一类具有饱和发生率的SEIS传染病模型全局稳定性研究

Global Stability of an SEIS Epidemic Model with Saturation Incidence

研究一类易感者和潜伏者都有新增常数输入,疾病具有饱和发生率的SEIS传染病模型.经计算得到模型的基本再生数,证明当基本再生数>1时,模型只存在惟一的地方病平衡点的结论,并利用特征方程和Hurwitz判据分析地方病平衡点的局部稳定性,通过采用第二加性复合矩阵理论证明地方病平衡点的全局渐近稳定性.

In this paper,an SEIS epidemic model with a saturation incidence rate and constant re-cruitments both for the susceptibles and the exposed individuals is investigated. After calculation, we give the expression for the basic reproduction number of the model, and it is also proved that the model has a unique endemic equilibrium if the basic reproduction number is greater than uni-ty. With characteristic equation and Hurwitz criterion,the local stability of the endemic equilibri-um is analyzed. Using the second additive compound matrix theory, the global asymptotic stability of the endemic equilibrium is also derived.