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Volume 7,     Number 4,     Winter 1999

 

GLOBAL STABILITY OF
SEIRS MODELS IN EPIDEMIOLOGY
MICHAEL Y. LI, JAMES S. MULDOWNEY AND P. VAN DEN DRIESSCHE

Abstract. SEIRS epidemiological models with general nonlinear incidence in a constant population are studied. Under the restriction that the rate of loss of immunity is either sufficiently small or sufficiently large, global asymptotic stability of the endemic equilibrium when it is unique is proved using a geometric approach to global stability for nonlinear autonomous systems. For the special case of bilinear incidence, this global result completes determination of a sharp threshold for the classical SEIRS model under the above restriction.

 

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