The field of disease ecology – the study of the spread and impact of parasites and pathogens within their host populations and communities – has a long history of using mathematical models. Dating back over 100 years, researchers have used mathematics to describe the spread of disease-causing agents, understand the relationship between host density and transmission and plan control strategies. The use of mathematical modelling in disease ecology exploded in the late 1970s and early 1980s through the work of Anderson and May (Anderson and May, 1978, 1981, 1992; May and Anderson, 1978), who developed the fundamental frameworks for studying microparasite (e.g. viruses, bacteria and protozoa) and macroparasite (e.g. helminth) dynamics, emphasizing the importance of understanding features such as the parasite's basic reproduction number (R0) and critical community size that form the basis of disease ecology research to this day. Since the initial models of disease population dynamics, which primarily focused on human diseases, theoretical disease research has expanded hugely to encompass livestock and wildlife disease systems, and also to explore evolutionary questions such as the evolution of parasite virulence or drug resistance. More recently there have been efforts to broaden the field still further, to move beyond the standard ‘one-host-one-parasite’ paradigm of the original models, to incorporate many aspects of complexity of natural systems, including multiple potential host species and interactions among multiple parasite species.

Modelling wildlife disease poses some unique challenges. Wildlife disease systems are data poor in comparison with human or livestock disease systems, and the impact of disease on population size is often the key question of interest. This review concentrates specifically on the application of dynamic models to evaluate and guide management strategies. Models have proved useful particularly in two areas. They have been widely used to evaluate vaccination strategies, both for protecting endangered species and for preventing spillover from wildlife to humans or livestock. They have also been extensively used to evaluate culling strategies, again both for diseases in species of conservation interest and to prevent spillover. In addition, models are important to evaluate the potential of parasites and pathogens as biological control agents. The review concludes by identifying some key research gaps, which are further development of models of macroparasites, deciding on appropriate levels of complexity, modelling genetic management and connecting models to data.

Epidemiological data are often fragmented, partial, and/or ambiguous and unable to yield the desired level of understanding of infectious disease dynamics to adequately inform control measures. Here, we show how the information contained in widely available serology data can be enhanced by integration with less common type-specific data, to improve the understanding of the transmission dynamics of complex multi-species pathogens and host communities. Using brucellosis in northern Tanzania as a case study, we developed a latent process model based on serology data obtained from the field, to reconstruct Brucella transmission dynamics. We were able to identify sheep and goats as a more likely source of human and animal infection than cattle; however, the highly cross-reactive nature of Brucella spp. meant that it was not possible to determine which Brucella species (B. abortus or B. melitensis) is responsible for human infection. We extended our model to integrate simulated serology and typing data, and show that although serology alone can identify the host source of human infection under certain restrictive conditions, the integration of even small amounts (5%) of typing data can improve understanding of complex epidemiological dynamics. We show that data integration will often be essential when more than one pathogen is present and when the distinction between exposed and infectious individuals is not clear from serology data. With increasing epidemiological complexity, serology data become less informative. However, we show how this weakness can be mitigated by integrating such data with typing data, thereby enhancing the inference from these data and improving understanding of the underlying dynamics.

The resurgence of pertussis in some countries that maintain high vaccination coverage has drawn attention to gaps in our understanding of the epidemiological effects of pertussis vaccines. In particular, major questions surround the nature, degree and durability of vaccine protection. To address these questions, we used mechanistic transmission models to examine regional time series incidence data from Italy in the period immediately following the introduction of acellular pertussis (aP) vaccine. Our results concur with recent animal-challenge experiments wherein infections in aP-vaccinated individuals proved as transmissible as those in naive individuals but much less symptomatic. On the other hand, the data provide evidence for vaccine-driven reduction in susceptibility, which we quantify via a synthetic measure of vaccine impact. As to the precise nature of vaccine failure, the data do not allow us to distinguish between leakiness and waning of vaccine immunity, or some combination of these. Across the range of well-supported models, the nature and duration of vaccine protection, the age profile of incidence and the range of projected epidemiological futures differ substantially, underscoring the importance of the remaining unknowns. We identify key data gaps: sources of data that can supply the information needed to eliminate these remaining uncertainties.

Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex life cycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their life cycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper, we review models of tick dynamics and summarize the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick-borne pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick-borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper, we identify gaps in the current knowledge and future modelling approaches. These include spatial models linked to environmental information and Geographic Information System maps, and development of new modelling techniques which model tick densities per host more explicitly.

With the recent global spread of a number of mosquito-borne viruses, there is an urgent need to understand the factors that contribute to the ability of viruses to expand into naïve populations. Using dengue and chikungunya viruses as case studies, we detail the necessary components of the expansion process: presence of the mosquito vector; introduction of the virus; and suitable conditions for local transmission. For each component we review the existing modelling approaches that have been used to understand recent emergence events or to assess the risk of future expansions. We identify gaps in our knowledge that are related to each of the distinct aspects of the human-mosquito transmission cycle: mosquito ecology; human–mosquito contact; mosquito–virus interactions; and human–virus interactions. Bridging these gaps poses challenges to both modellers and empiricists, but only through further integration of models and data will we improve our ability to better understand, and ultimately control, several infectious diseases that exert a significant burden on human health.

Although many parasites are transmitted between hosts by a suite of arthropod vectors, the impact of vector biodiversity on parasite transmission is poorly understood. Positive relationships between host infection prevalence and vector species richness (SR) may operate through multiple mechanisms, including (i) increased vector abundance, (ii) a sampling effect in which species of high vectorial capacity are more likely to occur in species-rich communities, and (iii) functional diversity whereby communities comprised species with distinct phenologies may extend the duration of seasonal transmission. Teasing such mechanisms apart is impeded by a lack of appropriate data, yet could highlight a neglected role for functional diversity in parasite transmission. We used statistical modelling of extensive host, vector and microparasite data to test the hypothesis that functional diversity leading to longer seasonal transmission explained variable levels of disease in a wildlife population. We additionally developed a simple transmission model to guide our expectation of how an increased transmission season translates to infection prevalence. Our study demonstrates that vector SR is associated with increased levels of disease reporting, but not via increases in vector abundance or via a sampling effect. Rather, the relationship operates by extending the length of seasonal transmission, in line with theoretical predictions.

In this paper we derive from first principles the expected body sizes of the parasite communities that can coexist in a mammal of given body size. We use a mixture of mathematical models and known allometric relationships to examine whether host and parasite life histories constrain the diversity of parasite species that can coexist in the population of any host species. The model consists of one differential equation for each parasite species and a single density-dependent nonlinear equation for the affected host under the assumption of exploitation competition. We derive threshold conditions for the coexistence and competitive exclusion of parasite species using invasion criteria and stability analysis of the resulting equilibria. These results are then used to evaluate the range of parasites species that can invade and establish in a target host and identify the ‘optimal’ size of a parasite species for a host of a given body size; ‘optimal’ is defined as the body size of a parasite species that cannot be outcompeted by any other parasite species. The expected distributions of parasites body sizes in hosts of different sizes are then compared with those observed in empirical studies. Our analysis predicts the relative abundance of parasites of different size that establish in the host and suggests that increasing the ratio of parasite body size to host body size above a minimum threshold increases the persistence of the parasite population.

Gastrointestinal nematodes represent important sources of economic losses in farmed ruminants, and the increasing frequency of anthelmintic resistance requires an increased ability to explore alternative strategies. Theoretical approaches at the crossroads of immunology and epidemiology are valuable tools in that context. In the case of Teladorsagia circumcincta in sheep, the immunological mechanisms important for resistance are increasingly well-characterized. However, despite the existence of a wide range of theoretical models, there is no framework integrating the characteristic features of this immune response into a tractable phenomenological model. Here, we propose to bridge that gap by developing a flexible modelling framework that allows for variability in nematode larval intake which can be used to track the variations in worm burdens. We parameterize this model using data from trickle infection of sheep and show that using simple immunological assumptions, our model can capture the dynamics of both adult worm burdens and nematode fecal egg counts. In addition, our analysis reveals interesting dose-dependent effects on the immune response. Finally, we discuss potential developments of this model and highlight how an improved cross-talk between empiricists and theoreticians would facilitate important advances in the study of infectious diseases.

Mathematical modelling provides an effective way to challenge conventional wisdom about parasite evolution and investigate why parasites ‘do what they do’ within the host. Models can reveal when intuition cannot explain observed patterns, when more complicated biology must be considered, and when experimental and statistical methods are likely to mislead. We describe how models of within-host infection dynamics can refine experimental design, and focus on the case study of malaria to highlight how integration between models and data can guide understanding of parasite fitness in three areas: (1) the adaptive significance of chronic infections; (2) the potential for tradeoffs between virulence and transmission; and (3) the implications of within-vector dynamics. We emphasize that models are often useful when they highlight unexpected patterns in parasite evolution, revealing instead why intuition yields the wrong answer and what combination of theory and data are needed to advance understanding.

Why is it that some parasites cause high levels of host damage (i.e. virulence) whereas others are relatively benign? There are now numerous reviews of virulence evolution in the literature but it is nevertheless still difficult to find a comprehensive treatment of the theory and data on the subject that is easily accessible to non-specialists. Here we attempt to do so by distilling the vast theoretical literature on the topic into a set of relatively few robust predictions. We then provide a comprehensive assessment of the available empirical literature that tests these predictions. Our results show that there have been some notable successes in integrating theory and data but also that theory and empiricism in this field do not ‘speak’ to each other very well. We offer a few suggestions for how the connection between the two might be improved.