a b s t r a c tThe drive to understand the invasion, spread and fade out of infectious disease in structured populations has produced a variety of mathematical models for pathogen dynamics in metapopulations. Very rarely are these models fully coupled, by which we mean that the spread of an infection within a subpopulation affects the transmission between subpopulations and vice versa. It is also rare that these models are accessible to biologists, in the sense that all parameters have a clear biological meaning and the biological assumptions are explained. Here we present an accessible model that is fully coupled without being an individual-based model. We use the model to show that the duration of an epidemic has a highly non-linear relationship with the movement rate between subpopulations, with a peak in epidemic duration appearing at small movement rates and a global maximum at large movement rates. Intuitively, the first peak is due to asynchrony in the dynamics of infection between subpopulations; we confirm this intuition and also show the peak coincides with successful invasion of the infection into most subpopulations. The global maximum at relatively large movement rates occurs because then the infectious agent perceives the metapopulation as if it is a single well-mixed population wherein the effective population size is greater than the critical community size.

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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 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 . 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 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 can be calculated and expressed in terms of the key determinants of epidemiological dynamics.

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.