Competitive exclusion and coexistence of a nonlocal diffusive two-strain SIS epidemic model with Neumann boundary condition

Competitive exclusion and coexistence phenomena are fundamental inquiries in the exploration of the various manifestations of a pathology. Furthermore, the long-distance dispersal of individuals frequently alters the dynamics of an epidemic. In this manuscript, we introduce a nonlocal diffusive two-strain SIS model with Neumann boundary conditions in a spatially heterogeneous landscape. Initially, we derive the explicit expressions of the basic reproduction number and the invasion reproduction number corresponding to each strain using variational methods. Subsequently, we rigorously establish the phenomena of competitive exclusion and coexistence, and comprehensively analyze their asymptotic behaviors of the endemic steady states as diffusive diffusion rates evolve. Finally, we unveil that the combined influences of the heterogeneous environment and individual movement lead to the emergence of coexistence between the two strains.