The effect of local prevention in an SIS model with diffusion

The effect of spatially partial prevention of infectious disease is considered as an application of population models in inhomogeneous environments. The area is divided into two ractangles, and the local contact rate between infectives and susceptibles is sufficiently reduced in one rectangle. The dynamics of the infection considered here is that described by an SIS model with diffusion. Then the problem can be reduced to a Fisher type equation, which has been fully studied by many authors, under some conditions. The steady states of the linearized equation are considered, and a Nagylaki type result for predicting whether the infection will become extinct over time or not is obtained. This result leads to some necessary conditions for the extinction of the infection.