Mathematical analysis of the dynamics of some reaction-diffusion models for infectious diseases

Abstract

We study some reaction-diffusion systems for infectious diseases and investigate how the dynamics is impacted by the movement of populations and spatial heterogeneity of the environment. General conditions for the existence, uniqueness and stability of the coexistence steady states are established. Our analysis revealed two mechanisms for the coexistence of strains: (i) when the ratio of the transmission probability of two strains falls into some intermediate ranges; (ii) when the diffusion rate of two strains falls into proper ranges. Interestingly, when there is no coexistence of strains, it is possible for the “weak” strain to be dominant for some intermediate range of diffusion rates, in strong contrast to small and large diffusion cases where the “weak” strain always goes extinct.