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.


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