On an SIS epidemic model with power‐like nonlinear incidence and with/without cross‐diffusion

Abstract We study global existence, boundedness, and convergence of nonnegative classical solutions to a Neumann initial‐boundary value problem for the following possibly cross‐diffusive SIS (susceptible–infected–susceptible) epidemic model with power‐like infection mechanism generalizing the standard mass action incidence: in a bounded smooth domain . The infection force of the form with is a natural extension of the classical mass action type , and the cross‐diffusive term with describes the effect that susceptible individuals tend to move away from higher density of infected populations. Global existence and boundedness of classical solutions are established in certain parameter ranges, and threshold/nonthreshold long‐time behaviors of global bounded solutions are also detected. Our findings significantly improve and extend previous related studies.