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An SIS patch model with variable transmission coefficients. (English) Zbl 1218.92064
Summary: 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.
##### MSC:
 92D30 Epidemiology 37N25 Dynamical systems in biology 65C40 Computational Markov chains (numerical analysis)
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