Multi-strain SIS dynamics with coinfection across heterogeneous patches

We investigate a spatially structured Susceptible-Infected-Susceptible (SIS) model with coinfection, multiple interacting strains, and host movement across a network of heterogeneous patches. Motivated by the need to capture how local epidemiological processes and spatial connectivity jointly shape multi-strain pathogen dynamics, we consider a metacommunity framework in which hosts migrate between interconnected habitats. Under assumptions of strain similarity and slow migration, and following the continuous-space formulation of Le et al. (2023), we derive a reduced discrete model that separates fast epidemiological dynamics from slow strain dynamics. The fast variables describe the total densities of susceptible, singly infected, and co-infected hosts within each patch, while the slow variables track strain frequencies locally. These frequencies evolve according to a replicator-like equation that combines local selection with an explicit migration term modulated by patch heterogeneity. The model allows N strains to differ across multiple epidemiological traits- such as transmission, clearance, and coinfection interactions - both within and between P patches, leading to complex and potentially non-intuitive system behavior. By leveraging the analytical tractability of the reduced framework, we characterize how spatial structure, host movement, and environmental heterogeneity influence key ecological outcomes, including coexistence, competitive exclusion, and spatial segregation of strains. Illustrating numerically low-dimensional cases (N=2, P=2, 3), we show how the interplay between local dynamics and spatial coupling shapes global system behavior. More broadly, this framework provides a tractable and mechanistically grounded approach for studying multi-strain pathogen dynamics in heterogeneous environments, contributing to ongoing efforts to bridge ecological realism, computational feasibility, and analytical insight in spatial ecology and infectious diseases.