Spatial profiles of a reaction-diffusion epidemic model with nonlinear incidence mechanism and constant total population

Abstract

This paper examines a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and constant total population. The infection mechanism in the model is described by a nonlinear term of the form $S^q{I}^p$ with $0<p\le 1$ and $q>0$. We explore the spatial profiles of the endemic equilibrium with respect to small movement rates of susceptible and/or infected populations. Our results extend and improve existing results in the literature, providing further insights into how transmission mechanisms and population mobility limitations impact the spread of infectious diseases. We reinforce and complement the theoretical results with numerical simulations.