Global dynamics of a spatially heterogeneous diffusive two-strain epidemic model with varying total population

This work investigates the dynamics of solutions to a diffusive two-strain epidemic model with varying total population size. First, assuming a spatially homogeneous environment, we show that the long-term dynamics of the diffusive model mirrors that of the corresponding system of ODE epidemic model. In this setting, we establish that the competitive-exclusion principle holds. However, when the environment is spatially heterogeneous, the global dynamics of the diffusive epidemic model is more challenging. Under some biologically meaningful assumptions, we establish results concerning the existence, uniqueness, and global stability of coexistence endemic equilibrium. Our findings highlight the complex interplay between population movement and spatial heterogeneity in shaping the dynamics of multi-strain infectious diseases.