一类潜伏期和染病期具有不同传染率的SEIQR传染病模型的稳定性

Stability of an SEIQR Epidemic Model with Different Infection Rates in the Latent Period and the Infected Period

文章研究了一类潜伏期具有饱和传染率且染病期具有双线性传染率的SEIQR流行病模型,求得了模型的基本再生数R_(0),并证明了当R_(0)<1时,模型存在唯一的无病平衡点P_(0)且P_(0)全局渐近稳定;当R_(0)>1时,模型存在两个平衡点,无病平衡点P_(0)不稳定,且当2Aβ1<md时,地方病平衡点P^(*)全局渐近稳定.最后,利用数值模拟验证了结论的正确性并讨论了隔离对传染病模型的影响.

An SEIQR epidemic model with saturating infection rate in incubation period and double linear infection rate in infection period was established in this paper,and give the basic regeneration number R_(0)of the model.It was proved that the diseasefree equilibrium P_(0)is unique and globally asymptotically stable when R_(0)<1;The model have two equilibrium points when R_(0)>1,and the diseasefree equilibrium P_(0)was unstable and endemic equilibrium P^(∗)was global stability if 2Aβ1<md.Finally,the correctness of the conclusion was validated by numerical simulation and the effect of isolation on infectious disease model were discussed.