Invasion and Persistence of Infectious Agents in Fragmented Host Populations

Abstract

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.

Epidemiological, evolutionary, and economic determinants of eradication tails

“…Plugging a standard SIS model into the framework of Jesse et al (2011) allows us to assess endemicity, analyze properties of the stationary state, and the action of selection on disease properties. To speak about the effect of investment cost structure, we make some simple additional assumptions.…”

“…The framework of Jesse et al (2011) requires us to specify the compartments, the patch size, all relevant transitions and all corresponding transition rates (which may be state-dependent).…”

“…Co-infections or immunity are not considered; recovered hosts become susceptible again. With patch state frequencies described by a vector p and the disperser pool states described by a vector d , the dynamical equations take the pseudo-linear form (Jesse et al, 2011) ( )…”

“…For our case of populations spread over a large number of small, equallyconnected patches, Metz and Gyllenberg (2001) showed that a suitable fitness proxy is found in m R , the number of secondary patch invasions resulting from a single primary patch invasion, obtained as the dominant eigenvalue of a matrix describing the complete reinvasion cycle from patch to patch via a "disperser pool". Jesse et al (2011) discussed the application of this idea to general compartment models as used in epidemiology and introduced a calculation framework to obtain m R values for such models in a straight-forward manner (for related approaches to this problem see, e.g., Ball et al, 1997;Pellis et al, 2012).…”

“…While this seems self-evident, it may happen that, given all other parameters, even a disease-free host population cannot survive, or that with a viable host population, the disease still cannot become endemic for the adaptive trait under consideration (here: infectivity and host mobility as linked by the trade-off function). Viability and endemicity can be assessed by calculating the invasion fitness for hosts in an empty landscape, or of strains in a disease-free host population, respectively (Jesse et al, 2011).…”