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Global stability of an epidemic model in a patchy environment. (English) Zbl 1216.34054

The authors consider an SIR compartment epidemic model in a patch environment where individuals in each compartment can travel among patches. They derive the basic reproduction number \(\mathcal{R}_0\) and prove that the disease free equilibrium is globally asymptotically stable if \(\mathcal{R}_0 \leq 1\). When \(\mathcal{R}_0 > 1\), they obtain some sufficient conditions under which there is a unique endemic equilibrium which is globally asymptotically stable.

MSC:

34D23 Global stability of solutions to ordinary differential equations
92D30 Epidemiology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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