Divide and conquer? Persistence of infectious agents in spatial metapopulations of hosts

Persistence of an infectious agent in a population is an important issue in epidemiology. It is assumed that spatially fragmenting a population of hosts increases the probability of persistence of an infectious agent and that movement of hosts between the patches is vital for that. The influence of migration on persistence is however often studied in mean-field models, whereas in reality the actual distance travelled can be limited and influence the movement dynamics. We use a stochastic model, where within- and between-patch dynamics are coupled and movement is modelled explicitly, to show that explicit consideration of movement distance makes the relation between persistence of infectious agents and the metapopulation structure of its hosts less straightforward than previously thought. We show that the probability of persistence is largest at an intermediate movement distance of the host and that spatially fragmenting a population of hosts is not necessarily beneficial for persistence.     

Invasion and persistence of plant parasites in a spatially structured host population

Spatial structure is of central importance in the dynamics of plant-parasite interactions and is imposed by the growth habit and distribution of host plants and by parasite dispersal which is frequently restricted. To investigate the effects of spatial heterogeneity on the dynamics of plant parasites we introduce a simple model for epidemic development within a spatially structured host population. Here the host population is subdivided into a number of patches which are linked to allow for transmission from one patch to another with the connections defining the spatial structure of the host population. Three key parameters are identified that play a critical role in the ability of the parasite to invade and persist within the host population: the within-patch parasite basic reproductive number which characterises the infection dynamics at the local spatial scale; and the neighbourhood of interaction which describes which patches interact with which and the strength of coupling between patches within the neighbourhood which together characterise the spread of the parasite over larger spatial scales. Using both deterministic and stochastic formulations of the model, we investigate how the thresholds and probabilities of invasion and persistence are affected by these parameters, by demographic stochasticity and by differences in the initial level of infection.     

Cities and villages: infection hierarchies in a measles metapopulation

An important issue in the dynamics of directly transmitted microparasites is the relationship between infection probability and host density. We use models and extensive spatio-temporal data for the incidence of measles to examine evidence for spatial heterogeneity in transmission probability, in terms of urban–rural hierarchies in infection rate. Pre-vaccination measles data for England and Wales show strong evidence for urban–rural heterogeneities in infection rate – the proportion of urban cases rises significantly before major epidemics. The model shows that this effect is consistent with a higher infection rate in large cities, though small towns have epidemic characteristics intermediate between town and country. Surprisingly, urban and rural areas of the same population size have a similar propensity for local extinction of infection. A spatial map of urban–rural correlations reveals complex regional patterns of synchronization of towns and cities. The hierarchical heterogeneities in infection persist into the vaccine era; their implications for disease persistence and control are discussed.     

Spatial dynamics and molecular ecology of North American rabies

Rabies, caused by a single-stranded RNA virus, is arguably the most important viral zoonotic disease worldwide. Although endemic throughout many regions for millennia, rabies is also undergoing epidemic expansion, often quite rapid, among wildlife populations across regions of Europe and North America. A current rabies epizootic in North America is largely attributable to the accidental introduction of a particularly well-adapted virus variant into a naive raccoon population along the Virginia/West Virginia border in the mid-1970s. We have used the extant database on the spatial and temporal occurrence of rabid raccoons across the eastern United States to construct predictive models of disease spread and have tied patterns of emergence to local environmental variables, genetic heterogeneity, and host specificity. Rabies will continue to be a remarkable model system for exploring basic issues in the temporal and spatial dynamics of expanding infectious diseases and examining ties between disease population ecology and evolutionary genetics at both micro- and macro-evolutionary time scales.     

Invasion and persistence of infectious agents in fragmented host populations

One of the important questions in understanding infectious diseases and their prevention and control is how infectious agents can invade and become endemic in a host population. A ubiquitous feature of natural populations is that they are spatially fragmented, resulting in relatively homogeneous local populations inhabiting patches connected by the migration of hosts. Such fragmented population structures are studied extensively with metapopulation models. Being able to define and calculate an indicator for the success of invasion and persistence of an infectious agent is essential for obtaining general qualitative insights into infection dynamics, for the comparison of prevention and control scenarios, and for quantitative insights into specific systems. For homogeneous populations, the basic reproduction ratio R(0) plays this role. For metapopulations, defining such an 'invasion indicator' is not straightforward. Some indicators have been defined for specific situations, e.g., the household reproduction number R*. However, these existing indicators often fail to account for host demography and especially host migration. Here we show how to calculate a more broadly applicable indicator R(m) for the invasion and persistence of infectious agents in a host metapopulation of equally connected patches, for a wide range of possible epidemiological models. A strong feature of our method is that it explicitly accounts for host demography and host migration. Using a simple compartmental system as an example, we illustrate how R(m) can be calculated and expressed in terms of the key determinants of epidemiological dynamics.     

Evolution of Pathogen Specialisation in a Host Metapopulation: Joint Effects of Host and Pathogen Dispersal

Metapopulation processes are important determinants of epidemiological and evolutionary dynamics in host-pathogen systems, and are therefore central to explaining observed patterns of disease or genetic diversity. In particular, the spatial scale of interactions between pathogens and their hosts is of primary importance because migration rates of one species can affect both spatial and temporal heterogeneity of selection on the other. In this study we developed a stochastic and discrete time simulation model to specifically examine the joint effects of host and pathogen dispersal on the evolution of pathogen specialisation in a spatially explicit metapopulation. We consider a plant-pathogen system in which the host metapopulation is composed of two plant genotypes. The pathogen is dispersed by air-borne spores on the host metapopulation. The pathogen population is characterised by a single life-history trait under selection, the infection efficacy. We found that restricted host dispersal can lead to high amount of pathogen diversity and that the extent of pathogen specialisation varied according to the spatial scale of host-pathogen dispersal. We also discuss the role of population asynchrony in determining pathogen evolutionary outcomes.     

Spatial and temporal heterogeneity explain disease dynamics in a spatially explicit network model

There is an increasing recognition that individual-level spatial and temporal heterogeneity may play an important role in metapopulation dynamics and persistence. In particular, the patterns of contact within and between aggregates (e.g., demes) at different spatial and temporal scales may reveal important mechanisms governing metapopulation dynamics. Using 7 years of data on the interaction between the anther smut fungus (Microbotryum violaceum) and fire pink (Silene virginica), we show how the application of spatially explicit and implicit network models can be used to make accurate predictions of infection dynamics in spatially structured populations. Explicit consideration of both spatial and temporal organization reveals the role of each in spreading risk for both the host and the pathogen. This work suggests that the application of spatially explicit network models can yield important insights into how heterogeneous structure can promote the persistence of species in natural landscapes.     

Spatially structured superinfection and the evolution of disease virulence

When pathogen strains differing in virulence compete for hosts, spatial structuring of disease transmission can govern both evolved levels of virulence and patterns in strain coexistence. We develop a spatially detailed model of superinfection, a form of contest competition between pathogen strains; the probability of superinfection depends explicitly on the difference in levels of virulence. We apply methods of adaptive dynamics to address the interplay of spatial dynamics and evolution. The mean-field approximation predicts evolution to criticality; any small increase in virulence capable of dynamical persistence is favored. Both pair approximation and simulation of the detailed model indicate that spatial structure constrains disease virulence. Increased spatial clustering reduces the maximal virulence capable of single-strain persistence and, more importantly, reduces the convergent-stable virulence level under strain competition. The spatially detailed model predicts that increasing the probability of superinfection, for given difference in virulence, increases the likelihood of between-strain coexistence. When strains differing in virulence can coexist ecologically, our results may suggest policies for managing diseases with localized transmission. Comparing equilibrium densities from the pair approximation, we find that introducing a more virulent strain into a host population infected by a less virulent strain can sometimes reduce total host mortality and increase global host density.     

From host immunity to pathogen invasion: the effects of helminth coinfection on the dynamics of microparasites

Concurrent infections with multiple parasites are ubiquitous in nature. Coinfecting parasites can interact with one another in a variety of ways, including through the host's immune system via mechanisms such as immune trade-offs and immunosuppression. These within-host immune processes mediating interactions among parasites have been described in detail, but how they scale up to determine disease dynamic patterns at the population level is only beginning to be explored. In this review, we use helminth-microparasite coinfection as a model for examining how within-host immunological effects may influence the ecological outcome of microparasitic diseases, with a specific focus on disease invasion. The current literature on coinfection between helminths and major microparasitic diseases includes many studies documenting the effects of helminths on individual host responses to microparasites. In many cases, the observed host responses map directly onto parameters relevant for quantifying disease dynamics; however, there have been few attempts at integrating data on individual-level effects into theoretical models to extrapolate from the individual to the population level. Moreover, there is considerable variability in the particular combination of disease parameters affected by helminths across different microparasite systems. We develop a conceptual framework identifying some potential sources of such variability: Pathogen persistence and severity, and resource availability to hosts. We also generate testable hypotheses regarding diseases and the environmental contexts when the effects of helminths on microparasite dynamics should be most pronounced. Finally, we use a case study of helminth and mycobacterial coinfection in the African buffalo to illustrate both progress and challenges in understanding the population-level consequences of within-host immunological interactions, and conclude with suggestions for future research that will help improve our understanding of the effects of coinfection on dynamics of infectious diseases.     

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.     

Emergence, spread, persistence and fade-out of sylvatic plague in Kazakhstan

Predicting the dynamics of zoonoses in wildlife is important not only for prevention of transmission to humans, but also for improving the general understanding of epidemiological processes. A large dataset on sylvatic plague in the Pre-Balkhash area of Kazakhstan (collected for surveillance purposes) provides a rare opportunity for detailed statistical modelling of an infectious disease. Previous work using these data has revealed a host abundance threshold for epizootics, and climatic influences on plague prevalence. Here, we present a model describing the local space-time dynamics of the disease at a spatial scale of 20 × 20 km(2) and a biannual temporal scale, distinguishing between invasion and persistence events. We used a Bayesian imputation method to account for uncertainties resulting from poor data in explanatory variables and response variables. Spatial autocorrelation in the data was accounted for in imputations and analyses through random effects. The results show (i) a clear effect of spatial transmission, (ii) a high probability of persistence compared with invasion, and (iii) a stronger influence of rodent abundance on invasion than on persistence. In particular, there was a substantial probability of persistence also at low host abundance.     

Integrodifference models for persistence in fragmented habitats

Integrodifference models of growth and dispersal are analyzed on finite domains to investigate the effects of emigration, local growth dynamics and habitat heterogeneity on population persistence. We derive the bifurcation structure for a range of population dynamics and present an approximation that allows straighforward calculation of the equilibrium populations in terms of local growth dynamics and dispersal success rates. We show how population persistence in a heterogeneous environment depends on the scale of the heterogeneity relative to the organism's characteristic dispersal distance. When organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence.     

Human mobility patterns predict divergent epidemic dynamics among cities

The epidemic dynamics of infectious diseases vary among cities, but it is unclear how this is caused by patterns of infectious contact among individuals. Here, we ask whether systematic differences in human mobility patterns are sufficient to cause inter-city variation in epidemic dynamics for infectious diseases spread by casual contact between hosts. We analyse census data on the mobility patterns of every full-time worker in 48 Canadian cities, finding a power-law relationship between population size and the level of organization in mobility patterns, where in larger cities, a greater fraction of workers travel to work in a few focal locations. Similarly sized cities also vary in the level of organization in their mobility patterns, equivalent on average to the variation expected from a 2.64-fold change in population size. Systematic variation in mobility patterns is sufficient to cause significant differences among cities in infectious disease dynamics—even among cities of the same size—according to an individual-based model of airborne pathogen transmission parametrized with the mobility data. This suggests that differences among cities in host contact patterns are sufficient to drive differences in infectious disease dynamics and provides a framework for testing the effects of host mobility patterns in city-level disease data.     

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.     

Spatial dynamics of pertussis in a small region of Senegal

Extended time-series analysis of infectious diseases raises two issues: the spread of disease, and its persistence in space and time. Most studies are based on both data and models, corresponding to conditions encountered in developed countries. The present work sought to determine the impact of local heterogeneity on these two issues, regarding pertussis in tropical conditions. First, we tested the 'cities and villages' model in a small community of 30 villages in rural Senegal. Second, we focused on the impact of population size and density, as well as geographic distance, on population dynamics of pertussis. Results showed that pertussis initially arrived in urban centres, and then spread to surrounding areas. Both population size and density are implicated in the persistence of pertussis within the study area, whereas geographical distance between villages is not. This is the first study on pertussis in a developing country carried out on a very fine spatial scale. Furthermore, it confirms previous results for measles in England and Wales.     

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.     

Seasonality and the dynamics of infectious diseases

Seasonal variations in temperature, rainfall and resource availability are ubiquitous and can exert strong pressures on population dynamics. Infectious diseases provide some of the best-studied examples of the role of seasonality in shaping population fluctuations. In this paper, we review examples from human and wildlife disease systems to illustrate the challenges inherent in understanding the mechanisms and impacts of seasonal environmental drivers. Empirical evidence points to several biologically distinct mechanisms by which seasonality can impact host–pathogen interactions, including seasonal changes in host social behaviour and contact rates, variation in encounters with infective stages in the environment, annual pulses of host births and deaths and changes in host immune defences. Mathematical models and field observations show that the strength and mechanisms of seasonality can alter the spread and persistence of infectious diseases, and that population-level responses can range from simple annual cycles to more complex multiyear fluctuations. From an applied perspective, understanding the timing and causes of seasonality offers important insights into how parasite–host systems operate, how and when parasite control measures should be applied, and how disease risks will respond to anthropogenic climate change and altered patterns of seasonality. Finally, by focusing on well-studied examples of infectious diseases, we hope to highlight general insights that are relevant to other ecological interactions.     

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.     

Linking demography and host dispersal to Trichuris arvicolae distribution in a cyclic vole species

Spatial structure in the distribution of pathogen infection can influence both epidemiology and host-parasite coevolutionary processes. It may result from the spatial heterogeneity of intrinsic and extrinsic factors, or from the local population dynamics of hosts and parasites. In this study, we investigated the effects of landscape, host dispersal and demography (population abundance and phase of the fluctuation) on the distribution of a gastro-intestinal nematode Trichuris arvicolae in the fossorial water vole Arvicola terrestris sherman. This rodent exhibits outbreaks occurring regularly in Franche-Comté (France). Thirteen out-of-phase populations were studied in autumn 2003. They exhibited highly different T. arvicolae prevalences. The heterogeneity in prevalences was not explained by population structure, landscape or vole abundance, but by the phase of the vole population fluctuations. Populations at the end of the high density phase showed null prevalence whereas populations in increase or outbreak phases exhibited higher prevalences. Population genetic analyses based on microsatellites revealed significant differentiation between vole populations, and higher dispersal rates of young voles compared with old ones. These younger individuals were also infected more frequently than older voles. This suggested a role of host dispersal in the distribution of T. arvicolae. However, there was a strong discrepancy between the spatial patterns of prevalence and of host genetics or demographic phase. Genetic differentiation and differences in demographic phase exhibited significant spatial autocorrelations whereas prevalence did not. We concluded that the distribution of T. arvicolae is influenced by vole dispersal, although this effect might be overwhelmed by local adaptation processes or environmental conditions.     

Spatio-Temporal Environmental Correlation and Population Variability in Simple Metacommunities

Natural populations experience environmental conditions that vary across space and over time. This variation is often correlated between localities depending on the geographical separation between them, and different species can respond to local environmental fluctuations similarly or differently, depending on their adaptation. How this emerging structure in environmental correlation (between-patches and between-species) affects spatial community dynamics is an open question. This paper aims at a general understanding of the interactions between the environmental correlation structure and population dynamics in spatial networks of local communities (metacommunities), by studying simple two-patch, two-species systems. Three different pairs of interspecific interactions are considered: competition, consumer–resource interaction, and host–parasitoid interaction. While the results paint a relatively complex picture of the effect of environmental correlation, the interaction between environmental forcing, dispersal, and local interactions can be understood via two mechanisms. While increasing between-patch environmental correlation couples immigration and local densities (destabilising effect), the coupling between local populations under increased between-species environmental correlation can either amplify or dampen population fluctuations, depending on the patterns in density dependence. This work provides a unifying framework for modelling stochastic metacommunities, and forms a foundation for a better understanding of population responses to environmental fluctuations in natural systems.