数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1247-1259.

• 论文 • 上一篇    

一类具有接种和潜伏期的传染病模型及动力学分析

张鑫喆, 贺国峰, 黄刚   

  1. 中国地质大学数学与物理学院 武汉 430074
  • 收稿日期:2018-11-28 修回日期:2019-03-20 发布日期:2019-11-08
  • 通讯作者: 黄刚 E-mail:huanggang@cug.edu.cn
  • 基金资助:
    国家自然科学基金(11571326)

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

Zhang Xinzhe, He Guofeng, Huang Gang   

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan 430074
  • Received:2018-11-28 Revised:2019-03-20 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (11571326)

摘要: 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.

关键词: 疫苗接种, 潜伏期, Lyapunov泛函, 全局渐近稳定

Abstract: 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.

Key words: Vaccination, Latent period, Lyapunov functional, Globally asymptotically stable

中图分类号: 

  • O175.1