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Volume 20,     Number 2,     Summer 2012

 

ON THE GLOBAL STABILITY OF SEIRS
MODELS IN EPIDEMIOLOGY
YUANJI CHENG AND XIUXIANG YANG

Abstract. The global stability of SEIRS models with nonlinear incidence rates was conjectured in [15] and has been stated as an outstanding open question for classical bilinear models in [13]. By applying the Poincare-Bendixson property of dynamic systems in space, the authors in [11] have proven the conjecture for the bilinear model with a suciently long average immunity period, and in [13] the authors have shown the case with a suciently long average infection period. In this paper, we solve the open problem for the bilinear case completely, and furthermore have relaxed the constraint on the general nonlinear transmission function for global stability.

 

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