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Volume 19,     Number 4,     Winter 2011

 

GLOBAL STABILITY OF A 9-DIMENSIONAL
HSV-2 EPIDEMIC MODEL
Dedicated to Prof. H. I. Freedman on the occasion of his 70th birthday
ZHILAN FENG, ZHIPENG QIU AND ZI SANG

Abstract. This paper focuses on the global stability of a 9-dimensional epidemiological model for the transmission dynamics of HSV-2. The model incorporates heterosexual interactions in which a single male population and two groups of female populations with different activity levels are considered. The method of global Lyapunov functions as well as the LaSalle Invariance Principle are used to show that the basic reproduction number provides a sharp threshold which completely determines the global dynamics of the model. That is, in the case when the production number is less than or equal to one, the disease-free equilibrium is globally asymptotically stable; whereas in the case when the reproduction number is greater than one, a unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region and the disease will persist at the endemic equilibrium if it is initially present.

 

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