中文摘要：

研究一类具有一般非线性接触率和疫苗有效期的时滞SEIQR传染病模型,确定决定疾病传播与否的阈值,得到无病平衡点和地方病平衡点。利用Hurwitz准则,给出无病平衡点局部渐近稳定的充分条件;通过构造Lyapunov泛函方法及La Salle不变准则,分析无病平衡点及地方病平衡点全局渐近稳定性;利用Hopf分支理论讨论了地方病平衡点处Hopf分支的存在性。

英文摘要：

Consider a class of time delayed SEIQR epidemic models with general nonlinear contact rate and vaccination valid term. The threshold for the spread of the disease is determined, and the diseasefree equilibrium point and the endemic equilibrium point are obtained. With Hurwitz criterion, sufficient conditions for the local asymptotic stability of the disease-free equilibrium are given. The global asymptotical stability of disease-free point and the endemic equilibrium point are proved through Liapunov function and LaSalle invariant principle. Furthermore, the existence of Hopf bifurcation on the endemic equilibrium is discussed by Hopf bifurcation theorems.