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Volume 17,     Number 1,     Spring 2009

 

GLOBAL STABILITY OF AN EPIDEMIC MODEL
IN A PATCHY ENVIRONMENT
MICHAEL Y. LI AND ZHISHENG SHUAI

Abstract. We investigate an SIR compartmental epidemic model in a patchy environment where individuals in each compartment can travel among n patches. We derive the basic reproduction number R0 and prove that, if R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable. In the case of R0 > 1, we derive sufficient conditions under which the endemic equilibrium is unique and globally asymptotically stable.

 

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