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 R0R0 is determined. It is shown that the disease-free equilibrium is globally asymptotically stable if R0⩽1R0⩽1, and the disease is uniformly persistent and there exists at least one endemic equilibrium if R0>1R0>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 R0>1R0>1. Numerical calculations are performed to illustrate some results for the case with two patches.

► During outbreaks of serious infectious diseases such as the SARS outbreak in 2003 and the H1N1 influenza pandemic in 2009, public media has massive reports on the diseases.
► People follow the reports and choose to protect themselves by reducing their social activities and direct contacts with others which leads to a reduction of effective contacts.
► 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.