摘要
研究了一类具有不同一般形式的接触率β1(N),β2(N)和β3(N)且潜伏者,染病者和移出者均具有传染力的SEIR传染病模型,得到疾病流行与否的阈值——基本再生数R0.运用Liapunov函数方法,证明了当R0<1时,无病平衡点E0全局渐近稳定,疾病最终消失;利用Hurwitz判据定理,证明了当R0>1时,E0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.
A type of SEIR epidemic model with different general contact ratesβ1(N),β2(N)andβ3(N),having infective force in all the latent,infected and immune periods,was studied.And the threshold,basic reproductive number R0 which determines whether a disease is extinct or not,was obtained.By using the Liapunov function method,it was proved that the disease-free equilibrium E0 is globally asymptotically stable and the disease eventually goes away if R0<1.It was also proved that in the case where R0>1,E0 is unstable and the unique endemic equilibrium E*is locally asymptotically stable by Hurwitz criterion theory.It is shown that when disease-induced death rate and elimination rate are zero,the unique endemic equilibriumE*is globally asymptotically stable and the disease persists.
基金
国家自然科学基金(11201277
11402054)资助
