摘要
研究了一类潜伏类和移出类均具有传染力的SEIR传染病模型,得到了疾病流行与否的阈值:基本再生数R_0.运用Liapunov函数方法,证明了当R_0<1时,无病平衡点E_0全局渐近稳定,疾病最终消失;利用Hurwitz判据定理,证明了当R_0>1时,E_0不稳定,地方病平衡点E*局部渐近稳定;当因病死亡率和剔除率为零时,地方病平衡点E*全局渐近稳定,疾病持续存在.最后,进行了计算机数值模拟来进一步验证理论结果的正确性.
A type of SEIR epidemic model with infective force in the latent and immune period was studied.And the threshold,basic reproductive number R_0 which determines whether a disease is extinct or not,was obtained.By using the Liapunov function method,it was proved that the disease-free equilibriumE_0 is globally asymptotically stable and that the disease eventually goes away if R_0<1.It was also proved that in the case where R_0>1,E_0 is unstable and the unique endemic equilibriumE*is locally asymptotically stable by Hurwitz criterion theory.It was shown that when disease-induced death rate and elimination rate are zero,the unique endemic equilibriumE*is globally asymptotically stable and the disease persists.Finally,numerical simulation was given to illustrate the theoretical analysis.
基金
国家自然科学基金(11201277
11402054)
安徽省自然科学基金重点项目(KJ2015A308
KJ2015A331)资助
关键词
基本再生数
平衡点
全局渐近稳定性
LIAPUNOV函数
轨道渐近稳定
basic reproductive number
equilibrium
global asymptotically stability
Liapunov function
orbital asymptotical stability
