ASYMPTOTIC PROFILES OF ENDEMIC EQUILIBRIUM OF A DIFFUSIVE SIS EPIDEMIC SYSTEM WITH NONLINEAR INCIDENCE FUNCTION IN A HETEROGENEOUS ENVIRONMENT

We consider an SIS epidemic reaction-diffusion system with nonlinear incidence function of the form (SIp)-I-q (0 < p < 1, q > 0) whose total population number is conserved all the time. We establish the asymptotic behavior of endemic equilibrium with respect to small mobility of either the susceptible or infected population. In comparison with the findings of X. Wen, J. Ji, and B. Li; and Y. Wu and X. Zou for the SIS model with the bilinear incidence function, our results show that a nonlinear incidence mechanism may enhance the disease persistence provided that the total population number is small and the mobility of the susceptible population is controlled to be small.