An SIS patch model with variable transmission coefficients.

In this paper, an SIS patch model with non-constant transmission coefficients is formulated to investigate the effect of media coverage and human movement on the spread of infectious diseases among patches. The basic reproduction number R(0) is determined. It is shown that the disease-free equilibrium is globally asymptotically stable if R(0)≤1, and the disease is uniformly persistent and there exists at least one endemic equilibrium if R(0)>1. In particular, when the disease is non-fatal and the travel rates of susceptible and infectious individuals in each patch are the same, the endemic equilibrium is unique and is globally asymptotically stable as R(0)>1. Numerical calculations are performed to illustrate some results for the case with two patches.