具有指数出生的麻疹传染病模型的稳定性分析

Stability analysis of measles model with exponential born

建立了一类具有指数出生、标准发生率的SVEIR麻疹传染病模型,考虑了新生儿的免疫接种.计算得到模型的平衡点,通过线性化、Hurwitz判据和构造Lyapunov函数等方法研究了模型平衡点的稳定性问题.当R0<1时,模型仅存在全局渐近稳定的无病平衡点;当R0> 1时,无病平衡点不稳定,地方性平衡点全局渐近稳定.得出结论,增加新生儿的免疫接种,延长潜伏期或者尽量在潜伏期内将麻疹疾病治愈好,降低疾病的传染率等因素,从而达到将麻疹疾病消灭的结果.

In this paper,a measles epidemic model with exponential birth and standard inci-dence was established. The model＇s equilibrium point was calculated, and the stability of themodel＇s equilibrium point was studied by use the linearization, Hurwitz criterion and Lya-punov functions. When R0 〈 1, the model only hada globally asymptotically stable disease-free equilibrium ; When R0 〉 1, the disease-free equilibrium was unstable, the local equilib-rium was globally asymptotically stable. It could be concluded that increase the immunizationof newborns, extend the incubation period, or try to cure measles diseases in the incubationperiod, reduce the transmission rate of diseases and other factors, so as to achieve the elimi-nation of measles diseases.