QUALITATIVE ANALYSIS OF AN EPIDEMIC
MODEL

DONGMEI XIAO AND YUGUI ZHOU

Abstract. In this paper we consider an epidemic model with a complete form of the non-monotonic incidence rate of [18]. This non-monotonic incidence rate describes the effects of psychological factor, protection measures and intervention policies when a serious disease arouses widespread horror and the number of infective is getting larger. By carrying out the qualitative analysis of the model, we show that when a basic reproduction number is less than one, there exist some values of parameters such that the model has a local stable disease free equilibrium and a local stable endemic equilibrium at the same time, and there also exist other values of parameters such that the model has a global stable disease-free equilibrium. These results reveal rich dynamics in the model.