一类具有接种和潜伏期的传染病模型及动力学分析

Dynamical Properties of a Delayed Epidemic Model with Vaccination and Saturation Incidence

该文提出并研究了一类具有接种和非线性感染率的SVEIR传染病模型,其中时滞用来刻画疾病的潜伏期.讨论了模型平衡点的存在性和局部稳定性以及系统的一致持续性.进一步,通过构造合适的Lyapunov泛函得到平衡点的全局渐近稳定性:当基本再生数小于或等于1,无病平衡点全局渐近稳定,此时疾病将会消除;当基本再生数大于1时,地方病平衡点全局渐近稳定,此时疾病将会持续流行.最后,通过数值模拟验证了前面的理论分析结果,并对疾病的传播和控制给出了合理建议.

In this paper,we propose and study a delayed SVEIR epidemic model with vaccination and saturation incidence.The existence and local stability of equilibria are addressed.By using Lyapunov functionals and Lyapunov-LaSalle invariance principle,it shows that if the basic reproduction number is less than or equal to one,the disease-free equilibrium is globally asymptotically stable and the disease will disappear;and if the basic reproduction number is greater than one,the endemic equilibrium is globally asymptotically stable and the disease will persist.Some numerical simulations are performed to illustrate our analytic results.