a pathogen is likely to either invade the population or fade out on a fast timescale compared to changes in environmental conditions, the IER closely matches the CER. However, if this is not the case, the IER and the CER can be significantly different, and so the CER should be used. This demonstrates the need to consider future changes in environmental conditions carefully when assessing the risk posed by emerging pathogens. [ABSTRACT FROM AUTHOR]

• We present the first model for the coupled dynamics between follicles and hormones. • Model simulations support the hypothesis that ovarian follicles grow in waves. • Stochasticity in the follicular growth equation causes cycle-to-cycle variability. • Approximate Bayesian Computation enables parameter exploration in stochastic models. • Model analysis shows that none of the model parameters is particularly sensitive. We present a modelling and simulation framework for the dynamics of ovarian follicles and key hormones along the hypothalamic-pituitary–gonadal axis throughout consecutive human menstrual cycles. All simulation results (hormone concentrations and ovarian follicle sizes) are in biological units and can easily be compared to clinical data. The model takes into account variability in follicles' response to stimulating hormones, which introduces variability between cycles. The growth of ovarian follicles in waves is an emergent property in our model simulations and further supports the hypothesis that follicular waves are also present in humans. We use Approximate Bayesian Computation and cluster analysis to construct a population of virtual subjects and to study parameter distributions and sensitivities. The model can be used to compare and optimize treatment protocols for ovarian hyperstimulation, thus potentially forming the integral part of a clinical decision support system in reproductive endocrinology. [ABSTRACT FROM AUTHOR]

We use a mathematical model to show that if symmetric stem cell division is regulated by differentiated cells, then changes in the population dynamics of the differentiated cells can lead to changes in the population dynamics of the stem cells. More precisely, the relative fitness of the stem cells can be affected by modifying the death rate of the differentiated cells. This result is interesting because stem cells are less sensitive than differentiated cells to environmental factors, such as medical therapy. Our result implies that stem cells can be manipulated indirectly by medical treatments that target the differentiated cells. [ABSTRACT FROM AUTHOR]

Emergence of new lateral roots from within the primary root in Arabidopsis has been shown to be regulated by the phytohormone auxin, via the expression of the auxin influx carrier LAX 3, mediated by the ARF7 /19 IAA 14 signalling module ( Swarup et al., 2008 ). A single cell model of the LAX 3 and IAA1 4 auxin response was formulated and used to demonstrate that hysteresis and bistability may explain the experimentally observed ‘all-or-nothing’ LAX3 spatial expression pattern in cortical cells containing a gradient of auxin concentrations. The model was tested further by using a parameter fitting algorithm to match model output with qRT-PCR mRNA expression data following exogenous auxin treatment. It was found that the model is able to show good agreement with the data, but only when the exogenous auxin signal is degraded over time, at a rate higher than that measured in the experimental medium, suggesting the triggering of an endogenous auxin homeostasis mechanism. Testing the model over a more physiologically relevant range of extracellular auxin shows bistability and hysteresis still occur when using the optimised parameters, providing the rate of LAX3 active auxin transport is sufficiently high relative to passive diffusion. [ABSTRACT FROM AUTHOR]

A numerical model of neurovascular coupling (NVC) is presented based on neuronal activity coupled to vasodilation/contraction models via the astrocytic mediated perivascular K + and the smooth muscle cell Ca 2+ pathway. Luminal agonists acting on P2Y receptors on the endothelial cell surface provide a flux of IP 3 into the endothelial cytosol. This concentration of IP 3 is transported via gap junctions between endothelial and smooth muscle cells providing a source of sacroplasmic derived Ca 2+ in the smooth muscle cell. The model is able to relate a neuronal input signal to the corresponding vessel reaction. Results indicate that blood flow mediated IP 3 production via the agonist ATP has a substantial effect on the contraction/dilation dynamics of the SMC. The resulting variation in cytosolic Ca 2+ can enhance and inhibit the flow of blood to the cortical tissue. IP 3 coupling between endothelial and smooth muscle cells seems to be important in the dynamics of the smooth muscle cell. The VOCC channels are, due to the hyperpolarisation from K + SMC efflux, almost entirely closed and do not seem to play a significant role during neuronal activity. The current model shows that astrocytic Ca 2+ is not necessary for neurovascular coupling to occur in contrast to a number of experiments outlining the importance of astrocytic Ca 2+ in NVC, however this Ca 2+ pathway is not the only one mediating NVC. Importantly agonists in flowing blood have a significant influence on the endothelial and smooth muscle cell dynamics. [ABSTRACT FROM AUTHOR]

Efficient adaptation strategies to changing environmental conditions are essential for bacteria to survive and grow. Fundamental restructuring of their metabolism is usually mediated by corresponding gene regulation. Here, often several different environmental stimuli have to be integrated into a reasonable, energy-efficient response. Fast fluctuations and overshooting have to be filtered out. The gene regulatory network for the anaerobic adaptation of the pathogenic bacterium Pseudomonas aeruginosa is organized as a feed-forward loop (FFL), which is a three-gene network motif composed of two transcription factors (Anr for oxygen, NarxL for nitrate) and one target (Nar for nitrate reductase). The upstream transcription factor (Anr) induces the downstream transcription factor (NarXL). Both regulators act together positively by inducing the target (Nar) via a direct and indirect regulation path (coherent type-1 FFL). Since full promoter activity is only achieved when both transcription factors are present the target operon is expressed with a delay. Thus, in response to environmental stimuli (oxygen, nitrate), signals are mediated and processed in a way that short pulses are filtered out. In this study we analyze a special kind of FFL called FFL k by means of a family of ordinary differential equation models. The secondary FFL regulator (NarXL) is expressed constitutively but further induced in the presence of the upstream stimuli. This FFL modification has substantial influence on the response time and cost-benefit ratio mediated by environmental fluctuations. In order to find conditions where this regulatory network motif might be beneficial, we analyzed various models and environments. We describe the observed evolutional advantage of FFL k and its role in environmental adaptation and pathogenicity. [ABSTRACT FROM AUTHOR]

• Genetic mutations in SARS-CoV-2 emerge, and some of them appears more contagious than historical strains. • The transmission advantage of genetic variants is an innate biological feature that is difficult to be altered by artificial factors. • We demonstrate that NPIs could lead to changes in transmission advantage. • Our findings highlight the important roles of NPIs not only in controlling epidemics but also in slowing the growth of variants. As the COVID-19 pandemic continues, genetic mutations in SARS-CoV-2 emerge, and some of them are found more contagious than the previously identified strains, acting as the major mechanism for many large-scale epidemics. The transmission advantage of mutated variants is widely believed as an innate biological feature that is difficult to be altered by artificial factors. In this study, we explore how non-pharmaceutical interventions (NPI) may affect transmission advantage. A two-strain compartmental epidemic model is proposed and simulated to investigate the biological mechanism of the relationships among different NPIs, the changes in transmissibility of each strain and transmission advantage. Although the NPIs are effective in flattening the epidemic curve, we demonstrate that NPIs probably lead to a decline in transmission advantage, which is likely to occur if the NPIs become intensive. Our findings uncover the mechanistic relationship between NPIs and transmission advantage dynamically, and highlight the important role of NPIs not only in controlling the intensity of epidemics but also in slowing or even containing the growth of the proportion of variants. [ABSTRACT FROM AUTHOR]

Developing effective therapeutic interventions for pathological conditions associated with abnormal oxygen transport to muscle fibres critically depends on the objective characterisation of capillarity. Local indices of capillary supply have the potential to identify the onset of fine-scale tissue pathologies and dysregulation. Detailed tissue geometry, such as muscle fibre size, has been incorporated into such measures by considering the distribution of Voronoi polygons (VP) generated from planar capillary locations as a representation of capillary supply regions. Previously, detailed simulations have predicted that this is generally accurate for muscle tissue with uniform oxygen uptake. Here we extend this modelling framework to heterogeneous muscle for the assessment of capillary supply capacity under maximal sustainable oxygen consumption. We demonstrate for muscle with heterogeneous fibre properties that VP theoretically provide a computationally simple but often accurate representation of trapping regions (TR), which are predicted from biophysical transport models to represent the areas of tissue supplied by individual capillaries. However, this use of VP may become less accurate around large fibres, and at the interface of fibres of largely different oxidative capacities. In such cases, TR may provide a more robust representation of capillary supply regions. Additionally, given VP can only approximate oxygen delivery by capillaries, we show that their generally close relationship to TR suggests that (1) fibre type distribution may be tightly regulated to avoid large fibres with high oxidative capacities, (2) the anatomical fibre distribution is also tightly regulated to prevent a large surface area of interaction between metabolically dissimilar fibres, and (3) in chronically hypoxic tissues capillary distribution is more important in determining oxygen supply than the spatial heterogeneity of fibre demand. [ABSTRACT FROM AUTHOR]

Abstract: Human T-lymphotropic virus type I (HTLV-I) causes chronic infection for which there is no cure or neutralising vaccine. HTLV-I has been clinically linked to the development of adult T-cell leukaemia/lymphoma (ATL), an aggressive blood cancer, and HAM/TSP, a progressive neurological and inflammatory disease. Infected individuals typically mount a large, persistently activated CD8+ cytotoxic T-lymphocyte (CTL) response against HTLV-I-infected cells, but ultimately fail to effectively eliminate the virus. Moreover, the identification of determinants to disease manifestation has thus far been elusive. A key issue in current HTLV-I research is to better understand the dynamic interaction between persistent infection by HTLV-I and virus-specific host immunity. Recent experimental hypotheses for the persistence of HTLV-I in vivo have led to the development of mathematical models illuminating the balance between proviral latency and activation in the target cell population. We investigate the role of a constantly changing anti-viral immune environment acting in response to the effects of infected T-cell activation and subsequent viral expression. The resulting model is a four-dimensional, non-linear system of ordinary differential equations that describes the dynamic interactions among viral expression, infected target cell activation, and the HTLV-I-specific CTL response. The global dynamics of the model is established through the construction of appropriate Lyapunov functions. Examining the particular roles of viral expression and host immunity during the chronic phase of HTLV-I infection offers important insights regarding the evolution of viral persistence and proposes a hypothesis for pathogenesis. [Copyright &y& Elsevier]

Abstract: Recent studies have provided evidence of a significant role of the Hageman factor in pathologic clot formation. Since auto-activation of the Hageman factor triggers the intrinsic coagulation pathway, we study the dynamics of pathologic clot formation considering the intrinsic pathway as the predominant mechanism of this process. Our methodological approach to studying the dynamics of clot formation is based on mathematical modelling. Activation of the blood coagulation cascade, particularly its intrinsic pathway, is known to involve platelets. Therefore, equations accounting for the effects of activated platelets on the intrinsic pathway activation are included in our model. This brings about a considerable increase in the values of kinetic constants involved in the model of the principal biochemical processes resulting in clot formation. The purpose of this study is to elucidate the mechanism of pathologic clot formation. Since the time window of thrombolysis is 3&#x2013;6h, we hypothesize that in many cases the rate of pathologic clot formation is much lower than that of haemostatic clot. This assumption is used to simplify the mathematical model and to estimate kinetic constants of biochemical reactions that initiate pathologic clot formation. The insights we gained from our mathematical model may lead to new approaches to the prophylaxis of pathologic clot formation. We believe that one of the most efficient ways to prevent pathologic clot formation is simultaneous inhibition of activated factors &#x0425;II and &#x0425;I. [ABSTRACT FROM AUTHOR]

• The immunology underlying autoimmune myocarditis is captured in a mathematical model. • Disease outcomes can be represented by multiple non-negative steady states. • Immune checkpoint inhibitors lower the threshold for disease development. • Different patients and their risk of disease can be explored using the model. Autoimmune myocarditis is a rare, but frequently fatal, side effect of immune checkpoint inhibitors (ICIs), a class of cancer therapies. Despite extensive experimental work on the causes, development and progression of this disease, much still remains unknown about the importance of the different immunological pathways involved. We present a mathematical model of autoimmune myocarditis and the effects of ICIs on its development and progression to either resolution or chronic inflammation. From this, we gain a better understanding of the role of immune cells, cytokines and other components of the immune system in driving the cardiotoxicity of ICIs. We parameterise the model using existing data from the literature, and show that qualitative model behaviour is consistent with disease characteristics seen in patients in an ICI-free context. The bifurcation structures of the model show how the presence of ICIs increases the risk of developing autoimmune myocarditis. This predictive modelling approach is a first step towards determining treatment regimens that balance the benefits of treating cancer with the risk of developing autoimmune myocarditis. [ABSTRACT FROM AUTHOR]

• Novel operationalisation of the role of the subjective perspective of consciousness in the control of behaviour. • Novel account of appraisal, drive and theory of mind based on that operationalization. • Model accounts for psychophysical relationships between appraisal and distance. • Model generates adaptive and maladaptive behaviours as a function of interpretable parameters. Consciousness has been hypothesized to operate as a global workspace, which accesses and integrates multimodal information in a unified manner, supports expectation violation monitoring and reduction, and the motivation, programming and control of action. One important yet open issue concerns how the subjective perspective at the core of consciousness, and subjective properties of manifestation of the environment in such perspective as an embodied experience, play a role in such process. We operationalised the concept of subjective perspective using the principles of the Projective Consciousness Model (PCM), based on the projective geometrical concept of Field of Consciousness. We show how these principles can account for documented relationships between appraisal and distance as an inverse distance law, yield a generative model of affective and epistemic drives based on purely subjective parameters, such as the apparent size of objects, and can be generalised to implement Theory of Mind, in a manner that is consistent with simulation theory. We used simulations of artificial agents, based on psychological rationale, to demonstrate how different model parameters could generate a variety of emergent adaptive and maladaptive behaviours that are relevant to developmental and clinical psychology: the ability to be resilient in the face of obstacles through imaginary projections, the emergence of social approach and joint attention behaviours, the ability to take advantage of false beliefs attributed to others, the emergence of avoidance behaviours as observed in social anxiety disorders, the presence of restricted interests as observed in autism spectrum disorders. The simulation of agents was applied to a specific robotic context, and agents' behaviours were demonstrated by controlling the corresponding robots. Our results contribute to advance the scientific understanding of the causal relationships between core aspects of the phenomenology of consciousness and its functions in human cybernetics. [ABSTRACT FROM AUTHOR]

• Environmentally stressed M. smegmatis growth is rigorously investigated and modelled. • The effect of carbon, nitrogen, and pH stress is determined experimentally. • A mechanistic model accurately predicts bacterial growth under environmental stress. • The model explicitly captures pH variation and growth decoupled nitrogen uptake. • The model is analyzed in terms of parameter identifiability and critically evaluated. Mycobacterium tuberculosis can exist within a host for lengthy periods, tolerating even antibiotic challenge. This non-heritable, antibiotic tolerant "persister" state, is thought to underlie latent Tuberculosis (TB) infection and a deeper understanding thereof could inform treatment strategies. In addition to experimental studies, mathematical and computational modelling approaches are widely employed to study persistence from both an in vivo and in vitro perspective. However, specialized models (partial differential equations, agent-based, multiscale, etc.) rely on several difficult to determine parameters. In this study, a dynamic mathematical model was developed to predict the response of Mycobacterium smegmatis (a model organism for M. tuberculosis) grown in batch culture and subjected to a range of in vitro environmental stresses. Lag phase dynamics, pH variations and internal nitrogen storage were mechanistically modelled. Experimental results were used to train model parameters using global optimization, with extensive subsequent model validation to ensure extensibility to more complex modelling frameworks. This included an identifiability analysis which indicated that seven of the thirteen model parameters were uniquely identifiable. Non-identifiable parameters were critically evaluated. Model predictions compared to validation data (based on experimental results not used during training) were accurate with less than 16% maximum absolute percentage error, indicating that the model is accurate even when extrapolating to new experimental conditions. The bulk growth model can be extended to spatially heterogeneous simulations such as an agent-based model to simulate in vitro granuloma models or, eventually, in vivo conditions, where distributed environmental conditions are difficult to measure. [ABSTRACT FROM AUTHOR]

Abstract: Background. Interventions aimed at minimizing the spread of blood borne infections among Injecting Drug Users (IDU) are impeded by limitations in resources. To enhance their efficiency, it may be beneficial to target specific behavioural subpopulations, distinguished by syringe sharing tendencies. Methods. We used mathematical modelling to explore the effects of two types of intervention: removal of individuals from the injecting population and risk decrease at group-level (e.g. distribution of syringes). We computed the direct effects of intervention on the probability of obtaining and spreading infection as a function of baseline risk behaviour. Population level effects of (targeted) intervention were explored using a differential equations model, which incorporated two levels of risk. Results. Within most scenarios of risk distribution considered, HIV could be substantially reduced or eliminated by targeting high risk IDU only. Conversely, higher incidence reductions for HCV were reached in many scenarios when targeting low risk IDU. The potential for preventing infections by removal of uninfected IDU increases with baseline risk, but so does the probability that an IDU is already infected before being reached by intervention. Decreasing risk is likely to only delay rather than prevent infection for IDU borrowing many syringes, especially for a very infectious disease such as HCV. Conclusions. The efficiency of intervention on injecting drug users may be much enhanced by targeting specific risk subgroups. However, the optimal targeting policy depends strongly on the infection under consideration. [Copyright &y& Elsevier]

Abstract: Alkaline pH adaptation represents an important environmental stress response in Aspergillus nidulans. It is mediated by the pal signalling pathway and the PacC transcription factor. Although studied extensively experimentally, the activation mechanism of PacC has not been quantified, and it is not clear how this activation is regulated. Here, by constructing mathematical models, we first show that the pattern of PacC activation observed in previously published experiments cannot be explained based on existing knowledge about PacC activation. Extending the model with a negative feedback loop is necessary to produce simulation results that are consistent with the data, suggesting the existence of a negative feedback loop in the PacC activation process. This extended model is then validated against published measurements for cells with drug treatment and mutant cells. Furthermore, we investigate the role of an intermediate form of PacC in the PacC activation process, and propose experiments that can be used to test our predictions. Our work illustrates how mathematical models can be used to uncover regulatory mechanisms in the transcription regulation, and generate hypotheses that guide further laboratory investigations. [Copyright &y& Elsevier]

Abstract: HIV viral blips are characterized by intermittent episodes of detectable low-level viraemia which return spontaneously to an undetectable level in patients with full suppression of viraemia . The precise mechanisms responsible for viraemia blips and their clinical significance are not known. In this work, we analyze HIV blips using a mathematical model describing basic host–pathogen interactions, in particular regulatory processes involving CD4+, CD8+ T-cells and the virus. We show that under adequate conditions, this interaction system can be excitable and small perturbations of the system by external stimuli can generate robust viral load (VL) blips of regular or irregular frequency and peak amplitudes. Importantly, our analysis showed that direct perturbations of the viral load (by latent reservoirs or opportunistic diseases for example) more efficiently trigger VL blips on contrary to direct perturbations of the immune system, in particular the levels of uninfected CD4+ and cytotoxic CD8+ T-cells. This feature is shown to rely on specific stability properties in this interaction system. Our analysis moreover suggests that blips should be of low clinical significance since any other VL or immune system perturbations could trigger transient viraemia under adequate excitability conditions. [Copyright &y& Elsevier]

Abstract: Auxin and cytokinin are key hormonal signals that control the cellular architecture of the primary root and the initiation of new lateral root organs in the plant Arabidopsis thaliana. Both developmental processes are regulated by cross-talk between these hormones and their signalling pathways. In this paper, sub-cellular and multi-cellular mathematical models are developed to investigate how interactions between auxin and cytokinin influence the size and location of regions of division and differentiation within the primary root, and describe how their cross-regulation may cause periodic branching of lateral roots. We show how their joint activity may influence tissue-specific oscillations in gene expression, as shown in Moreno-Risueno et al. (2010) and commented upon in Traas and Vernoux (2010), and we propose mechanisms that may generate synchronisation of such periodic behaviours inside a cell and with its neighbours. Using a multi-cellular model, we also analyse the roles of cytokinin and auxin in specifying the three main regions of the primary root (elongation, transition and division zones), our simulation results being in good agreement with independent experimental observations. We then use our model to generate testable predictions concerning the effect of varying the concentrations of the auxin efflux transporters on the sizes of the different root regions. In particular, we predict that over-expression of the transporters will generate a longer root with a longer elongation zone and a smaller division zone than that of a wild type root. This root will contain fewer cells than its wild type counterpart. We conclude that our model can provide a useful tool for investigating the response of cell division and elongation to perturbations in hormonal signalling. [Copyright &y& Elsevier]

Abstract: A mathematical model was constructed to simulate the bovine oestrous cycle by using nonlinear differential equations to describe the biological mechanisms which regulate the cycle. The model predicts circulating concentrations of gonadotrophin-releasing hormone, follicle-stimulating hormone, luteinizing hormone, oestradiol, inhibin and progesterone. These hormones collectively provide control and feedback mechanisms between the hypothalamus, pituitary gland and ovaries, which regulate ovarian follicular dynamics, corpus luteum function and ovulation. When follicular growth parameters are altered, the model predicts that cows will exhibit either two or three follicular waves per cycle, as seen in practice. Changes in other parameters allow the model to simulate: effects of nutrition on follicle recruitment and size of the ovulatory follicle; effects of negative energy balance on postpartum anoestrus; and effects of pharmacological intervention on hormone profiles and timing of ovulation. It is concluded that this model provides a sound basis for exploring factors that influence the bovine oestrous cycle in order to test hypotheses about nutritional and hormonal influences which, with further validation, should help to design dietary or pharmacological strategies for improving reproductive performance in cattle. [Copyright &y& Elsevier]

Abstract: During the 2009 A/H1N1 influenza pandemic, very strict interventions including campus quarantine (Fengxiao) (restrictions on the movements of university personnel) were taken in mainland China to slow down the initial spread of the disease from the university network to a wider community. The decision for implementation and/or relaxation of Fengxiao depends on the assessment of the level of infection within the university network compared with that in the wider community and on the degree of interruption of normal academic activities and the associated social/economic costs. However, the most important consideration influencing the decision is whether the initiation and termination of Fengxiao can alter the pattern of disease spread in the entire community for effective prevention and control of the emerging disease. Here we formulate and analyze a dynamic model to evaluate the effectiveness of Fengxiao as a social distance measure for curbing the outbreak in major cities of China. Using data from the initial laboratory-confirmed cases admitted to the 8th Hospital of Xi''an (the capital city of the Shaanxi Province), we estimated the reproduction number for the period under consideration in the range 1.273–1.784 and concluded that the population''s mobility, combined with the suspension of the Fengxiao strategy, was a key factor contributing to a subsequent epidemic wave. Fengxiao in China is a reversal of the usual strategy of school closures adopted in many other countries, but the lessons learnt from it may be useful for disease management in other countries where restrictions on the movements across a facility boundary and close monitoring of the infection within the facility are feasible in the long term. [Copyright &y& Elsevier]