Derivation of a spatial replicator system with environmental heterogeneity from a co-colonization SIS model with N strains and P patches

Abstract

The interplay between local and regional processes in the dynamics of ecological communities remains a challenge to model, analyze and predict. This is especially notable in infectious diseases with multiple strains, where several layers of heterogeneity can interact, including strain biological traits and environmental heterogeneity among locations where disease can spread. Motivated by this challenge, here we study a Susceptible-Infected-Susceptible (SIS) model with co-colonization and multiple interacting strains where hosts move between a set of inter-connected patches. Under strain similarity and slow migration rate, we derive a fast-slow approximation of the global metacommunity dynamics, resulting in a spatial replicator system for N strains across P patches. In contrast to a discretization approach on the spatial slow-fast PDE originally derived in(Le and Madec, 2023), here the slow-fast reduction is managed ab-initio by a new approach using strongly the Perron-Frobenius Theorem for Metzler matrices, which simplifies and clarifies the structure of the co-colonization system.