一个具非单调传染率的SEIR传染病模型的全局稳定性(英文)

Glogal Stability of a SEIR Epidemic Model with Nonmonotone Incidence Rate

本文研究一类描述某种严重疾病的传染数目变大时在心理上产生影响的非单调传染率的SEIR传染病模型.研究表明模型的动力行为和疾病的爆发完全由基本再生数R_0决定.当R_0≤1时,无病平衡点是全局稳定的,疾病消亡;当R_0>1时,地方病平衡点是全局稳定的,疾病持续且发展成地方病.

In this paper,a SEIR epidemic model with nonmonotone incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infective is getting larger,is investigated.It is shown that the global dynamics and the outcome of the disease are completely determined by the basic reproduction number R0.If R0≤1 holds,then the disease-free equilibrium is globally stable and the disease dies out.If R_01 holds,then the unique endemic equilibrium is globally stable and the disease persists at an endemic equilibrium state.