Multiplicity of endemic equilibria for a diffusive SIS epidemic model with mass-action transmission mechanism

We study a diffusive SIS epidemic model with mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria when the basic reproduction number, $\mathcal{R}_0$, is either less than one or greater than one. Previous studies have left open the question of extinction of disease or persistence when $\mathcal{R}_0