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.     

Dynamics of a feline virus with two transmission modes within exponentially growing host populations.

Feline panleucopenia virus (FPLV) was introduced in 1977 on Marion Island (in the southern Indian Ocean) with the aim of eradicating the cat population and provoked a huge decrease in the host population within six years. The virus can be transmitted either directly through contacts between infected and healthy cats or indirectly between a healthy cat and the contaminated environment: a specific feature of the virus is its high rate of survival outside the host. In this paper, a model was designed in order to take these two modes of transmission into account. The results showed that a mass-action incidence assumption was more appropriate than a proportionate mixing one in describing the dynamics of direct transmission. Under certain conditions the virus was able to control the host population at a low density. The indirect transmission acted as a reservoir supplying the host population with a low but sufficient density of infected individuals which allowed the virus to persist. The dynamics of the infection were more affected by the demographic parameters of the healthy hosts than by the epidemiological ones. Thus, demographic parameters should be precisely measured in field studies in order to obtain accurate predictions. The predicted results of our model were in good agreement with observations.     

Spatiotemporal Model of Barley and Cereal Yellow Dwarf Virus Transmission Dynamics with Seasonality and Plant Competition

Many generalist pathogens are influenced by the spatial distributions and relative abundances of susceptible host species. The spatial structure of host populations can influence patterns of infection incidence (or disease outbreaks), and the effects of a generalist pathogen on host community dynamics in a spatially heterogeneous community may differ from predictions derived via simple models. In this paper, we model the transmission of a generalist pathogen within a patch framework that incorporates the movement of vectors between discrete host patches to investigate the effects of local host community composition and vector movement rates on disease dynamics.     

Modelling Disease Introduction as Biological Control of Invasive Predators to Preserve Endangered Prey

Invasive species are a significant cause of bio-diversity loss particularly in island ecosystems. It has been suggested to release pathogenic parasites as an efficient control measure of these mostly immune-naïve populations. In order to explore the potential impacts of such bio-control approach, we construct and investigate mathematical models describing disease dynamics in a host population that acts as a predator embedded in a simple food chain. The consequences of Feline Immunodeficiency Virus (FIV) introduction into a closed ecosystem are addressed using a bi-trophic system, comprising an indigenous prey (birds) and an introduced predator (cats). Our results show that FIV is unlikely to fully eradicate cats on sub-Antarctic islands, but it can be efficient in depressing their population size, allowing for the recovery of the endangered prey. Depending on the ecological setting and disease transmission mode (we consider proportionate mixing as well as mass action), successful pathogen invasion can induce population oscillations that are not possible in the disease-free predator–prey system. These fluctuations can be seen as a mixed blessing from a management point of view. On the one hand, they may increase the extinction risk of the birds. On the other hand, they provide an opportunity to eradicate cats more easily in combination with other methods such as trapping or culling.     

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.     

Measles on the edge: coastal heterogeneities and infection dynamics

Mathematical models can help elucidate the spatio-temporal dynamics of epidemics as well as the impact of control measures. The gravity model for directly transmitted diseases is currently one of the most parsimonious models for spatial epidemic spread. This model uses distance-weighted, population size-dependent coupling to estimate host movement and disease incidence in metapopulations. The model captures overall measles dynamics in terms of underlying human movement in pre-vaccination England and Wales (previously established). In spatial models, edges often present a special challenge. Therefore, to test the model's robustness, we analyzed gravity model incidence predictions for coastal cities in England and Wales. Results show that, although predictions are accurate for inland towns, they significantly underestimate coastal persistence. We examine incidence, outbreak seasonality, and public transportation records, to show that the model's inaccuracies stem from an underestimation of total contacts per individual along the coast. We rescue this predicted 'edge effect' by increasing coastal contacts to approximate the number of per capita inland contacts. These results illustrate the impact of 'edge effects' on epidemic metapopulations in general and illustrate directions for the refinement of spatiotemporal epidemic models.     

病原菌与自然植物种群Ⅱ病原菌与植物种群生物学

病原菌在自然植物种群中普遍存在,其对寄主植物的生长发育,对寄主植物种群的大小、结构、动态、遗传和进化等都有重要影响。本文着重论述：１）病原菌对寄主植物个体的影响;２）病原菌对寄主植物种群生物学的影响;３）菌病发生的空间格局;４）病原菌感染的种群模型。     

Persistence of an infectious disease in a subdivided population

The transmission dynamics of a communicable disease in a subdivided population where the spread among groups follows the proportionate mixing model while the within-group transmission can correspond to preferred mixing, proportionate mixing among subgroups, or mixing between social and nonsocial subgroups, is analyzed. It is shown that the threshold condition for the disease to persist is that either (i) the disease can persist within at least one group through intragroup contacts, or--if (i) does not hold--(ii) the intergroup transmission is sufficiently high. The among-group transmission is computed as an average where each subgroup's reproductive number is weighted according to its intragroup activity level squared and the total number of cases that one infectious individual will cause through intragroup contacts. The model thus allows for a study of the relative importance of communitywide disease transmission and of disease transmission within geographically or socially separate groups.     

Variation in plant quality and the population dynamics of herbivores: there is nothing average about aphids

In the attempt to use results from small-scale studies to make large-scale predictions, it is critical that we take into account the greater spatial heterogeneity encountered at larger spatial scales. An important component of this heterogeneity is variation in plant quality, which can have a profound influence on herbivore population dynamics. This influence is particularly relevant when we consider that the strength of density dependence can vary among host plants and that the strength of density dependence determines the difference between exponential and density- dependent growth. Here, we present some simple models and analyses designed to examine the impact of variable plant quality on the dynamics of insect herbivore populations, and specifically the consequences of variation in the strength of density dependence among host plants. We show that average values of herbivore population growth parameters, calculated from plants that vary in quality, do not predict overall population growth. Furthermore, we illustrate that the quality of a few individual plants within a larger plant population can dominate herbivore population growth. Our results demonstrate that ignoring spatial heterogeneity that exists in herbivore population growth on plants that differ in quality can lead to a misunderstanding of the mechanisms that underlie population dynamics.     

Transmission assumptions generate conflicting predictions in host-vector disease models: a case study in West Nile virus

This review synthesizes the conflicting outbreak predictions generated by different biological assumptions in host–vector disease models. It is motivated by the North American outbreak of West Nile virus, an emerging infectious disease that has prompted at least five dynamical modelling studies. Mathematical models have long proven successful in investigating the dynamics and control of infectious disease systems. The underlying assumptions in these epidemiological models determine their mathematical structure, and therefore influence their predictions. A crucial assumption is the host–vector interaction encapsulated in the disease-transmission term, and a key prediction is the basic reproduction number, R ₀. We connect these two model elements by demonstrating how the choice of transmission term qualitatively and quantitatively alters R ₀ and therefore alters predicted disease dynamics and control implications. Whereas some transmission terms predict that reducing the host population will reduce disease outbreaks, others predict that this will exacerbate infection risk. These conflicting predictions are reconciled by understanding that different transmission terms apply biologically only at certain population densities, outside which they can generate erroneous predictions. For West Nile virus, R ₀ estimates for six common North American bird species indicate that all would be effective outbreak hosts.     

The influence of host dynamics on the clonal composition of Escherichia coli populations

Species, be they plant or animal, vary in their capacity for population growth or decline. Populations of the same species may also differ in their capacity for population change. A series of mathematical models were developed with the aim of determining if host population dynamics could influence the clonal composition of the Escherichia coli community in that host population. The biological assumptions underlying the models are described in some detail. Analytical and numerical approaches were used to investigate the behaviour of these models. The results demonstrate that host dynamics can have a profound influence on the E. coli clonal composition of the host population. This outcome is largely independent of the nature of the assumptions underlying the models. The ways in which the predictions of these models may be tested empirically are discussed, as are the implications of these models for understanding the nature of host-bacterial pathogen dynamics.     

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.     

Disease‐structured N‐mixture models: A practical guide to model disease dynamics using count data

Obtaining inferences on disease dynamics (e.g., host population size, pathogen prevalence, transmission rate, host survival probability) typically requires marking and tracking individuals over time. While multistate mark–recapture models can produce high‐quality inference, these techniques are difficult to employ at large spatial and long temporal scales or in small remnant host populations decimated by virulent pathogens, where low recapture rates may preclude the use of mark–recapture techniques. Recently developed N‐mixture models offer a statistical framework for estimating wildlife disease dynamics from count data. N‐mixture models are a type of state‐space model in which observation error is attributed to failing to detect some individuals when they are present (i.e., false negatives). The analysis approach uses repeated surveys of sites over a period of population closure to estimate detection probability. We review the challenges of modeling disease dynamics and describe how N‐mixture models can be used to estimate common metrics, including pathogen prevalence, transmission, and recovery rates while accounting for imperfect host and pathogen detection. We also offer a perspective on future research directions at the intersection of quantitative and disease ecology, including the estimation of false positives in pathogen presence, spatially explicit disease‐structured N‐mixture models, and the integration of other data types with count data to inform disease dynamics. Managers rely on accurate and precise estimates of disease dynamics to develop strategies to mitigate pathogen impacts on host populations. At a time when pathogens pose one of the greatest threats to biodiversity, statistical methods that lead to robust inferences on host populations are critically needed for rapid, rather than incremental, assessments of the impacts of emerging infectious diseases.     

Modeling optimal treatment strategies in a heterogeneous mixing model

Background

Many mathematical models assume random or homogeneous mixing for various infectious diseases. Homogeneous mixing can be generalized to mathematical models with multi-patches or age structure by incorporating contact matrices to capture the dynamics of the heterogeneously mixing populations. Contact or mixing patterns are difficult to measure in many infectious diseases including influenza. Mixing patterns are considered to be one of the critical factors for infectious disease modeling.

Methods

A two-group influenza model is considered to evaluate the impact of heterogeneous mixing on the influenza transmission dynamics. Heterogeneous mixing between two groups with two different activity levels includes proportionate mixing, preferred mixing and like-with-like mixing. Furthermore, the optimal control problem is formulated in this two-group influenza model to identify the group-specific optimal treatment strategies at a minimal cost. We investigate group-specific optimal treatment strategies under various mixing scenarios.

Results

The characteristics of the two-group influenza dynamics have been investigated in terms of the basic reproduction number and the final epidemic size under various mixing scenarios. As the mixing patterns become proportionate mixing, the basic reproduction number becomes smaller; however, the final epidemic size becomes larger. This is due to the fact that the number of infected people increases only slightly in the higher activity level group, while the number of infected people increases more significantly in the lower activity level group. Our results indicate that more intensive treatment of both groups at the early stage is the most effective treatment regardless of the mixing scenario. However, proportionate mixing requires more treated cases for all combinations of different group activity levels and group population sizes.

Conclusions

Mixing patterns can play a critical role in the effectiveness of optimal treatments. As the mixing becomes more like-with-like mixing, treating the higher activity group in the population is almost as effective as treating the entire populations since it reduces the number of disease cases effectively but only requires similar treatments. The gain becomes more pronounced as the basic reproduction number increases. This can be a critical issue which must be considered for future pandemic influenza interventions, especially when there are limited resources available.

     

Depression of host population abundance by direct life cycle macroparasites

Simple population models are used to identify the factors which determine the degree to which direct life cycle macroparasites depress their host populations from disease free equilibrium levels. The impact of parasitic infection is shown to be related to a range of biological characteristics of the host and parasite. The most important theoretical predictions are as follows: (1) certain threshold conditions must be satisfied (concerning host density and the rates of host and parasite reproduction) to enable the pathogen to persist with the host population; (2) parasites of low to intermediate pathogenicity are the most effective suppressors of host population growth while highly pathogenic species are likely to cause their own extinction but not that of their host; (3) the statistical distribution of parasite numbers per host has a major influence on the degree of host population depression; (4) host population with high reproductive potential are better able to withstand the impact of pathogens; (5) density dependent constraints on parasite population growth within, or on the host, whether induced by competition for finite resources or immunological attack, restrict the regulatory influence of the parasites; (6) parasites with the ability to multiply directly within the host are the most effective suppressors of host population growth and may cause the extinction of the host and hence themselves.Theoretical predictions are discussed in light of (a) the use of pathogens as biological control agents of pest species and (b) the effects of disease control on host population growth.     

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton–Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.     

Management measures to control a feline leukemia virus outbreak in the endangered Iberian lynx

The feline leukemia virus (FeLV) is a retrovirus that affects domestic cats all over the world. Its pathogenic effects generally include anemia, immunosuppression or tumors. Dissemination over populations is linked to cat sociality, because the virus is transmitted by direct contact. Although the domestic cat is its common host, FeLV infection has also been described in some wild felids. In the Iberian lynx Lynx pardinus , some sporadic FeLV infection cases have been reported since 1994, but an outbreak with the involvement of several animals has never been described until now. During spring 2007, an FeLV outbreak hit the Doñana (SW Spain) population. The infection rapidly spread throughout the densest subpopulation throughout Doñana. Infected animals showed very acute anemic disease, most of them dying in <6 months. To avoid FeLV dissemination, a control program was carried out that included removal of viremic lynxes, vaccination of negative individuals and reduction of the feral cat population. The program was implemented both in Doñana and in Sierra Morena populations. In Doñana, around 80% of the total lynx population and 90% of the outbreak focus subpopulation were evaluated. Seven out of the 12 infected individuals found died and two reverted to latency; the remaining viremic animals have been kept in captivity. The outbreak appears to have been successfully confined to the subpopulation where the virus appeared and no more cases have been found since August 2007. In the larger Sierra Morena population, 8% of the lynx population was surveyed. Thirty-four uninfected Iberian lynxes were vaccinated at least once. The FeLV prevalence was found to be 27% in the Doñana population and 0% in the Sierra Morena population.     

Population dynamics of a vertically transmitted, parasitic sex ratio distorter and its amphipod host

We investigate the population dynamics of a vertically transmitted, parasitic sex ratio distorter ( Nosema granulosis ) and its amphipod host ( Gammarus duebeni ), using field measurements to quantify and test alternative theoretical models of the interaction. We measure parasite, host population and transmission parameters at four locations on the Isle of Cumbrae, Scotland at monthly intervals for two years. We develop a simple infinite population model and test its predictions for parasite prevalence using field measurements of the parameters. Parasite prevalence is maintained at relatively low levels at all four sites (20–42%), consistently below that predicted. The parasite imposes a slight fitness cost on its host by reducing female fecundity, but this cost cannot account for the relatively low prevalences observed. We also investigate the importance of population structure, comparing parasite prevalence across sites and sampling intervals to look for evidence of spatial and temporal asynchrony as predicted by metapopulation models. We find significant temporal and spatial heterogeneity in parasite prevalence although there was also evidence that parasite dynamics were synchronous across sites. These data suggest that the parasite is unlikely to drive local population dynamics through cycles of extinction and recolonization at the scale measured. As the host (adult) population sex ratio was male-biased, local population crashes are unlikely to be induced by the parasite, contrary to theoretical predictions.     

The spatial distribution of plant populations, disease dynamics and evolution of resistance

Empirical studies of the interaction between the anther smut fungus Microbotryum violaceum and its host plant Lychnis alpina were combined with modelling approaches to investigate how variation in the spatial distribution of host populations influences disease dynamics and variation in resistance. Patterns of disease incidence and prevalence were surveyed in three contrasting systems of natural L . alpina populations where there is substantial variation in spatial structure, ranging from large continuous populations through to small isolated patches. Disease incidence (fraction of populations where disease was present) was highest in the continuous situation, and lowest in the most isolated populations. The reverse was true for prevalence (fraction of individuals diseased). To better understand the long-term ecological and evolutionary consequences of differences in among population spatial structure, we developed a two-dimensional spatially explicit simulation model in which host-population spacing was modelled by varying the percentage of sites suitable for the host. The general patterns of disease incidence and prevalence generated in the simulations corresponded well with the patterns observed in natural populations of L. alpina and M. violaceum ; i.e. the fraction of sites with disease increased while the average disease prevalence in diseased populations decreased when host populations became more connected. One likely explanation for the differences in disease incidence and prevalence seen in natural populations is that the evolution of host resistance varies as a function of the degree of fragmentation. This is supported by simulation results that were qualitatively similar to the survey data when resistance was allowed to vary, but not when hosts were assumed to be uniformly susceptible. In the former, the frequency of resistance increased markedly as host populations became more connected.