A periodic epidemic model in a patchy environment ✩

An epidemic model in a patchy environment with periodic coefficients is investigated in this paper. By employing the persistence theory, we establish a threshold between the extinction and the uniform persistence of the disease. Further, we obtain the conditions under which the positive periodic solution is globally asymptotically stable. At last, we present two examples and numerical simulations. © 2006 Elsevier Inc. All rights reserved.