Coexistence of a two-strain SIS reaction-diffusion model with saturated incidence

A two-strain SIS reaction-diffusion epidemic model with saturated incidence rate is investigated. The uniform boundedness of the classical solutions for the model is established. The reproduction numbers and invasion numbers for both strains, as well as the basic reproduction number, are defined implicitly. The disease-free equilibrium is locally stable when the basic reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium is established under certain conditions. Furthermore, the global attractivity of both strain-1 and strain-2 equilibria is confirmed under certain conditions, leading to competitive exclusion. Coexistence of both strains is demonstrated in two cases: (ⅰ) a heterogeneous environment with identical saturation coefficients for both strains, and (ⅱ) a homogeneous environment with distinct saturation coefficients for each strain. The results indicate that when the reproduction number of one strain exceeds that of the other, the coexistence of both strains is determined by the saturation coefficient of the strain with the higher reproduction number. Finally, numerical simulations are conducted to validate the theoretical results.