Spatiotemporal Evolution of Coinfection Dynamics: A Reaction-Diffusion Model

This paper investigates the impact of spatial heterogeneity on the interaction between similar strains in a dynamical system of coinfecting strains with spatial diffusion. The SIS model studied is a reaction-diffusion system with spatially heterogeneous coefficients. The study considers two limiting cases: asymptotically slow and fast diffusion coefficients. When the diffusion coefficient is small, the slow system is shown to be a semilinear system of "replicator equations," describing the spatiotemporal evolution of the strains' frequencies. This system is of the reaction-advection-diffusion type, with an additional advection term that explicitly involves the heterogeneity of the associated neutral system. In the case of fast diffusion, traditional methods of aggregating variables are used to reduce the spatialized SIS problem to a homogenized SIS system, on which the results of the non-spatial model can be applied directly.