Fatal disease and demographic Allee effect: population persistence and extinction

If a healthy stable host population at the disease-free equilibrium is subject to the Allee effect, can a small number of infected individuals with a fatal disease cause the host population to go extinct? That is, does the Allee effect matter at high densities? To answer this question, we use a susceptible-infected epidemic model to obtain model parameters that lead to host population persistence (with or without infected individuals) and to host extinction. We prove that the presence of an Allee effect in host demographics matters even at large population densities. We show that a small perturbation to the disease-free equilibrium can eventually lead to host population extinction. In addition, we prove that additional deaths due to a fatal infectious disease effectively increase the Allee threshold of the host population demographics.     

Fatal disease and demographic Allee effect: population persistence and extinction

If a healthy stable host population at the disease-free equilibrium is subject to the Allee effect, can a small number of infected individuals with a fatal disease cause the host population to go extinct? That is, does the Allee effect matter at high densities? To answer this question, we use a susceptible–infected epidemic model to obtain model parameters that lead to host population persistence (with or without infected individuals) and to host extinction. We prove that the presence of an Allee effect in host demographics matters even at large population densities. We show that a small perturbation to the disease-free equilibrium can eventually lead to host population extinction. In addition, we prove that additional deaths due to a fatal infectious disease effectively increase the Allee threshold of the host population demographics.     

A diffusive SI model with Allee effect and application to FIV

A minimal reaction-diffusion model for the spatiotemporal spread of an infectious disease is considered. The model is motivated by the Feline Immunodeficiency Virus (FIV) which causes AIDS in cat populations. Because the infected period is long compared with the lifespan, the model incorporates the host population growth. Two different types are considered: logistic growth and growth with a strong Allee effect. In the model with logistic growth, the introduced disease propagates in form of a travelling infection wave with a constant asymptotic rate of spread. In the model with Allee effect the spatiotemporal dynamics are more complicated and the disease has considerable impact on the host population spread. Most importantly, there are waves of extinction, which arise when the disease is introduced in the wake of the invading host population. These waves of extinction destabilize locally stable endemic coexistence states. Moreover, spatially restricted epidemics are possible as well as travelling infection pulses that correspond either to fatal epidemics with succeeding host population extinction or to epidemics with recovery of the host population. Generally, the Allee effect induces minimum viable population sizes and critical spatial lengths of the initial distribution. The local stability analysis yields bistability and the phenomenon of transient epidemics within the regime of disease-induced extinction. Sustained oscillations do not exist.     

The importance of environmental spatial heterogeneity and host social structure in disease transmission

[First paragraph]The spatial structure of a host population determines the spatial probability distribution of interaction between individuals, and therefore influences the spatio-temporal dynamics of disease transmission within the host population (Keeling, 1999; Gudelj and White, 2004). Nigel Barlow recognised this and included non-linear transmission in his later models (Barlow, 1991), simulating the result of spatial heterogeneity of risk in susceptible hosts. These models produced behaviour that could not be found in models with homogeneously mixed host populations: more rapid disease dynamics and a greater robustness of disease to control measures. However, in this model there was no causal mechanism driving the initial spatial heterogeneity of risk in host individuals. Environmental heterogeneity is likely to be a key factor in determining the spatial distribution of host individuals (Cronin and Reeve, 2005). We attempted to explore how environmental heterogeneity may affect disease dynamics via its influence on the spatial distribution of host individuals. We developed a spatially explicit stochastic model that incorporated spatially variable host density distributions, primarily driven by environmental heterogeneity.     

How do toxicants affect epidemiological dynamics?

Populations are formed of their constituent interacting individuals, each with their own respective within‐host biological processes. Infection not only spreads within the host organism but also spreads between individuals. Here we propose and study a multilevel model which links the within‐host statuses of immunity and parasite density to population epidemiology under sublethal and lethal toxicant exposure. We analyse this nested model in order to better understand how toxicants impact the spread of disease within populations. We demonstrate that outbreak of infection within a population is completely determined by the level of toxicant exposure, and that it is maximised by intermediate toxicant dosage. We classify the population epidemiology into five phases of increasing toxicant exposure and calculate the conditions under which disease will spread, showing that there exists a threshold toxicant level under which epidemics will not occur. In general, higher toxicant load results in either extinction of the population or outbreak of infection. The within‐host statuses of the individual host also determine the outcome of the epidemic at the population level. We discuss applications of our model in the context of environmental epidemiology, predicting that increased exposure to toxicants could result in greater risk of epidemics within ecological systems. We predict that reducing sublethal toxicant exposure below our predicted safe threshold could contribute to controlling population level disease and infection.     

Harvesting can increase severity of wildlife disease epidemics

Theoretical studies of wildlife population dynamics have proved insightful for sustainable management, where the principal aim is to maximize short-term yield, without risking population extinction. Surprisingly, infectious diseases have not been accounted for in harvest models, which is a major oversight because the consequences of parasites for host population dynamics are well-established. Here, we present a simple general model for a host species subject to density dependent reproduction and seasonal demography. We assume this host species is subject to infection by a strongly immunizing, directly transmitted pathogen. In this context, we show that the interaction between density dependent effects and harvesting can substantially increase both disease prevalence and the absolute number of infectious individuals. This effect clearly increases the risk of cross-species disease transmission into domestic and livestock populations. In addition, if the disease is associated with a risk of mortality, then the synergistic interaction between hunting and disease-induced death can increase the probability of host population extinction.     

Parasite strain coexistence in a heterogeneous host population

Heterogeneity in host susceptibility and transmissibility to parasite attack allows a lower transmission rate to sustain an epidemic than is required in homogeneous host populations. However, this heterogeneity can leave some hosts with little susceptibility to disease, and at high transmission rates, epidemic size can be smaller than for diseases where the host population is homogeneous. In a heterogeneous host population, we model natural selection in a parasite population where host heterogeneity is exploited by different strains to varying degrees. This partitioning of the host population allows coexistence of competing parasite strains, with the heterogeneity-exploiting strains infecting the more susceptible hosts, in the absence of physiological tradeoffs and spatial heterogeneity, and even for markedly different transmission rates. In our model, intermediate-strategy parasites were selected against: should coexistence occur, an equilibrium is reached where strains occupied only the extreme ends of trait space, under appropriate conditions selecting for lower R₀.     

Social networks of disease spread in the lower Illinois valley: a simulation approach

This study illustrates the use of disease modeling and simulation techniques to the study of the spread of disease within and between social networks. A Reed-Frost type model of disease spread is used to construct a simulation of the spread of tuberculosis within three prehistoric populations of the Lower Illinois River Valley during Middle Woodland, Late Woodland, and Mississippian times. A high and low population size was modeled for each time period. Late Woodland model 2 (low population estimate) is the only model that experienced pathogen extinction with host survival. The rest of the models experienced rapid and severe host population decline. The results of the simulation suggest that a social network size of between 180 and 440 persons is required under the conditions of this model for host-pathogen coexistence (i.e., endemicity) to occur. The severe population decline experienced by these populations suggests that tuberculosis as modeled here could not have existed in these populations. Future refinements of modeling and simulation techniques can provide additional insights into how disease spreads among social contacts.     

Modelling transmission of vector-borne pathogens shows complex dynamics when vector feeding sites are limited

The relationship between species richness and the prevalence of vector-borne disease has been widely studied with a range of outcomes. Increasing the number of host species for a pathogen may decrease infection prevalence (dilution effect), increase it (amplification), or have no effect. We derive a general model, and a specific implementation, which show that when the number of vector feeding sites on each host is limiting, the effects on pathogen dynamics of host population size are more complex than previously thought. The model examines vector-borne disease in the presence of different host species that are either competent or incompetent (i.e. that cannot transmit the pathogen to vectors) as reservoirs for the pathogen. With a single host species present, the basic reproduction ratio R(0) is a non-monotonic function of the population size of host individuals (H), i.e. a value [Formula: see text] exists that maximises R(0). Surprisingly, if [Formula: see text] a reduction in host population size may actually increase R(0). Extending this model to a two-host species system, incompetent individuals from the second host species can alter the value of [Formula: see text] which may reverse the effect on pathogen prevalence of host population reduction. We argue that when vector-feeding sites on hosts are limiting, the net effect of increasing host diversity might not be correctly predicted using simple frequency-dependent epidemiological models.     

Models of epidemics and endemicity in genetically variable host populations

A discrete time genetics model is developed for populations that are undergoing selection due to infectious disease. It is assumed that the generation time of the host and infectious agent are non-synchronous and that only the host population is evolving. Two classes of epidemic processes are considered. The first class is for infectious agents that confer immunity following infection, while the second class is for those that do not confer immunity. The necessary and sufficient conditions are found in order for the disease to persist in a stable polymorphic host population. These conditions are shown to depend on the density of susceptibles, the selection coefficients, and the severity and class of the disease process.     

Impact of life stage specific immune priming on invertebrate disease dynamics

The immune response of a host can have important impacts on host‐pathogen interactions, but investment in immunity often changes dynamically across the life history of a host. One form of investment involves the induction of a primed immune response against previously encountered pathogens that protects the host from re‐infection. In addition to providing immediate protective effects, immune priming can also provide two types of ‘delayed’ protection against pathogens: priming across life stages (ontogenic priming) and priming across generations (trans‐generational priming). Consequently both types of immune priming have the potential to mediate life history variability in host–pathogen interactions, which could have important consequences for disease prevalence and dynamics as well as for the demographic structure of the host population. Here we develop a stage‐structured SIRS model for an invertebrate host to explore the relative and combined impact of ontogenic priming and trans‐generational priming on infection prevalence, host population size, and population age structure. Our model predicts that both types of immune priming can dramatically reduce disease prevalence at equilibrium, but their individual and combined effects on population size and age structure depend on the magnitude of tradeoffs between immune protection and reproduction as well as on the symmetry of infection parameters between life stages. This model underscores the potential importance of life‐history based immune investment patterns for disease dynamics and highlights the need for wide‐spread empirical estimation of parameters that represent the maintenance of immune priming in insects.     

Disease propagation in connected host populations with density-dependent dynamics: the case of the Feline Leukemia Virus

Spatial heterogeneity is a strong determinant of host-parasite relationships, however local-scale mechanisms are often not elucidated. Generally speaking, in many circumstances dispersal is expected to increase disease persistence. We consider the case when host populations show density-dependent dynamics and are connected through the dispersal of individuals. Taking the domestic cats (Felis catus)--Feline Leukemia Virus (FeLV) as a toy model of host-microparasite system, we predict the disease dynamics when two host populations with distinct or similar structures are connected together and to the surrounding environment by dispersal. Our model brings qualitatively different predictions from one-population models. First, as expected, biologically realistic rates of dispersal may allow FeLV to persist in sets of populations where the virus would have gone extinct otherwise, but a reverse outcome is also possible: eradication of FeLV from a small population by connexion to a larger population where it is not persistent. Second, overall prevalence as well as depression of host population size due to infection are both enhanced by dispersal, even at low dispersal rates when disease persistence is not achieved in the two populations. This unexpected prediction is probably due to the combination of dispersal with density-dependent population dynamics. Third, the dispersal of non-infectious cats has more influence on virus prevalence than the dispersal of infectious. Finally, prevalence and depression of host population size are both related to the rate of dispersion, to the health status of individuals dispersing and to the dynamics of host populations.     

Body-size scaling in an SEI model of wildlife diseases

A number of wildlife pathogens are generalist and can affect different host species characterized by a wide range of body sizes. In this work we analyze the role of allometric scaling of host vital and epidemiological rates in a Susceptible-Exposed-Infected (SEI) model. Our analysis shows that the transmission coefficient threshold for the disease to establish in the population scales allometrically (exponent = 0.45) with host size as well as the threshold at which limit cycles occur. In contrast, the threshold of the basic reproduction number for sustained oscillations to occur is independent of the host size and is always greater than 5. In the case of rabies, we show that the oscillation periods predicted by the model match those observed in the field for a wide range of host sizes.The population dynamics of the SEI model is also analyzed in the case of pathogens affecting multiple coexisting hosts with different body sizes. Our analyses show that the basic reproduction number for limit cycles to occur depends on the ratio between host sizes, that the oscillation period in a multihost community is set by the smaller species dynamics, and that intermediate interspecific disease transmission can stabilize the epidemic occurrence in wildlife communities.     

Pathogen invasion and host extinction in lattice structured populations

We examined the propagation of an infectious disease and the eventual extinction of the host population in a lattice-structured population. Both the host colonization and pathogen transmission processes are assumed to be restricted to act between the nearest neighbor sites. The model is analyzed by an improved version of pair approximation (IPA). Pair approximation is a technique to trace the dynamics of the number of nearest neighbor pairs having particular states, and IPA takes account of the clustering property of lattice models more precisely. The results are checked by computer simulations. The analysis shows: (i) in a one-dimensional lattice population, a pathogen cannot invade a host population no matter how large is the transmission rate; (ii) in a two-dimensional lattice population, pathogens will drive the host to extinction if the transmission rate is larger than a threshold. These results indicate that spatially structured population models may give qualitatively different results from conventional population models, such as Lotka-Volterra ones, without spatial structure.     

Modelling the transmission dynamics of Theileria annulata: model structure and validation for the Turkish context

A mathematical model that describes the transmission dynamics of Theileria annulata is proposed that consists of 2 host components: the Hyalomma tick population and a compartmental model of T. annulata infection in the cattle population. The model was parameterized using data describing tick infestation and the infection status of cattle in Turkey from 2006 to 2008. The tick attachment rates are highly seasonal and because of the temporal separation of infectious and susceptible ticks virtually all ticks are infected by carrier cattle, so that annual peaks of disease in cattle do not impact on infection in the Hyalomma tick population. The impact of intervention measures that target the tick population both on the host and in the environment and their impact on the transmission of T. annulata were investigated. Interventions that have a limited 'one-off' impact and interventions that have a more permanent impact were both considered. The results from the model show the importance of targeting ticks during the period when they have left their first host as nymphs but have yet to feed on their second host.     

Endemic disease in host populations with fully specified demography

This study explores the epidemiology of an aerogenically transmitted infectious disease following an S.I.R. pattern in a host population with completely specified age-specified maternity and mortality schedules. A fully age-structured demographic-epidemiologic model is developed, and its demographic and epidemiologic behaviour is explored in numerical studies. The impact of variations in host population demographic structure upon the effect of immunization programs is also studied.     

Individual and Population-Level Impacts of an Emerging Poxvirus Disease in a Wild Population of Great Tits

Emerging infectious diseases of wildlife can have severe effects on host populations and constitute a pressing problem for biodiversity conservation. Paridae pox is an unusually severe form of avipoxvirus infection that has recently been identified as an emerging infectious disease particularly affecting an abundant songbird, the great tit (Parus major), in Great Britain. In this study, we study the invasion and establishment of Paridae pox in a long-term monitored population of wild great tits to (i) quantify the impact of this novel pathogen on host fitness and (ii) determine the potential threat it poses to population persistence. We show that Paridae pox significantly reduces the reproductive output of great tits by reducing the ability of parents to fledge young successfully and rear those young to independence. Our results also suggested that pathogen transmission from diseased parents to their offspring was possible, and that disease entails severe mortality costs for affected chicks. Application of multistate mark-recapture modelling showed that Paridae pox causes significant reductions to host survival, with particularly large effects observed for juvenile survival. Using an age-structured population model, we demonstrate that Paridae pox has the potential to reduce population growth rate, primarily through negative impacts on host survival rates. However, at currently observed prevalence, significant disease-induced population decline seems unlikely, although pox prevalence may be underestimated if capture probability of diseased individuals is low. Despite this, because pox-affected model populations exhibited lower average growth rates, this emerging infectious disease has the potential to reduce the resilience of populations to other environmental factors that reduce population size.     

Demographic Processes Drive Increases in Wildlife Disease following Population Reduction

Population reduction is often used as a control strategy when managing infectious diseases in wildlife populations in order to reduce host density below a critical threshold. However, population reduction can disrupt existing social and demographic structures leading to changes in observed host behaviour that may result in enhanced disease transmission. Such effects have been observed in several disease systems, notably badgers and bovine tuberculosis. Here we characterise the fundamental properties of disease systems for which such effects undermine the disease control benefits of population reduction.By quantifying the size of response to population reduction in terms of enhanced transmission within a generic non-spatial model, the properties of disease systems in which such effects reduce or even reverse the disease control benefits of population reduction are identified. If population reduction is not sufficiently severe, then enhanced transmission can lead to the counter intuitive perturbation effect, whereby disease levels increase or persist where they would otherwise die out. Perturbation effects are largest for systems with low levels of disease, e.g. low levels of endemicity or emerging disease.Analysis of a stochastic spatial meta-population model of demography and disease dynamics leads to qualitatively similar conclusions. Moreover, enhanced transmission itself is found to arise as an emergent property of density dependent dispersal in such systems. This spatial analysis also shows that, below some threshold, population reduction can rapidly increase the area affected by disease, potentially expanding risks to sympatric species.Our results suggest that the impact of population reduction on social and demographic structures is likely to undermine disease control in many systems, and in severe cases leads to the perturbation effect. Social and demographic mechanisms that enhance transmission following population reduction should therefore be routinely considered when designing control programmes.     

Host genetics and population structure effects on parasitic disease

Host genetic factors exert significant influences on differential susceptibility to many infectious diseases. In addition, population structure of both host and parasite may influence disease distribution patterns. In this study, we assess the effects of population structure on infectious disease in two populations in which host genetic factors influencing susceptibility to parasitic disease have been extensively studied. The first population is the Jirel population of eastern Nepal that has been the subject of research on the determinants of differential susceptibility to soil-transmitted helminth infections. The second group is a Brazilian population residing in an area endemic for Trypanosoma cruzi infection that has been assessed for genetic influences on differential disease progression in Chagas disease. For measures of Ascaris worm burden, within-population host genetic effects are generally more important than host population structure factors in determining patterns of infectious disease. No significant influences of population structure on measures associated with progression of cardiac disease in individuals who were seropositive for T. cruzi infection were found.     

Competitive exclusion in a vector-host model for the dengue fever

 We study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each induces host immunity but only certain degree of cross-immunity to heterologous serotypes. Our model has been constructed to study both the epidemiological trends of the disease and conditions that permit coexistence in competing strains. Dengue is in the Americas an epidemic disease and our model reproduces this kind of dynamics. We consider two viral strains and temporary cross-immunity. Our analysis shows the existence of an unstable endemic state (‘saddle’ point) that produces a long transient behavior where both dengue serotypes cocirculate. Conditions for asymptotic stability of equilibria are discussed supported by numerical simulations. We argue that the existence of competitive exclusion in this system is product of the interplay between the host superinfection process and frequency-dependent (vector to host) contact rates. Received 4 December 1995; received in revised form 5 March 1996