Abstract

In this talk, I will present our recent work on an SIS epidemic reaction-diffusion model with standard incidence and a saturated treatment term. Unlike classical models with a linear recovery rate, the basic reproduction number R_0 no longer acts as a threshold for disease extinction or persistence. We establish several results on the global dynamics of the system, demonstrating that the disease may either die out or persist even when R_0=1. In a homogeneous environment, we identify parameter regimes that govern the existence and non-existence of spatial patterns when R_0<1. This behavior sharply contrasts with the case R_0≥1, where no pattern formation occurs. This is a joint work with Huicong Li, Jinzhe Suo and Zhi-An Wang.