The SIS model with diffusion of virus in the environment.

In this paper, we propose an SIS-type reaction-diffusion equations, which contains both direct transmission and indirect transmission via free-living and spatially diffusive bacteria/virus in the contaminated environment, motivated by the dynamics of hospital infections. We establish the basic reproduction number ₀ which can act as threshold level to determine whether the disease persists or not. In particular, if ₀<1 ="" ="" ="" ="" ="" ="" ="" ="" ="".