Multi-strain SIS dynamics with coinfection across heterogeneous patches

We study a Susceptible-Infected-Susceptible (SIS) model with coinfection and multiple interacting strains where hosts move between a set of inter-connected patches. Under strain similarity and slow migration, we obtain a discrete model, following the corresponding continuous space model derived in (Le and Madec, 2023). In this model, the fast variables are total prevalence of susceptibles, single-infected and co-infected hosts in each patch ( S, I, D ). The slow variables are strain frequencies ( z ) in each patch. These local strain frequencies in each patch are governed by a replicator-like equation, where an additional contribution arises from migration, scaled explicitly by emergent patch heterogeneity. In our model, the strains can vary epidemiologically within- and between-patches along several traits, including transmission rates, clearance rates, priority effects and pairwise susceptibilities to coinfection; a complexity that totally defies straightforward prediction of their ecological outcome. However, harnessing the analytical advantage of this model reduction, we can investigate several key scenarios for the outcome of the coupled P-patch N-strain system. We focus on the global and local factors that promote or hinder coexistence, and on regimes that favour spatial segregation of strains, or ultimately competitive exclusion. The analytical tractability of this meta-population model, illustrated with several examples for N = 2 strains and 2-3 patches, makes it a useful framework for application to general multi-species co-colonization systems with migration across heterogeneous environments.