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Antibiotic resistance is one of the major challenges that we are facing today. The frequent overuse of antibiotics is one of the main reasons for the development of resistance. A mathematical model of bacterial population dynamics is used, where drug administration and absorption mechanics are implemented to evaluate the fitness of automatically designed treatments. To maximise the probability of curing the host while minimising the total drug used we have explored treatments with different daily dosages and lengths. Two multi-objective population-based methods, a well-known evolutionary algorithm and a particle swarm optimisation algorithm are tuned and contrasted when solving the posed treatment design problem. The best solutions found by our approach suggest treatments ranging from five to seven days with a high initial dose, followed by lower doses, use lower amounts of the drug than the standard common practice of fixed daily dosages over ten days.

Mass production and use of antibiotics has led to the rise of resistant bacteria, a problem possibly exacerbated by inappropriate and non-optimal application. Antibiotic treatment often follows fixed-dose regimens, with a standard dose of antibiotic administered equally spaced in time. But are such fixed-dose regimens optimal or can alternative regimens be designed to increase efficacy? Yet, few mathematical models have aimed to identify optimal treatments based on biological data of infections inside a living host. In addition, assumptions to make the mathematical models analytically tractable limit the search space of possible treatment regimens (e.g. to fixed-dose treatments). Here, we aimed to address these limitations by using experiments in a Galleria mellonella (insect) model of bacterial infection to create a fully parametrised mathematical model of a systemic Vibrio infection. We successfully validated this model with biological experiments, including treatments unseen by the mathematical model. Then, by applying artificial intelligence, this model was used to determine optimal antibiotic dosage regimens to treat the host to maximise survival while minimising total antibiotic used. As expected, host survival increased as total quantity of antibiotic applied during the course of treatment increased. However, many of the optimal regimens tended to follow a large initial ‘loading’ dose followed by doses of incremental reductions in antibiotic quantity (dose ‘tapering’). Moreover, application of the entire antibiotic in a single dose at the start of treatment was never optimal, except when the total quantity of antibiotic was very low. Importantly, the range of optimal regimens identified was broad enough to allow the antibiotic prescriber to choose a regimen based on additional criteria or preferences. Our findings demonstrate the utility of an insect host to model antibiotic therapies in vivo and the approach lays a foundation for future regimen optimisation for patient and societal benefits., Author summary Research into optimal antibiotic use to improve efficacy is far behind that of cancer care, where personalised treatment is common. The integration of mathematical models with biological observations offers hope to optimise antibiotic use, and in this present study an in vivo insect model of systemic Vibrio infection was used for the first time to determine critical model parameters for optimal antibiotic treatment. By this approach, the optimal regimens tended to result from a large initial ‘loading’ dose followed by subsequent doses of incremental reductions in antibiotic quantity (dose ‘tapering’). The approach and findings of this study opens a new avenue towards optimal application of our precious antibiotic arsenal and may lead to more effective treatment regimens for patients, thus reducing the health and economic burdens associated with bacterial infections. Importantly, it can be argued that until we understand how to use a single antibiotic optimally, it is unlikely we will identify optimal ways to use multiple antibiotics simultaneously.

One hundred years after the 1918 influenza outbreak, are we ready for the next pandemic? This paper addresses the need to identify and develop collaborative, interdisciplinary and cross-sectoral approaches to modelling of infectious diseases including the fields of not only human and veterinary medicine, but also plant epidemiology. Firstly, the paper explains the concepts on which the most common epidemiological modelling approaches are based, namely the division of a host population into susceptible, infected and removed (SIR) classes and the proportionality of the infection rate to the size of the susceptible and infected populations. It then demonstrates how these simple concepts have been developed into a vast and successful modelling framework that has been used in predicting and controlling disease outbreaks for over 100 years. Secondly, it considers the compartmental models based on the SIR paradigm within the broader concept of a ‘disease tetrahedron’ (comprising host, pathogen, environment and man) and uses it to review the similarities and differences among the fields comprising the ‘OneHealth’ approach. Finally, the paper advocates interactions between all fields and explores the future challenges facing modellers. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’. This issue is linked with the subsequent theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’.

The increase in antibiotic resistant bacteria poses a threat to the continued use of antibiotics to treat bacterial infections. The overuse and misuse of antibiotics has been identified as a significant driver in the emergence of resistance. Finding optimal treatment regimens is therefore critical in ensuring the prolonged effectiveness of these antibiotics. This study uses mathematical modelling to analyse the effect traditional treatment regimens have on the dynamics of a bacterial infection. Using a novel approach, a genetic algorithm, the study then identifies improved treatment regimens. Using a single antibiotic the genetic algorithm identifies regimens which minimise the amount of antibiotic used while maximising bacterial eradication. Although exact treatments are highly dependent on parameter values and initial bacterial load, a significant common trend is identified throughout the results. A treatment regimen consisting of a high initial dose followed by an extended tapering of doses is found to optimise the use of antibiotics. This consistently improves the success of eradicating infections, uses less antibiotic than traditional regimens and reduces the time to eradication. The use of genetic algorithms to optimise treatment regimens enables an extensive search of possible regimens, with previous regimens directing the search into regions of better performance.

Increasing concerns about the changing environment and the emergence of pathogens that cross species boundaries have added to the urgency of understanding the dynamics of complex ecological systems infected by pathogens. Of particular interest is the often counterintuitive way in which infection and predation interact and the consequent difficulties in designing control strategies to manage the system. To understand the mechanisms involved, we focus on the pathogen exclusion problem, using control maps (on which the network of exclusion thresholds are plotted) in order to readily identify which exclusion strategies will work and why others will not. We apply this approach to the analysis of parasite exclusion in two game bird ecologies. For higher dimensions, we propose a computational scheme that will generate the optimal exclusion strategy, taking into account all operational constraints on the pathogen invasion matrix, populations, and controls. The situation is further complicated when external forcing distorts pathogen thresholds. This distortion is highly sensitive to the lags between forcing components, a sensitivity that can be exploited by management using correctly lagged cyclically varying controls to reduce the effort involved in pathogen exclusion.

Many studies of the evolution of life-history traits assume that the underlying population dynamical attractor is stable point equilibrium. However, evolutionary outcomes can change significantly in different circumstances. We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The size of this region decreases as we move through the region of 2-cycles. There is a further discontinuous fall in the size of the branching region during the transition to 4-cycles. We extend our results numerically and with simulations to higher-period cycles and chaos. Simulations show that chaotic population dynamics can evolve from equilibrium and vice-versa.

Models reveal that sexually antagonistic co-evolution exaggerates female resistance and male persistence traits. Here we adapt an established model by including directional sexual selection acting against persistence. We find similar equilibria to previous models showing that sexually antagonistic co-evolution can be limited by counteracting sexual, as well as, natural selection. We tested the model using empirical data for the seaweed fly, Coelopa ursina, in which body size acts as a persistence and a resistance trait. Our model can generate continuous co-evolutionary cycles and stable equilibria, however, all simulations using empirically derived parameter estimates reach stable equilibria. Thus, stable equilibria might be more common in nature than continuous co-evolutionary cycles, suggesting that sexual conflict is unlikely to promote speciation. The model predicts male biased sexual size dimorphism for C. ursina, comparable with empirically observed values. Male persistence is shown to be more sensitive than female resistance to changes in model parameters.

Gyrodactylus salaris (Monogenea, Platyhelminthes) is a notifiable freshwater pathogen responsible for causing catastrophic damage to wild Atlantic salmon stocks, most notably in Norway. In some strains of Baltic salmon (e.g., from the river Neva) however, the impact is greatly reduced due to some form of innate resistance that regulates parasite numbers, resulting in fewer host mortalities. Gyrodactylus salaris is known from 17 European states; its status in a further 35 states remains unknown; the UK, the Republic of Ireland and certain watersheds in Finland are free of the parasite. Thus, the parasite poses a serious threat if it emerges in Atlantic salmon rearing regions throughout Europe. At present, infections are generally controlled via extreme measures such as the treatment of entire river catchments with the biocide rotenone, in order to remove all hosts, before restocking with the original genetic stock. The use of rotenone in this way in EU countries is unlikely as it would be in contravention of the Water Framework Directive. Not only are such treatments economically and environmentally costly, they also eradicate the potential for any host/parasite evolutionary process to occur. Based on previous studies, UK salmon stocks have been shown to be highly susceptible to infection, analogous to Norwegian stocks. The present study investigates the impact of a G. salaris outbreak within a naïve salmon population in order to determine long-term consequences of infection and the likelihood of coexistence. Simulation of the salmon/ G. salaris system was carried out via a deterministic mathematical modelling approach to examine the dynamics of host-pathogen interactions. Results indicated that in order for highly susceptible Atlantic strains to evolve a resistance, both a moderate-strong deceleratingly costly trade-off on birth rate and a lower overall cost of the immune response are required. The present study provides insights into the potential long term impact of G. salaris if introduced into G. salaris-free territories and suggests that in the absence of external controls salmon populations are likely to recover to high densities nearing 90% of that observed pre-infection.

Phagocytosis is defined as the ingestion of particulates over 0.5 microm in diameter and is associated with cells of the immune system such as macrophages or monocytes. Neurones are not generally recognized to be phagocytic. Using light, confocal, time-lapse and electron microscopy, we carried out a wide range of in-vitro and in-vivo experiments to examine the phagocytic capacity of different neuronal cell types. We demonstrated phagocytosis of material by neurones, including cell debris and synthetic particles up to 2.8 microm in diameter. We showed phagocytosis in different neuronal types, and demonstrated that debris can be transported from neurite extremities to cell bodies and persist within neurones. Flow cytometry analysis demonstrated the lack of certain complement receptors on neurones but the presence of others, including integrin receptors known to mediate macrophage phagocytosis, indicating that a restricted set of phagocytosis receptors may mediate this process. Neuronal phagocytosis occurs in vitro and in vivo, and we propose that this is a more widespread and significant process than previously recognized. Neuronal phagocytosis may explain certain inclusions in neurones during disease, cell-to-cell spread of disease, neuronal death during disease progression and provide a potential mechanism for therapeutic intervention through the delivery of particulate drug carriers.

Maternal effects, where the conditions experienced by mothers affect the phenotype of their offspring, are widespread in nature and have the potential to influence population dynamics. However, they are very rarely included in models of population dynamics. Here, we investigate a recently discovered maternal effect, where maternal food availability affects the feeding rate of offspring so that well-fed mothers produce fast-feeding offspring. To understand how this maternal effect influences population dynamics, we explore novel predator–prey models where the consumption rate of predators is modified by changes in maternal prey availability. We address the ‘paradox of enrichment', a theoretical prediction that nutrient enrichment destabilizes populations, leading to cycling behaviour and an increased risk of extinction, which has proved difficult to confirm in the wild. Our models show that enriched populations can be stabilized by maternal effects on feeding rate, thus presenting an intriguing potential explanation for the general absence of ‘paradox of enrichment' behaviour in natural populations. This stabilizing influence should also reduce a population's risk of extinction and vulnerability to harvesting.

A key feature of the vertebrate adaptive immune system is acquired immune memory, whereby hosts launch a faster and heightened response when challenged by previously encountered pathogens, preventing full infection. Here, we use a mathematical model to explore the role of ecological and epidemiological processes in shaping selection for costly acquired immune memory. Applying the framework of adaptive dynamics to the classic SIR (Susceptible-Infected-Recovered) epidemiological model, we focus on the conditions that may lead hosts to evolve high levels of immunity. Linking our work to previous theory, we show how investment in immune memory may be greatest at long or intermediate host lifespans depending on whether immunity is long lasting. High initial costs to gain immunity are also found to be essential for a highly effective immune memory. We also find that high disease infectivity and sterility, but intermediate virulence and immune period, increase selection for immunity. Diversity in host populations through evolutionary branching is found to be possible but only for a limited range of parameter space. Our model suggests that specific ecological and epidemiological conditions have to be met for acquired immune memory to evolve.

Gyrodactylus salaris is a notifiable freshwater ectoparasite of salmonids. Its primary host is Atlantic salmon (Salmo salar), upon which infections can cause death, and have led to massive declines in salmon numbers in Norway, where the parasite is widespread. Different strains of S. salar vary in their susceptibility, with Atlantic strains (such as those found in Norway) exhibiting no resistance to the parasite, and Baltic strains demonstrating an innate resistance sufficient to regulate parasite numbers on the host causing it to either die out or persist at a low level. In this study, Leslie matrix and compartmental models were used to generate data that demonstrated the population growth of G. salaris on an individual host is dependent on the total number of offspring per parasite, its longevity and the timing of its births. The data demonstrated that the key factor determining the rate of G. salaris population growth is the time at which the parasite first gives birth, with rapid birth rate giving rise to large population size. Furthermore, it was shown that though the parasite can give birth up to four times, only two births are required for the population to persist as long as the first birth occurs before a parasite is three days old. As temperature is known to influence the timing of the parasite's first birth, greater impact may be predicted if introduced to countries with warmer climates than Norway, such as the UK and Ireland which are currently recognised to be free of G. salaris. However, the outputs from the models developed in this study suggest that temperature induced trade-offs between the total number of offspring the parasite gives birth to and the first birth timing may prevent increased population growth rates over those observed in Norway.

This paper uses a mathematical framework to investigate the impact of increased movement in response to disturbance caused by disease control strategies. Implementation of invasive disease control strategies such as culling may cause species to disperse beyond their natural range, thus aiding the spread of infection to otherwise infection free areas. Both linear and non-linear dispersal functions are compared with constant per capita dispersal in a coupled two patch SI model. For highly virulent or infrequently transmitted pathogens, it is found that an increase of dispersal due to control requires a higher level of disease control than in the constant dispersal model. Patches which may be sources or reservoirs of infection are investigated and it is found that if dispersal increases in response to control, then all patches, reservoir or not, must be targeted. The single host two patch model is then extended to a two host wildlife/livestock system with one species ‘wildlife' free to move between patches and the other ‘livestock' confined. In the two host case, control of one species alone will only achieve successful pathogen exclusion if that species is a reservoir for infection.

Argulus foliaceus is a macroparasite which can have a significant impact on yield in recreational trout fisheries, partly by increasing fish mortalities but also by reducing the appetite of infected fish, making them less likely to respond to bait. The aim of this paper is to determine the impact of four commonly used fish stocking methods both on the parasite dynamics, and on fisheries' yields. The wider consequences of the resultant reduction in host feeding are also of interest. To this end four different stocking methods were incorporated into Anderson and May's macroparasite model, which comprises three differential equations representing the host, attached parasite and free-living parasite populations. To each of these a reduction in the fish capture rate, inversely linked to the mean parasite burden, is added and the effects interpreted. Results show that (1) the common practise of increasing the stocking rate as catches drop may be counterproductive; (2) in the absence of any wild population of reservoir hosts, the parasite will be unable to survive if the stocking rate does not exceed the rate of capture; (3) compensatory stocking to account for fish mortalities can have disastrous consequences on yield; and (4) the parasite can, under certain circumstances, maintain the host population by preventing their capture.

Knowing how to control a pathogen that infects more than one host species is of increasing importance because the incidence of such infections grows with continuing environmental change. Of concern are infections transmitted from wildlife to humans or livestock. To determine which options are available to control a pathogen in these circumstances, we analyze the pathogen invasion matrix for the multihost susceptible-infected-susceptible model. We highlight the importance of both community structure and the column sum or row sum index, an indicator of both force of infection and community stability. We derive a set of guidelines for constructing culling strategies and suggest a hybrid strategy that has the advantages of both the bottom-up and the top-down approaches, which we study in some detail. The analysis holds for an arbitrary number of host species, enabling the analysis of large-scale ecological systems and systems with spatial dimensions. We test the robustness of our methods by making two changes in the structure of the underlying dynamic model, adding direct competition and introducing frequency-dependent infection transmission. In particular, we show that the introduction of an additional host can eliminate the pathogen rather than eliminate the resident host. The discussion is illustrated with a reference to bovine tuberculosis.

Traditionally, to determine the possible evolutionary behaviour of an ecological system using adaptive dynamics, it is necessary to calculate the fitness and its derivatives at a singular point. We investigate the claim that the possible evolutionary behaviour can be predicted directly from the population dynamics, without the need for calculation, by applying three criteria - one based on the form of the density dependent rates and two on the role played by the evolving parameters. Taking a general continuous time model, with broad ecological range, we show that the claim is true. Initially, we assume that individuals enter in class 1 and move through population classes sequentially; later we relax these assumptions and find that the criteria still apply. However, when we consider models where the evolving parameters appear non-linearly in the dynamics, we find some aspects of the criteria fail; useful but weaker results on possible evolutionary behaviour now apply.

Trade-off shapes are crucial to evolutionary outcomes. However, due to different ecological feedbacks their implications may depend not only on the trade-off being considered but also the ecological scenario. Here, we apply a novel geometric technique, trade-off and invasion plots (TIPs), to examine in detail how the shape of trade-off relationships affect evolutionary outcomes under a range of classic ecological scenarios including Lotka-Volterra type and host-parasite interactions. We choose models of increasing complexity in order to gain an insight into the features of ecological systems that determine the evolutionary outcomes. In particular we focus on when evolutionary attractors, repellors and branching points occur and how this depends on whether the costs are accelerating (benefits become 'increasingly' costly), decelerating (benefits become 'decreasingly' costly) or constant. In all cases strongly accelerating costs lead to attractors while strongly decelerating ones lead to repellors, but with weaker relationships, this no longer holds. For some systems weakly accelerating costs may lead to repellors and decelerating costs may lead to attractors. In many scenarios it is weakly decelerating costs that lead to branching points, but weakly accelerating and linear costs may also lead to disruptive selection in particular ecological scenarios. Using our models we suggest a classification of ecological interactions, based on three distinct criteria, that can produce one of four fundamental TIPs which allow for different evolutionary behaviour. This provides a baseline theory which may inform the prediction of evolutionary outcomes in similar yet unexplored ecological scenarios. In addition we discuss the implications of our results to a number of specific life-history trade-offs in the classic ecological scenarios represented by our models.

In this study we use the theory of adaptive dynamics firstly to explore the differences in evolutionary behaviour of a generalist predator (or more specifically an omnivorous or intraguild predator) in a predator-prey model, with a Holling Type II functional response, when two distinct forms for the carrying capacity are used. The first of these involves the carrying capacity as an emergent property, whilst in the second it appears explicitly in the dynamics. The resultant effect this has on the intraspecific competition in each case is compared. Taking an identical trade-off in each case, we find that only with an emergent carrying capacity is evolutionary branching possible. Our study then concentrates solely on the case where the carrying capacity appears explicitly. Using the same model as above, but choosing alternate trade-offs, we find branching can occur with an explicit carrying capacity. Our investigation finishes by taking a more general functional response in an attempt to derive a condition for when branching can or cannot occur. For a predator-prey model, branching cannot occur if the functional response can be separated into two components, one a function of the population densities, X and Z, and the other a function of the evolving parameter z (traded off against the intrinsic growth rate), i.e. if F(z,X,Z) = F(1)(z)F(2)(X,Z). This search for evolutionary branching is motivated by its possible role in speciation.

The purpose of this paper is to take an entirely geometrical path to determine the evolutionary properties of ecological systems subject to trade-offs. In particular we classify evolutionary singularities in a geometrical fashion. To achieve this, we study trade-off and invasion plots (TIPs) which show graphically the outcome of evolution from the relationship between three curves. The first invasion boundary (curve) has one strain as resident and the other strain as putative invader and the second has the roles of the strains reversed. The parameter values for one strain are used as the origin with those of the second strain varying. The third curve represents the trade-off. All three curves pass through the origin or tip of the TIP. We show that at this point the invasion boundaries are tangential. At a singular TIP, in which the origin is an evolutionary singularity, the invasion boundaries and trade-off curve are all tangential. The curvature of the trade-off curve determines the region in which it enters the singular TIP. Each of these regions has particular evolutionary properties (EUS, CS, SPR and MI). Thus we determine by direct geometric argument conditions for each of these properties in terms of the relative curvatures of the trade-off curve and invasion boundaries. We show that these conditions are equivalent to the standard partial derivative conditions of adaptive dynamics. The significance of our results is that we can determine whether the singular strategy is an attractor, branching point, repellor, etc. simply by observing in which region the trade-off curve enters the singular TIP. In particular we find that, if and only if the TIP has a region of mutual invadability, is it possible for the singular strategy to be a branching point. We illustrate the theory with an example and point the way forward.

In his final article Andrew Hoyle touches on some of the more subtle and complex issues that surround the concept of patient safety and how these can affect the future of our professional lives

In the second of three articles, Andrew Hoyle looks at the concepts underlying risk analysis

For general practitioners, prescribing drugs such as lithium or Ritalin can cause all sorts of problems for them and their patients. Andrew Hoyle reflects on the risks of being a courageous GP prescriber

A vast theoretical literature has explored the evolutionary dynamics of parasite virulence. The classic result from this modelling work is that, assuming a saturating transmission–virulence trade-off, there is a single evolutionary optimum where the parasite optimizes the epidemiological R 0 . However, there are an increasing number of models that have shown how ecological and epidemiological feedbacks to evolution can instead result in the creation and maintenance of multiple parasite strains. Here, we fully explore one such example, where recovered hosts have a limited ‘immune range’ resulting in partial cross-immunity to parasite strains that they have not previously encountered. Taking an adaptive dynamics approach, we show that, provided this immune range is not too wide, high levels of diversity can evolve and be maintained through multiple branching events. We argue that our model provides a more realistic picture of disease dynamics in vertebrate host populations and may be a key explanatory factor in the high levels of parasite diversity seen in natural systems.