高维传染病模型的Lyapunov函数构造
Lyapunov Functions for Higher-Dimensional Epidemiological Models
DOI: 10.12677/AAM.2020.912259, PDF,    科研立项经费支持
作者: 栾培译, 李 静：临沂大学数学与统计学院，山东 临沂
关键词: Lypunov函数；传染病模型；地方病平衡点；全局稳定性；Lypunov Function； Epidemiological Models； Endemic Equilibrium State； Global Stability
摘要: 本文主要研究几类传染病模型如SIR，SIRS，SIS和SEIR模型的Lypunov函数构造方法，从而获得传染病模型全局稳定性的结论。
Abstract: Lypunov functions for classical epidemiological models are introduced such as SIR, SIRS, SIS and SEIR. Global stability of some epidemiological models is also established.
文章引用：栾培译, 李静. 高维传染病模型的Lyapunov函数构造[J]. 应用数学进展, 2020, 9(12): 2222-2227. https://doi.org/10.12677/AAM.2020.912259

参考文献

[1] Lyapunov, A.M. (1992) The General Problem of the Stability of Motion. Taylor &Francis, London.
[2] Busenberg, S. and Cooke, K. (1993) Vetically Transmitted Diseases in Humans: Models and Dynamics. Springer, Berlin. [Google Scholar] [CrossRef] 
[3] Anderson, R.M. and May, R.M. (1991) Infectious Diseases in Humans: Dynamics and Control. Oxford University Press, Oxford.
[4] Li, M.Y. and Muldowney, J.S. (1995) Global Stability for the SEIR Model in Epidemiology. Mathematical Biosciences, 125, 155-164. [Google Scholar] [CrossRef] [PubMed]
[5] Goh, B.S. (1980) Management and Analysis of Biological Populations. Elsevier Science, Amsterdam.
[6] Cluskey, M. and Connell, C. (2009) Global Stability for an SEIR Epidemiological Model with Varying Infectivity and Infinite Delay. Mathematical Biosciences and Engineering, 6, 603-610. [Google Scholar] [CrossRef] [PubMed]

为你推荐