J Austral Math Soc Ser B 34 pp282--295, 1993.

Global stability of the endemic equilibrium and uniform persistence in epidemic models with speculation

Xiaodong Lin and Joseph W.-H. So

Abstract

We consider the epidemic model with subpopulations introduced in Hethcote [5]. It is shown that if the endemic equilibrium exists, then the system is uniformly persistent. Moreover, the endemic equilibrium is globally asymptotically stable under the assumption of small effective contact rates between different subpopulations.

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Authors

Xiaodong Lin

Department of Applied Mathematics, University of Waterloo, Ontario, Canada N2L 3G1.

Joseph W.-H. So

Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1.