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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。
A class of SEIQR epidemic model with general non-linear contact rate and vaccine expiration is studied to determine the threshold of determining whether the disease is transmitted or not. The disease-free equilibrium and endemic equilibrium are obtained. The Hurwitz criterion is used to give the sufficient condition for the local asymptotic stability of disease-free equilibrium. By constructing Lyapunov functional method and La Salle invariance criterion, the global asymptotic stability of disease-free equilibrium and endemic equilibrium is analyzed. Hopf bifurcation theory The existence of Hopf bifurcation at endemic disease equilibrium is discussed.