A pocket guide to host-parasite models

Incorporating Intracellular Processes in Virus Dynamics Models

In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus-host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.

An explicit immunogenetic model of gastrointestinal nematode infection in sheep

Gastrointestinal nematodes are a global cause of disease and death in humans, wildlife and livestock. Livestock infection has historically been controlled with anthelmintic drugs, but the development of resistance means that alternative controls are needed. The most promising alternatives are vaccination, nutritional supplementation and selective breeding, all of which act by enhancing the immune response. Currently, control planning is hampered by reliance on the faecal egg count (FEC), which suffers from low accuracy and a nonlinear and indirect relationship with infection intensity and host immune responses. We address this gap by using extensive parasitological, immunological and genetic data on the sheep–Teladorsagia circumcincta interaction to create an immunologically explicit model of infection dynamics in a sheep flock that links host genetic variation with variation in the two key immune responses to predict the observed parasitological measures. Using our model, we show that the immune responses are highly heritable and by comparing selective breeding based on low FECs versus high plasma IgA responses, we show that the immune markers are a much improved measure of host resistance. In summary, we have created a model of host–parasite infections that explicitly captures the development of the adaptive immune response and show that by integrating genetic, immunological and parasitological understanding we can identify new immune-based markers for diagnosis and control.

Assessing host extinction risk following exposure to Batrachochytrium dendrobatidis

Wildlife diseases are increasingly recognized as a major threat to biodiversity. Chytridiomycosis is an emerging infectious disease of amphibians caused by the fungus Batrachochytrium dendrobatidis (Bd). Using a mathematical model and simulations, we study its effects on a generic riparian host population with a tadpole and adult life stage. An analytical expression for the basic reproduction quotient, Qo, of the pathogen is derived. By sampling the entire relevant parameter space, we perform a statistical assessment of the importance of all considered parameters in determining the risk of host extinction, upon exposure to Bd. We find that Qo not only gives a condition for the initial invasion of the fungus, but is in fact the best predictor for host extinction. We also show that the role of tadpoles, which in some species tolerate infections, is ambivalent. While tolerant tadpoles may provide a reservoir for the fungus, thus facilitating its persistence or even amplifying its outbreaks, they can also act as a rescue buffer for a stressed host population. Our results have important implications for amphibian conservation efforts.

Exploiting parallels between livestock and wildlife: Predicting the impact of climate change on gastrointestinal nematodes in ruminants

Global change, including climate, policy, land use and other associated environmental changes, is likely to have a major impact on parasitic disease in wildlife, altering the spatio-temporal patterns of transmission, with wide-ranging implications for wildlife, domestic animals, humans and ecosystem health. Predicting the potential impact of climate change on parasites infecting wildlife will become increasingly important in the management of species of conservation concern and control of disease at the wildlife-livestock and wildlife-human interface, but is confounded by incomplete knowledge of host-parasite interactions, logistical difficulties, small sample sizes and limited opportunities to manipulate the system. By exploiting parallels between livestock and wildlife, existing theoretical frameworks and research on livestock and their gastrointestinal nematodes can be adapted to wildlife systems. Similarities in the gastrointestinal nematodes and the life-histories of wild and domestic ruminants, coupled with a detailed knowledge of the ecology and life-cycle of the parasites, render the ruminant-GIN host-parasite system particularly amenable to a cross-disciplinary approach.

A mechanistic model of developing immunity to Teladorsagia circumcincta infection in lambs

Acquired immunity influences the severity of parasitic disease, but modelling the effects of acquired immunity in helminth infections has proved challenging. This may be due to a lack of suitable immunological data, or to the perceived complexity of modelling the immune response. We have developed a model of T. circumcincta infection in domestic sheep that incorporates the effects of acquired immunity on parasite establishment and fecundity. A large data set from commercially managed populations of Scottish Blackface sheep was used, which included relationships between IgA activity and worm length, and between worm length and fecundity. Use was also made of a recently published meta-analysis of parasite establishment rates. This realistic but simple model of nematode infection emulates observed patterns of faecal egg counts. The end-of-season faecal egg counts are remarkably robust to perturbations in the majority of the parameters, possibly because of priming of the immune system early in the season, reducing parasite establishment and growth and, therefore, faecal egg counts. Lowering the amount of early infection leads to higher end-of-season egg counts. The periparturient rise in egg counts in ewes appears to have an important role in supplying infection for the priming of the immune response. This feedback in the immune priming suggests that nematode infections may be difficult to eliminate.

Seasonality, cohort-dependence and the development of immunity in a natural host-nematode system

Acquired immunity is known to be a key modulator of the dynamics of many helminth parasites in domestic and human host populations, but its relative importance in natural populations is more controversial. A detailed long-term dataset on the gastrointestinal nematode Trichostrongylus retortaeformis in a wild population of European rabbits (Oryctolagus cuniculus) shows clear evidence of seasonal acquired immunity in the age-structured infection profiles. By fitting a hierarchy of demographic infection-immunity models to the observed age-structured infection patterns, we are able to quantify the importance of different components (seasonality, immunity and host age structure) of the parasite dynamics. We find strong evidence that the hosts' immunocompetence waxes and wanes with the seasons, but also contains a lifelong cohort factor, possibly acting through a maternal effect dependent on the host's month of birth. These observations have important and broad implications for the ecology of parasite infection in seasonal natural herbivore systems.

The dynamic influence of genetic variation on the susceptibility of sheep to gastrointestinal nematode infection

The interaction between sheep and the nematode Teladorsagia circumcincta is one of the best understood of all host-parasite interactions. Following infection, there is considerable variation among lambs in the number of nematode eggs produced, the number of early fourth-stage larvae and the number of adult worms in the mucosa. These traits have a high variance to mean ratio (i.e. they are overdispersed or aggregated among hosts), they are skewed and approximately negative binomially distributed. The sources of overdispersion are differences among lambs in the ingestion of infective larvae and the immune response. Both forces can produce aggregation but their relative importance is unknown. The key components of variation can be identified by variance analysis. The sum of the average effects of polymorphic genes is known as additive genetic variation and this increases essentially from zero at one month of age to quite high values at six months of age. The major mechanism underlying genetic variation appears to be the differences among individuals in immune responses. Two of the major sources of variation in immune responses are differences in antigen recognition and differences in the type of cytokines produced. Genes that influence both these sources of variation are associated with differences in resistance to nematode infection. Therefore, much of the heterogeneity among animals in parasite transmission appears to be due to genetic variation in immune responsiveness.

Modelling parasitism and predation of mosquitoes by water mites

Parasitism and predation are two ecological interactions that can occur simultaneously between two species. This is the case of Culicidae (Insecta: Diptera) and water mites (Acari: Hydrachnidia). The larva mites are~parasites of aquatic and semiaquatic insects, and deutonymphs and adults are predators of insect larvae and eggs. Since several families of water mites are associated with mosquitoes there is an interest in the potential use of these mites as biological control agents. The aim of this paper is to use mathematical modelling and analysis to assess the impact of predation and parasitism in the mosquito population. We propose a system of ordinary differential equations to model the interactions among the larval and adult stages of mosquitoes and water mites. The model exhibits three equilibria: the first equilibrium point corresponds to the state where the two species are absent, the second one to the state where only mosquitoes are present (water mites need insects to complete their life cycle), and the third one is the coexistence equilibrium. We analyze conditions for the asymptotic stability of equilibria, supported by analytical and numerical methods. We discuss the different scenarios that appear when we change the parasitism and predation parameters. High rates of parasitism and moderate predation can drive two species to a stable coexistence.

Density dependence and overdispersion in the transmission of helminth parasites

The influence of density-dependent processes on the transmission of parasitic helminths is determined by both the severity of the regulatory constraints and the degree of parasite overdispersion among the host population. We investigate how overdispersed parasite distributions among humans influence transmission levels in both directly- and indirectly-transmitted nematodes (Ascaris lumbricoides and Onchocerca volvulus). While past work has assumed, for simplicity, that density dependence acts on the average worm load, here we model density-dependence as acting on individual parasite burdens before averaging across hosts. A composite parameter, which we call the effective transmission contribution, is devised to measure the number of transmission stages contributed by a given worm burden after incorporating over-dispersion in adult worm mating probabilities and other density-dependent mechanisms. Results indicate that the more overdispersed the parasite population, the greater the effect of density dependence upon its transmission dynamics. Strong regulation and parasite overdispersion make the relationship between mean worm burden and its effective contribution to transmission highly non-linear. Consequently, lowering the intensity of infection in a host population using chemotherapy may produce only a small decline in transmission (relative to its initial endemic level). Our analysis indicates that when parasite burden is low, intermediate levels of parasite clustering maximize transmission. Implications are discussed in relation to existing control programmes and the spread of anthelmintic resistance.

A Mathematical Model of the Population Dynamics of Heterakis Gallinarum in Turkeys (Meleagridis Gallopavo)

Heterakis gallinarum is a relatively nonpathogenic organism, but it is important as the transport host for the pathogenic protozoan Histomonas meleagridis. A mathematical model was developed to describe the population dynamics of Heterakis gallinarum in a turkey flock to study its kinetics in a number of hosts. The model includes quantitative (parasite burden) and qualitative (number of hosts without mature parasite) descriptions of these dynamics. To understand the role of Heterakis as a transport host, the various elements that delay the beginning of development of the parasite population (e.g., necessary delay of larval stage, the probability of having a male and female in the same host) were taken into account. From published data, the negative binomial distribution parameter k = 0.24, which described the aggregated distribution of the Heterakis among the hosts, was calculated. The sensibility study showed that when the k parameter decreased (i.e., when the population was more aggregated), infestation increased quantitatively (mean parasite burden increased) but not qualitatively (the number of host without mature parasite increased). The model demonstrated that the population dynamics of Heterakis takes time; for instance, with an aggregated population of Heterakis at d 90, the host is mainly free of adult parasite. These results may be used in the future to test the role of Heterakis in the spread of Histomonas.

A study of the role of the transmission mechanism in macroparasite aggregation

The dynamics of host-macroparasite infections pose considerable challenges for stochastic modelling because of the need to take into account a large number of relevant factors and many nonlinear interactions between them. This paper focuses attention on the infection transmission process and the effects of specific modelling assumptions about the mechanisms involved. Some dramatically simplified linear models are considered; they are based on multidimensional linear birth and death processes, and are designed to illuminate qualitative effects of interest. Both single and compound infections are allowed. It is shown that such simple models can generate and increase dispersion of parasite counts, even among homogeneous hosts.

The interface between epidemiology and population genetics

Modern biology increasingly integrates disparate disciplines. Here, Steve Paterson and Mark Viney examine the interface between epidemiology and population genetics. They argue that infection and inheritance can be considered as analogous processes, and that epidemiology and population genetics share many common features. They consider the potential for existing population genetic theory to dissect epidemiological patterns in field studies and they consider other relationships between genetics and epidemiology that provide a research challenge for the future.

The immunoepidemiology of nematode parasites of farmed animals: a mathematical approach

The population dynamics of farmed animals are controlled by humans, and often involve high host densities, which encourage higher parasite burdens than would be usual in wild animals. As a result, the immunity to reinfection acquired by the host is an important determinant of parasite population dynamics. For example, lambs are highly susceptible to gastrointestinal nematodes as they begin to graze, but develop an immunity that accounts for the observed within-year variation in parasite load and pasture contamination. In the longer term, control measures are compromised by the development of parasite strains resistant to chemotherapy, focusing attention on the development of 'natural' measures, including the selection for resistant hosts and the development of antiparasite vaccines. Mick Roberts here considers the immunoepidemiology of parasites of farmed animals on three levels: the interaction between the parasite and the host's immune system determining the individual's level of protection; the development of acquired immunity determining the within-year parasite population dynamics; and the long-term effects of control measures on the between-year parasite population dynamics.

Use of a mathematical model to study the control measures of the cattle tick Boophilus microplus population in New Caledonia

Boophilus microplus is a common cattle tick of great economic importance in various tropical and subtropical countries like New Caledonia. The proposed model describes the population dynamics of female Boophilus microplus in the absence of resistant ticks. It is a system of six difference equations which can be mathematically analyzed. The analysis of the system shows the great importance of the eigenvalue denoted by lambda1. The population of ticks increases if lambda1 < 1 and decreases if lambda1 > 1. The lambda1 eigenvalue depends, in particular, on the parasitic surviving rate and encounter rate between the larvae and the cows. The treatments decrease the parasitic surviving rate as the agronomic measures decrease the encounter rate. This model permits to quantify the conditions of treatments (or of the efficacy of a vaccine) and of agronomic measures by which the populations are controlled. It shows that the different treatment rhythms and the presence or not of the wild or domestic refuges plays a major role on the dynamics of tick population.

Modelling the persistence of measles

For vaccination programs to be effective, it is important to understand and predict the persistence of the disease. By considering the process at different scales (from the individual to the population level), several models allow the persistence of diseases, such as measles, to be captured.