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.