## 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