Please wait a minute...
高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (2): 157-164    DOI:
    
Analysis of stability and bifurcation of a SEIR epidemic model with nonlinear incidence
ZHANG Dao-xiang1,2, CAO Lei1
1.College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China
2. College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China
Download:   PDF(0KB)
Export: BibTeX | EndNote (RIS)      

Abstract  Considering the factor of hospital cure, an SEIR epidemic model with nonlinear incidence and nonlinear recovery rate is investigated. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. A backward bifurcation leading to bistability possibly occurs. The global stability of the model is further studied by using the Lyapunov function. The corresponding results in literatures are improved and extended.

Key words： SEIR epidemic model      stability      backward bifurcation      Lyapunov function     
Received: 24 March 2014      Published: 05 June 2018
CLC:  O175.1  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
ZHANG Dao-xiang
CAO Lei
Cite this article:

ZHANG Dao-xiang, CAO Lei. Analysis of stability and bifurcation of a SEIR epidemic model with nonlinear incidence. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 157-164.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I2/157


一类具有非线性发生率的SEIR疾病模型的稳定性和分支分析

考虑医院治疗的因素, 给出了一个具有非线性发生率和非线性康复率的SEIR模型, 讨论该模型的无病平衡点和地方病平衡点, 证明向后分支的出现; 进一步通过应用Lyapunov函数给出了它全局稳定性的分析. 所得结果改进和扩展了文献中的相应结果.

关键词： SEIR模型,  稳定性,  向后分支,  Lyapunov函数 
[1] LIU Jiang, ZHANG Long, JIANG Zhong-chuan, LI Yan-qing. Synchronous control on inverter system of grid connected high-power wind generators with nonlinear and pulse disturbance#br#[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 388-402.
[2] SHI Lei , XIAO Qing-kun , LIU Bao-qing. Existence and stability of front solutions of the amplitude equations for rotating magnetoconvection[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(2): 142-148.
[3] GAO Ping. Strong stability of $(\alpha,\beta)$-mixing sequences[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 405-412.
[4] TIAN Xiao-hong, XU Rui, WANG Zhi-li. Global exponential stability and Hopf bifurcation of inertial Cohen-Grossberg neural networks with time delays in leakage terms[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 428-440.
[5] LI Shao-e, FENG Wei-zhen. Practical stability of impulsive switched systems with time delay by Lyapunov-Razumikhin method[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 327-337.
[6] YANG Yu, ZHOU Jin-ling. Global stability of a diffusive virus dynamics model with Beddington-DeAngelis incidence function[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(2): 161-166.
[7] FU Jin-bo, CHEN Lan-sun, CHENG Rong-fu. Global stability of a delayed viral infection model with latent period and immune response[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 379-388.
[8] XU Chao-qun, LI Hong-en, YUAN San-ling. Study on a stochastic phage-bacteria model in which the death rate of phage is influenced by noise[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 253-261.
[9] YANG Xiao-zhong, ZHANG Xue, WU Li-fei. A kind of efficient difference method for time-fractional option pricing model[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 234-244.
[10] YANG Hong, ZHU Huan. Dynamical behavior of SIR epidemical model with time delay[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 165-170.