A diffusive SIS epidemic model in a heterogeneous environment: Random dispersion vs. nonlocal dispersion

This research studies a spatiotemporal SIS epidemic model that incorporates both long-range and small-range mobilities to represent the two distinct diffusion strategies, local and nonlocal. The nonlocal dispersion operator is used to capture the long-range mobility of the susceptible, which can diffuse freely through the studied domain. The random diffusion is employed to account for the limitations imposed on the movement of the infected, which are allowed to disperse locally in the neighborhood of the original point. We also assume that the studied space is heterogeneous, which means that all parameters are assumed to be space-dependent. This poses significant challenges to the stability analysis for the steady states as well as the discussion on the existence of endemic steady states, and studying the asymptotic profiles of endemic steady states. The analysis is conducted in terms of the basic reproduction number, which serves as a threshold parameter. We also investigate the asymptotic profiles of endemic steady states when dispersal rates tend to zero or infinity. The findings have implications for disease modeling and control due to insights into the effects of different mechanisms of mobility on epidemic dynamics and provide useful information on the efficiency of mobility control in containing the epidemic.