A fully coupled, mechanistic model for infectious disease dynamics in a metapopulation: Movement and epidemic duration

How Is the Risk of Major Sudden Infectious Epidemic Transmitted? A Grounded Theory Analysis Based on COVID-19 in China

The outbreak of a sudden infectious epidemic often causes serious casualties and property losses to the whole society. The COVID-19 epidemic that broke out in China at the end of December 2019, spread rapidly, resulting in large groups of confirmed diagnoses, and causing severe damage to China's society. This epidemic even now encompasses the globe. This paper takes the COVID-19 epidemic that has occurred in China as an example, the original data of this paper is derived from 20 Chinese media reports on COVID-19, and the grounded theory is used to analyze the original data to find the risk transmission rules of a sudden infectious epidemic. The results show that in the risk transmission of a sudden infectious epidemic, there are six basic elements: the risk source, the risk early warning, the risk transmission path, the risk transmission victims, the risk transmission inflection point, and the end of risk transmission. After a sudden infectious epidemic breaks out, there are three risk transmission paths, namely, a medical system risk transmission path, a social system risk transmission path, and a psychological risk transmission path, and these three paths present a coupling structure. These findings in this paper suggest that people should strengthen the emergency management of a sudden infectious epidemic by controlling of the risk source, establishing an efficient and scientific risk early warning mechanism and blocking of the risk transmission paths. The results of this study can provide corresponding policy implications for the emergency management of sudden public health events.

Targeted strategies for the management of wildlife diseases: the case of brucellosis in Alpine ibex

The management of infectious diseases in wildlife reservoirs is challenging and faces several limitations. However, detailed knowledge of host-pathogen systems often reveal heterogeneity among the hosts' contribution to transmission. Management strategies targeting specific classes of individuals and/or areas, having a particular role in transmission, could be more effective and more acceptable than population-wide interventions. In the wild population of Alpine ibex (Capra ibex-a protected species) of the Bargy massif (French Alps), females transmit brucellosis (Brucella melitensis) infection in ~90% of cases, and most transmissions occur in the central spatial units ("core area"). Therefore, we expanded an individual-based model, developed in a previous study, to test whether strategies targeting females or the core area, or both, would be more effective. We simulated the relative efficacy of realistic strategies for the studied population, combining test-and-remove (euthanasia of captured animals with seropositive test results) and partial culling of unmarked animals. Targeting females or the core area was more effective than untargeted management options, and strategies targeting both were even more effective. Interestingly, the number of ibex euthanized and culled in targeted strategies were lower than in untargeted ones, thus decreasing the conservation costs while increasing the sanitary benefits. Although there was no silver bullet for the management of brucellosis in the studied population, targeted strategies offered a wide range of promising refinements to classical sanitary measures. We therefore encourage to look for heterogeneity in other wildlife diseases and to evaluate potential strategies for improving management in terms of efficacy but also acceptability.

Spatial dynamics of pathogen transmission in communally roosting species: Impacts of changing habitats on bat-virus dynamics

The spatial organization of populations determines their pathogen dynamics. This is particularly important for communally roosting species, whose aggregations are often driven by the spatial structure of their environment.

We develop a spatially explicit model for virus transmission within roosts of Australian tree‐dwelling bats (Pteropus spp.), parameterized to reflect Hendra virus. The spatial structure of roosts mirrors three study sites, and viral transmission between groups of bats in trees was modelled as a function of distance between roost trees. Using three levels of tree density to reflect anthropogenic changes in bat habitats, we investigate the potential effects of recent ecological shifts in Australia on the dynamics of zoonotic viruses in reservoir hosts.

We show that simulated infection dynamics in spatially structured roosts differ from that of mean‐field models for equivalently sized populations, highlighting the importance of spatial structure in disease models of gregarious taxa. Under contrasting scenarios of flying‐fox roosting structures, sparse stand structures (with fewer trees but more bats per tree) generate higher probabilities of successful outbreaks, larger and faster epidemics, and shorter virus extinction times, compared to intermediate and dense stand structures with more trees but fewer bats per tree. These observations are consistent with the greater force of infection generated by structured populations with less numerous but larger infected groups, and may flag an increased risk of pathogen spillover from these increasingly abundant roost types.

Outputs from our models contribute insights into the spread of viruses in structured animal populations, like communally roosting species, as well as specific insights into Hendra virus infection dynamics and spillover risk in a situation of changing host ecology. These insights will be relevant for modelling other zoonotic viruses in wildlife reservoir hosts in response to habitat modification and changing populations, including coronaviruses like SARS‐CoV‐2.

Exploring artificial habitat fragmentation to control invasion by infectious wildlife diseases

One way to reduce the impacts of invading wildlife diseases is setting up fences that would reduce the spread of pathogens by limiting connectivity, similarly to exclusion fences that are commonly used to conserve threatened species against invasive predators. One of the problems with fences is that, while they may have the short-term benefit of impeding the spread of disease, this benefit may be offset by potential long-term ecological costs of fragmentation by fencing. However, managers facing situations where a pathogen has been detected near the habitat of a (highly) vulnerable species may be willing to explore such a trade-off. To aid such exploration quantitatively, we present a series of models trading off the benefits of fragmentation (potential reduction of disease impacts on susceptible individuals) against its costs (both financial and ecological, i.e. reduced viability in the patches created by fragmentation), and exploring the effects of fragmentation on non-target species richness. For all model variants we derive the optimal number of artificial patches. We show that pre-emptive disease fences may have benefits when the risk of disease exceeds the impacts of fragmentation, when fence failure rates are lower than a specific threshold, and when sufficient resources are available to implement optimal solutions. A useful step to initiate planning is to obtain information about the expected number of initial infection events and on the host's extinction threshold with respect to the focal habitat and management duration. Our approach can assist managers to identify whether the trade-offs support the decision to fence and how intensive fragmentation should be.

The persistence of a SIR disease in a metapopulation: Hendra virus epidemics in Australian black flying foxes (Pteropus alecto)

Understanding how emerging viruses persist in bat populations is a fundamental step to understand the processes by which viruses are transmitted from reservoir hosts to spillover hosts. Hendra virus, which has caused fatal infections in horses and humans in eastern Australia since 1994, spills over from its natural reservoir hosts, Pteropus bats (colloquially known as flying foxes). It has been suggested that the Hendra virus maintenance mechanism in the bat populations might be implicated with their metapopulation structure. Here, we examine whether a metapopulation consisting of black flying fox (P. alecto) colonies that are smaller than the critical community size can maintain the Hendra virus. By using the Gillespie algorithm, stochastic mathematical models were used to simulate a cycle, in which viral extinction and recolonisation were repeated in a single colony within a metapopulation. Given estimated flying fox immigration rates, the simulation results showed that recolonisation occurred more frequently than extinction, which indicated that infection would not go extinct in the metapopulation. Consequently, this study suggests that a collection of transient epidemics of Hendra virus in numerous colonies of flying foxes in Australia can support the long-term persistence of the virus at the metapopulation level.

Strong spatial embedding of social networks generates nonstandard epidemic dynamics independent of degree distribution and clustering

Some directly transmitted human pathogens, such as influenza and measles, generate sustained exponential growth in incidence and have a high peak incidence consistent with the rapid depletion of susceptible individuals. Many do not. While a prolonged exponential phase typically arises in traditional disease-dynamic models, current quantitative descriptions of nonstandard epidemic profiles are either abstract, phenomenological, or rely on highly skewed offspring distributions in network models. Here, we create large socio-spatial networks to represent contact behavior using human population-density data, a previously developed fitting algorithm, and gravity-like mobility kernels. We define a basic reproductive number [Formula: see text] for this system, analogous to that used for compartmental models. Controlling for [Formula: see text], we then explore networks with a household-workplace structure in which between-household contacts can be formed with varying degrees of spatial correlation, determined by a single parameter from the gravity-like kernel. By varying this single parameter and simulating epidemic spread, we are able to identify how more frequent local movement can lead to strong spatial correlation and, thus, induce subexponential outbreak dynamics with lower, later epidemic peaks. Also, the ratio of peak height to final size was much smaller when movement was highly spatially correlated. We investigate the topological properties of our networks via a generalized clustering coefficient that extends beyond immediate neighborhoods, identifying very strong correlations between fourth-order clustering and nonstandard epidemic dynamics. Our results motivate the observation of both incidence and socio-spatial human behavior during epidemics that exhibit nonstandard incidence patterns.

Trade-off between local transmission and long-range dispersal drives infectious disease outbreak size in spatially structured populations

Transmission of infectious diseases between immobile hosts (e.g., plants, farms) is strongly dependent on the spatial distribution of hosts and the distance-dependent probability of transmission. As the interplay between these factors is poorly understood, we use spatial process and transmission modelling to investigate how epidemic size is shaped by host clustering and spatial range of transmission. We find that for a given degree of clustering and individual-level infectivity, the probability that an epidemic occurs after an introduction is generally higher if transmission is predominantly local. However, local transmission also impedes transfer of the infection to new clusters. A consequence is that the total number of infections is maximal if the range of transmission is intermediate. In highly clustered populations, the infection dynamics is strongly determined by the probability of transmission between clusters of hosts, whereby local clusters act as multiplier of infection. We show that in such populations, a metapopulation model sometimes provides a good approximation of the total epidemic size, using probabilities of local extinction, the final size of infections in local clusters, and probabilities of cluster-to-cluster transmission. As a real-world example we analyse the case of avian influenza transmission between poultry farms in the Netherlands.

Transmission of infectious diseases between immobile hosts depends on the transmission characteristics of the infection and on the spatial distribution of hosts. Examples include infectious diseases of plants that are spread by wind or via vectors (e.g., Asiatic citrus canker spread between citrus trees), diseases that are transmitted between local host populations (e.g., sylvatic plague transmitted between rodents living in burrows), diseases of production animals that are spread between farms (e.g., avian influenza in poultry transmitted from farm to farm). We use spatial transmission modelling to investigate how the total number of infections over the course of an epidemic is determined by host clustering and spatial range of transmission. We find that for a given degree of clustering and infectivity of hosts, the number of infections is maximal if the spatial range of transmission is intermediate. In highly clustered populations we show that epidemic size can be approximated by a metapopulation model, illustrating that in such populations the transmission dynamics is dominated by transmission between clusters of hosts.

How mechanistic modelling supports decision making for the control of enzootic infectious diseases

Controlling enzootic diseases, which generate a large cumulative burden and are often unregulated, is needed for sustainable farming, competitive agri-food chains, and veterinary public health. We discuss the benefits and challenges of mechanistic epidemiological modelling for livestock enzootics, with particular emphasis on the need for interdisciplinary approaches. We focus on issues arising when modelling pathogen spread at various scales (from farm to the region) to better assess disease control and propose targeted options. We discuss in particular the inclusion of farmers' strategic decision-making, the integration of within-host scale to refine intervention targeting, and the need to ground models on data.

Neighbourhood contacts and trade movements drive the regional spread of bovine viral diarrhoea virus (BVDV)

To explore the regional spread of endemic pathogens, investigations are required both at within and between population levels. The bovine viral diarrhoea virus (BVDV) is such a pathogen, spreading among cattle herds mainly due to trade movements and neighbourhood contacts, and causing an endemic disease with economic consequences. To assess the contribution of both transmission routes on BVDV regional and local spread, we developed an original epidemiological model combining data-driven and mechanistic approaches, accounting for heterogeneous within-herd dynamics, animal movements and neighbourhood contacts. Extensive simulations were performed over 9 years in an endemic context in a French region with high cattle density. The most uncertain model parameters were calibrated on summary statistics of epidemiological data, highlighting that neighbourhood contacts and within-herd transmission should be high. We showed that neighbourhood contacts and trade movements complementarily contribute to BVDV spread on a regional scale in endemically infected and densely populated areas, leading to intense fade-out/colonization events: neighbourhood contacts generate the vast majority of outbreaks (72%) but mostly in low immunity herds and correlated to a rather short presence of persistently infected animals (P); trade movements generate fewer infections but could affect herds with higher immunity and generate a prolonged presence of P. Both movements and neighbourhood contacts should be considered when designing control or eradication strategies for densely populated region.

Microparasite dispersal in metapopulations: a boon or bane to the host population?

Although connectivity can promote host species persistence in a metapopulation, dispersal may also enable disease transmission, an effect further complicated by the impact that parasite distribution may have on host-parasite population dynamics. We investigated the effects of connectivity and initial parasite distribution (clustered or dispersed) on microparasite-host dynamics in experimental metapopulations, using guppies and Gyrodactylus turnbulli We created metapopulations of guppies divided into four subpopulations and introduced either a low level of parasites to all subpopulations (dispersed) or a high level of parasites to one subpopulation (clustered). Controlled migration among subpopulations occurred every 10 days. In additional trials, we introduced low or high levels of parasites to isolated populations. Parasites persisted longer in metapopulations than in isolated populations. Mortality was lowest in isolated populations with low-level introductions. The interaction of connectivity and initial parasite distribution influenced parasite abundance. With low-level introductions, connectivity helped the parasite persist longer but had little effect on the hosts. With high levels, connectivity also benefited the hosts, lowering parasite burdens. These findings have implications for disease management and species conservation.

Infectious Disease in Wild Animal Populations: Examining Transmission and Control with Mathematical Models

The mathematical modeling of ecological interactions is an essential tool in predicting the behavior of complex systems across landscapes. The scientific literature is growing with examples of models used to explore predator-prey interactions, resource selection, population growth, and dynamics of disease transmission. These models provide managers with an efficient alternative means of testing new management and control strategies without resorting to empirical testing that is often costly, time-consuming, and impractical. This chapter presents a review of four types of mathematical models used to understand and predict the spread of infectious diseases in wild animals: compartmental, metapopulation, spatial, and contact network models. Descriptions of each model’s uses and limitations are used to provide a look at the complexities involved in modeling the spread of diseases and the trade-offs that accompany selecting one modeling approach over another. Potential avenues for the improvement and use of these models in future studies are also discussed, as are specific examples of how each type of model has improved our understanding of infectious diseases in populations of wild animals.

Dynamic, spatial models of parasite transmission in wildlife: Their structure, applications and remaining challenges

Individual differences in contact rate can arise from host, group and landscape heterogeneity and can result in different patterns of spatial spread for diseases in wildlife populations with concomitant implications for disease control in wildlife of conservation concern, livestock and humans. While dynamic disease models can provide a better understanding of the drivers of spatial spread, the effects of landscape heterogeneity have only been modelled in a few well-studied wildlife systems such as rabies and bovine tuberculosis. Such spatial models tend to be either purely theoretical with intrinsic limiting assumptions or individual-based models that are often highly species- and system-specific, limiting the breadth of their utility. Our goal was to review studies that have utilized dynamic, spatial models to answer questions about pathogen transmission in wildlife and identify key gaps in the literature. We begin by providing an overview of the main types of dynamic, spatial models (e.g., metapopulation, network, lattice, cellular automata, individual-based and continuous-space) and their relation to each other. We investigate different types of ecological questions that these models have been used to explore: pathogen invasion dynamics and range expansion, spatial heterogeneity and pathogen persistence, the implications of management and intervention strategies and the role of evolution in host-pathogen dynamics. We reviewed 168 studies that consider pathogen transmission in free-ranging wildlife and classify them by the model type employed, the focal host-pathogen system, and their overall research themes and motivation. We observed a significant focus on mammalian hosts, a few well-studied or purely theoretical pathogen systems, and a lack of studies occurring at the wildlife-public health or wildlife-livestock interfaces. Finally, we discuss challenges and future directions in the context of unprecedented human-mediated environmental change. Spatial models may provide new insights into understanding, for example, how global warming and habitat disturbance contribute to disease maintenance and emergence. Moving forward, better integration of dynamic, spatial disease models with approaches from movement ecology, landscape genetics/genomics and ecoimmunology may provide new avenues for investigation and aid in the control of zoonotic and emerging infectious diseases.

The dynamics of disease in a metapopulation: The role of dispersal range

The establishment and spread of a disease within a metapopulation is influenced both by dynamics within each population and by the host and pathogen spatial processes through which they are connected. We develop a spatially explicit metapopulation model to investigate how the form of host and disease dispersal jointly influence the probability of disease establishment and invasion. We show that diseases are more likely to establish if both the host and the disease tend to disperse locally, since the former leads to the spatial aggregation of host populations in the environment while the latter facilitates the pathogen's exploitation of this spatial pattern. In contrast, local pathogen dispersal is likely to reduce the probability of subsequent disease spread because it increases the spatial segregation of infected and uninfected populations. The effects of local dispersal on disease dynamics are less pronounced when the pathogen spreads through the movement of infected hosts and more pronounced when pathogen dispersal is independent (for example through airborne viruses) though the details of host and pathogen biology can be important. These spatial effects tend to be more pronounced if the sites available for host occupation are themselves spatially aggregated.

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We explore disease spread in spatially structured metapopulations.

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Local host dispersal facilitates disease invasion but hinders disease persistence.

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These effects are strongest for diseases that spread independently of the host.

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They are also stronger in landscapes where the habitat sites are clumped in space.

Complex responses to movement-based disease control: when livestock trading helps

Livestock disease controls are often linked to movements between farms, for example, via quarantine and pre- or post-movement testing. Designing effective controls, therefore, benefits from accurate assessment of herd-to-herd transmission. Household models of human infections make use of R_*, the number of groups infected by an initial infected group, which is a metapopulation level analogue of the basic reproduction number R₀ that provides a better characterization of disease spread in a metapopulation. However, existing approaches to calculate R_* do not account for individual movements between locations which means we lack suitable tools for livestock systems. We address this gap using next-generation matrix approaches to capture movements explicitly and introduce novel tools to calculate R_* in any populations coupled by individual movements. We show that depletion of infectives in the source group, which hastens its recovery, is a phenomenon with important implications for design and efficacy of movement-based controls. Underpinning our results is the observation that R_* peaks at intermediate livestock movement rates. Consequently, under movement-based controls, infection could be controlled at high movement rates but persist at intermediate rates. Thus, once control schemes are present in a livestock system, a reduction in movements can counterintuitively lead to increased disease prevalence. We illustrate our results using four important livestock diseases (bovine viral diarrhoea, bovine herpes virus, Johne's disease and Escherichia coli O157) that each persist across different movement rate ranges with the consequence that a change in livestock movements could help control one disease, but exacerbate another.

Infectious Disease Dynamics in Heterogeneous Landscapes

Infectious diseases dynamics are affected by both spatial and temporal heterogeneity in their environments. Our ability to quantify and predict how this heterogeneity impacts risks of infection and disease emergence is the key to successful disease prevention efforts. Here, we review the literature on infectious diseases from human, agricultural, and wildlife ecosystems to describe the rapid ecological and evolutionary responses in pathogens to environmental heterogeneity, with expected impacts on their epidemiology. To date, the underlying network structures through which disease transmission proceeds have been notoriously difficult to quantify because of this variation. We show that with recent advances in statistical methods and genomic approaches, it is now more feasible than ever to trace disease transmission networks, the molecular underpinning of infection, and the environmental variation relevant to disease dynamics. We end by identifying major new opportunities and challenges in understanding disease dynamics in an ever-changing world.

Patients as Patches: Ecology and Epidemiology in Healthcare Environments

The modern healthcare system involves complex interactions among microbes, patients, providers, and the built environment. It represents a unique and challenging setting for control of the emergence and spread of infectious diseases. We examine an extension of the perspectives and methods from ecology (and especially urban ecology) to address these unique issues, and we outline 3 examples: (1) viewing patients as individual microbial ecosystems; (2) the altered ecology of infectious diseases specifically within hospitals; and (3) ecosystem management perspectives for infection surveillance and control. In each of these cases, we explore the accuracy and relevance of analogies to existing urban ecological perspectives, and we demonstrate a few of the potential direct uses of this perspective for altering research into the control of healthcare-associated infections. Infect Control Hosp Epidemiol. 2016;1507-1512.

Modelling of paratuberculosis spread between dairy cattle farms at a regional scale

Mycobacterium avium subsp. paratuberculosis (Map) causes Johne's disease, with large economic consequences for dairy cattle producers worldwide. Map spread between farms is mainly due to animal movements. Locally, herd size and management are expected to influence infection dynamics. To provide a better understanding of Map spread between dairy cattle farms at a regional scale, we describe the first spatio-temporal model accounting simultaneously for population and infection dynamics and indirect local transmission within dairy farms, and between-farm transmission through animal trade. This model is applied to Brittany, a French region characterized by a high density of dairy cattle, based on data on animal trade, herd size and farm management (birth, death, renewal, and culling) from 2005 to 2013 for 12,857 dairy farms. In all simulated scenarios, Map infection highly persisted at the metapopulation scale. The characteristics of initially infected farms strongly impacted the regional Map spread. Network-related features of incident farms influenced their ability to contaminate disease-free farms. At the herd level, we highlighted a balanced effect of the number of animals purchased: when large, it led to a high probability of farm infection but to a low persistence. This effect was reduced when prevalence in initially infected farms increased. Implications of our findings in the current enzootic situation are that the risk of infection quickly becomes high for farms buying more than three animals per year. Even in regions with a low proportion of infected farms, Map spread will not fade out spontaneously without the use of effective control strategies.

Refugia and connectivity sustain amphibian metapopulations afflicted by disease

Metapopulation persistence in fragmented landscapes depends on habitat patches that can support resilient local populations and sufficient connectivity between patches. Yet epidemiological theory for metapopulations has largely overlooked the capacity of particular patches to act as refuges from disease, and has suggested that connectivity can undermine persistence. Here, we show that relatively warm and saline wetlands are environmental refuges from chytridiomycosis for an endangered Australian frog, and act jointly with connectivity to sustain frog metapopulations. We coupled models of microclimate and infection probability to map chytrid prevalence, and demonstrate a strong negative relationship between chytrid prevalence and the persistence of frog populations. Simulations confirm that frog metapopulations are likely to go extinct when they lack environmental refuges from disease and lose connectivity between patches. This study demonstrates that environmental heterogeneity can mediate host-pathogen interactions in fragmented landscapes, and provides evidence that connectivity principally supports host metapopulations afflicted by facultative pathogens.

Dilution versus facilitation: Impact of connectivity on disease risk in metapopulations

Epidemiological studies have suggested that increasing connectivity in metapopulations usually facilitates pathogen transmission. However, these studies focusing on single-host systems usually neglect that increasing connectivity can increase species diversity which might reduce pathogen transmission via the 'dilution effect', a hypothesis whose generality is still disputed. On the other hand, studies investigating the generality of the dilution effect were usually conducted without considering habitat structure, which is surprising as species loss is often driven by habitat fragmentation. Using a simple general model to link fragmentation to the dilution effect, we determined the effect of connectivity on disease risk and explored when the dilution effect can be detected. We showed that landscape structure can largely modify the diversity-disease relationship. The net impact of connectivity on disease risk can be either positive or negative, depending on the relative importance of the facilitation effect (through increasing contact rates among patches) versus the dilution effect (via increasing species richness). We also demonstrated that different risk indices (i.e. infection prevalence and abundance of infected hosts) react differently to increasing connectivity and species richness. Our study may contribute to the current debate on the dilution effect, and a better understanding of the impacts of fragmentation on disease risks.

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.

Host resistance, population structure and the long-term persistence of bubonic plague: contributions of a modelling approach in the Malagasy focus

Although bubonic plague is an endemic zoonosis in many countries around the world, the factors responsible for the persistence of this highly virulent disease remain poorly known. Classically, the endemic persistence of plague is suspected to be due to the coexistence of plague resistant and plague susceptible rodents in natural foci, and/or to a metapopulation structure of reservoirs. Here, we test separately the effect of each of these factors on the long-term persistence of plague. We analyse the dynamics and equilibria of a model of plague propagation, consistent with plague ecology in Madagascar, a major focus where this disease is endemic since the 1920s in central highlands. By combining deterministic and stochastic analyses of this model, and including sensitivity analyses, we show that (i) endemicity is favoured by intermediate host population sizes, (ii) in large host populations, the presence of resistant rats is sufficient to explain long-term persistence of plague, and (iii) the metapopulation structure of susceptible host populations alone can also account for plague endemicity, thanks to both subdivision and the subsequent reduction in the size of subpopulations, and extinction-recolonization dynamics of the disease. In the light of these results, we suggest scenarios to explain the localized presence of plague in Madagascar.

Bubonic plague, known to have marked human history by three deadly pandemics, is an infectious disease which mainly circulates in wild rodent populations and is transmitted by fleas. Although this disease can be quickly lethal to its host, it has persisted on long-term in many rodent populations around the world. The reasons for this persistence remain poorly known. Two mechanisms have been invoked, but not yet explicitly and independently tested: first, the spatial structure of rodent populations (subdivision into several subpopulations) and secondly, the presence of, not only plague-susceptible rodents, but also plague-resistant ones. To gain insight into the role of the above two factors in plague persistence, we analysed a mathematical model of plague propagation. We applied our analyses to the case of Madagascar, where plague has persisted on central highlands since the 1920s and is responsible for about 30% of the human cases worldwide. We found that the long-term persistence of plague can be explained by the presence of any of the above two factors. These results allowed us to propose scenarios to explain the localized presence of plague in the Malagasy highlands, and help understand the persistence of plague in many wild foci.

Local persistence and extinction of plague in a metapopulation of great gerbil burrows, Kazakhstan

Speculation on how the bacterium Yersinia pestis re-emerges after years of absence in the Prebalkhash region in Kazakhstan has been ongoing for half a century, but the mechanism is still unclear. One of the theories is that plague persists in its reservoir host (the great gerbil) in so-called hotspots, i.e. small regions in which the conditions remain favourable for plague to persist during times where the conditions in the Prebalkhash region as a whole have become unfavourable for plague persistence. In this paper we use a metapopulation model that describes the dynamics of the great gerbil. With this model we study the minimum size of an individual hotspot and the combined size of multiple hotspots in the Prebalkhash region that would be required for Y. pestis to persist through an inter-epizootic period. We show that the combined area of hotspots required for plague persistence is so large that it would be unlikely to have been missed by existing plague surveillance. This suggests that persistence of plague in that region cannot solely be explained by the existence of hotspots, and therefore other hypotheses, such as survival in multiple host species, and persistence in fleas or in the soil should be considered as well.

Modelling the Dynamics of Host-Parasite Interactions: Basic Principles

Mathematical modelling is a valuable tool for the analysis of the infectious diseases spread. Dynamical models may help to represent and summarize available knowledge on transmission and disease evolution, to test assumptions and analyse scenarios, and to predict outcomes of the host-pathogen interactions. This chapter aims at introducing basic concepts and methods of epidemiological modelling, in order to provide a starting point for further developments. After positioning modelling in the process of disease investigation, we first present the main principles of model building and analysis, using simple biological and also mathematical systems. We then provide an overview of the methods that can be employed to describe more complex systems. Last, we illustrate how the modelling approach may help for different practical purposes, including evaluation of control strategies. A brief conclusion discusses the challenge of including genetic and molecular variability in epidemiological modelling.

Landscape genetics highlights the role of bank vole metapopulation dynamics in the epidemiology of Puumala hantavirus

Rodent host dynamics and dispersal are thought to be critical for hantavirus epidemiology as they determine pathogen persistence and transmission within and between host populations. We used landscape genetics to investigate how the population dynamics of the bank vole Myodes glareolus, the host of Puumala hantavirus (PUUV), vary with forest fragmentation and influence PUUV epidemiology. We sampled vole populations within the Ardennes, a French PUUV endemic area. We inferred demographic features such as population size, isolation and migration with regard to landscape configuration. We next analysed the influence of M. glareolus population dynamics on PUUV spatial distribution. Our results revealed that the global metapopulation dynamics of bank voles were strongly shaped by landscape features, including suitable patch size and connectivity. Large effective size in forest might therefore contribute to the higher observed levels of PUUV prevalence. By contrast, populations from hedge networks highly suffered from genetic drift and appeared strongly isolated from all other populations. This might result in high probabilities of local extinction for both M. glareolus and PUUV. Besides, we detected signatures of asymmetric bank vole migration from forests to hedges. These movements were likely to sustain PUUV in fragmented landscapes. In conclusion, our study provided arguments in favour of source-sink dynamics shaping PUUV persistence and spread in heterogeneous, Western European temperate landscapes. It illustrated the potential contribution of landscape genetics to the understanding of the epidemiological processes occurring at this local scale.

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.

Persistence of canine distemper virus in the Greater Yellowstone ecosystem's carnivore community

Canine distemper virus (CDV) is an acute, highly immunizing pathogen that should require high densities and large populations of hosts for long-term persistence, yet CDV persists among terrestrial carnivores with small, patchily distributed groups. We used CDV in the Greater Yellowstone ecosystem's (GYE) wolves (Canis lupus) and coyotes (Canis latrans) as a case study for exploring how metapopulation structure, host demographics, and multi-host transmission affect the critical community size and spatial scale required for CDV persistence. We illustrate how host spatial connectivity and demographic turnover interact to affect both local epidemic dynamics, such as the length and variation in inter-epidemic periods, and pathogen persistence using stochastic, spatially explicit susceptible-exposed-infectious-recovered simulation models. Given the apparent absence of other known persistence mechanisms (e.g., a carrier or environmental state, densely populated host, chronic infection, or a vector), we suggest that CDV requires either large spatial scales or multi-host transmission for persistence. Current GYE wolf populations are probably too small to support endemic CDV. Coyotes are a plausible reservoir host, but CDV would still require 50000-100000 individuals for moderate persistence (> 50% over 10 years), which would equate to an area of 1-3 times the size of the GYE (60000-200000 km2). Coyotes, and carnivores in general, are not uniformly distributed; therefore, this is probably a gross underestimate of the spatial scale of CDV persistence. However, the presence of a second competent host species can greatly increase the probability of long-term CDV persistence at much smaller spatial scales. Although no management of CDV is currently recommended for the GYE, wolf managers in the region should expect periodic but unpredictable CDV-related population declines as often as every 2-5 years. Awareness and monitoring of such outbreaks will allow corresponding adjustments in management activities such as regulated public harvest, creating a smooth transition to state wolf management and conservation after > 30 years of being protected by the Endangered Species Act.

Impact of the infection period distribution on the epidemic spread in a metapopulation model

Epidemic models usually rely on the assumption of exponentially distributed sojourn times in infectious states. This is sometimes an acceptable approximation, but it is generally not realistic and it may influence the epidemic dynamics as it has already been shown in one population. Here, we explore the consequences of choosing constant or gamma-distributed infectious periods in a metapopulation context. For two coupled populations, we show that the probability of generating no secondary infections is the largest for most parameter values if the infectious period follows an exponential distribution, and we identify special cases where, inversely, the infection is more prone to extinction in early phases for constant infection durations. The impact of the infection duration distribution on the epidemic dynamics of many connected populations is studied by simulation and sensitivity analysis, taking into account the potential interactions with other factors. The analysis based on the average nonextinct epidemic trajectories shows that their sensitivity to the assumption on the infectious period distribution mostly depends on , the mean infection duration and the network structure. This study shows that the effect of assuming exponential distribution for infection periods instead of more realistic distributions varies with respect to the output of interest and to other factors. Ultimately it highlights the risk of misleading recommendations based on modelling results when models including exponential infection durations are used for practical purposes.

Influence of infection rate and migration on extinction of disease in spatial epidemics

Extinction of disease can be explained by the patterns of epidemic spreading, yet the underlying causes of extinction are far from being well understood. To reveal a mechanism of disease extinction, a cellular automata model with both birth, death rate and migration is presented. We find that, in single patch, when the infection rate is small or large enough, the disease will disappear for a long time. When the invasion form is in the coexistence of stable spiral and turbulent wave state, the disease will persist. Also, we find that the migration has dual effects on the epidemic spreading. On one hand, in the extinction region of single patch, if the migration rate is large enough, there is a phase transition from the disease free to endemic state in two patches. On the other hand, migration will induce extinction in the regime, which can ensure the persistence of the disease in single patch, due to emergence of anti-phase synchrony. The results obtained well reveal the effect of infection rate and migration on the extinction of the disease, which enriches the finding in the filed of epidemiology and may provide some new ideas to control the disease in the real world.

Modelling the spread of Bovine Viral Diarrhoea Virus (BVDV) in a managed metapopulation of cattle herds

In numerous epidemiological models developed within a metapopulation framework, it is assumed that a single infected individual introduced into a patch infects the whole patch and that the proportion of infected individuals into infected patches is consistent over time and among patches. If this approach is relevant for rapidly spreading pathogens, it is less appropriate for moderately spreading pathogens, like the Bovine Viral Diarrhoea Virus (BVDV), characterized by a variability in within-patch prevalence. Our objective is to study the respective influence of neighbouring relationships and animal movements on the spread of BVDV in a managed metapopulation of 100 cattle herds. Infection dynamics is represented by two coupled stochastic compartmental models in discrete-time: a within-herd and a between-herd models. Animal movements are mechanistically modelled. They largely influence the BVDV persistence, the prevalence in infected herds and the epidemic size. Neighbouring relationships only influence epidemic size. Whatever the neighbouring relationships, the infection does not persist in the metapopulation without animal movement between herds. The proposed model can be easily adapted for different herd contact structures.

Variations in MIC value caused by differences in experimental protocol

The minimal inhibitory concentration (MIC) of an antibiotic for a microorganism quantifies the effectiveness in reducing growth or the bactericidal ability of the compound. Measurements of MIC's carried out using different protocols should be comparable. Several of the factors that influence the outcome of the measurement vary between protocols. Variations in the MIC estimate were examined for E. coli and amoxicillin as well as tetracycline and for Pseudomonas putida and enrofloxacin. Duration of the measurement, density of the starting culture, the use of optical density or cell counts to determine growth and the induction of resistance can cause differences of a factor of up to 8 in the MIC value. While this does not hamper the reporting of trends by researchers adhering to the same protocol, it may affect assessments based on the absolute value of the MIC of a given combination of microorganism and antibiotic.