An SIS patch model with variable transmission coefficients

Abstract

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.