[1]吴长青,黄勇庆,朱长荣*.一类SIRS传染病模型的稳定性[J].四川师范大学学报(自然科学版),2018,(05):596-601.[doi:10.3969/j.issn.1001-8395.2018.05.005]
 WU Changqing,HUANG Yongqing,ZHU Changrong.Stability of One SIRS Epidemic Model[J].Journal of SichuanNormal University,2018,(05):596-601.[doi:10.3969/j.issn.1001-8395.2018.05.005]
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一类SIRS传染病模型的稳定性()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年05期
页码:
596-601
栏目:
基础理论
出版日期:
2018-06-15

文章信息/Info

Title:
Stability of One SIRS Epidemic Model
文章编号:
1001-8395(2018)05-0596-06
作者:
吴长青12 黄勇庆3 朱长荣1*
1.重庆大学 数学与统计学院, 重庆 401331; 2.重庆育才中学, 重庆 400050; 3.重庆第一中学, 重庆 400030
Author(s):
WU Changqing12 HUANG Yongqing3 ZHU Changrong1
1.College of Mathematics and Statistics, Chongqing University, Chongqing 401331; 2.Chongqing Yucai High School, Chongqing 400050; 3.The First Middle School of Chongqing, Chongqing 400030
关键词:
局部稳定性 稳定平衡点 不稳定平衡点 退化平衡点
Keywords:
local stability stable equilibrium unstable equilibrium degenerate equilibrium
分类号:
O193
DOI:
10.3969/j.issn.1001-8395.2018.05.005
文献标志码:
A
摘要:
在总人口非常数条件下,研究了一类SIRS传染病模型的所有非负平衡点,以及平衡点的存在性、局部稳定性.运用微分方程定性理论证明了三维系统在不同条件下地方病平衡点分别是稳定平衡点、不稳定平衡点或退化平衡点.使用数学软件Matlab进行数值模拟,模拟结果很好地说明了本文结论的正确性.
Abstract:
The dynamics of an SIRS epidemic model are studied.With the assumption that the total population is non-constant, the stabilities of the model in R3 are considered.By using dynamic system theory, we show that the model has up to three equilibria.The positive equilibrium can be stable, unstable or degenerate for different parameter values.Using the mathematical software Matlab, we carry out some simulations to illustrate all the theoretical results.

参考文献/References:

[1] KERMACK W O, MCKENDRICK A G. Contributions to the mathematical theory of epidemics[J]. Bull Math Biol,1991,53(1):57-87.
[2] WANG W D. Backward bifurcation of an epidemic model with treatment[J]. Math Biosci,2006,201(1/2):58-71.
[3] XIAO Y J, ZHANG W P, DENG G F, et al. Stability and Bogdanv-Takens bifurcation of an SIS epidemic model with saturated treatment function[J]. Math Problem Engine,2015,2015:1-14.
[4] SONG Z G, XU J, LI Q H. Local and Global Bifurcations in an SIRS Epidemic Model[J]. Appl Math Comput,2009,214(2):534-547.
[5] ZHANG J H, JIA J W, SONG X Y. Analysis of an SEIR epidemic model with saturated incidence and saturated treatment function[J]. Sci World J,2014,2014:910421.
[6] BRAUER F, CARLOS C C. Mathematical Models in Population Biology and Epidemiology[M]. New York:Springer-Verlag,2012.
[7] 马知恩,周义昌,王稳地. 传染病动力学的数学建模与研究[M]. 北京:科学出版社,2004.
[8] LIU W M, HETHCOTE H W, LEVIN S A. Dynamical behavior of epidemiological models with nonlinear incidence rates[J]. J Math Biol,1987,25(4):359-380.
[9] RUAN S G, WANG W D. Dynamical behavior of an epidemic model with a nonlinear incidence rate[J]. J Diff Eqns,2003,188(1):135-163.
[10] ZHU H, CAMPELL S A, WOLKOWICZ G S K. Bifurcation analysis of a predator-prey system with nonmonotonic functional response[J]. SIAM J Appl Math,2002,63(2):636-682.

备注/Memo

备注/Memo:
收稿日期:2017-04-07 接受日期:2017-05-15
基金项目:国家自然科学基金(11671058)
*通信作者简介:朱长荣(1973—),男,教授,主要从事微分方程与动力系统的研究,E-mail:zhuchangrong126@126.com
更新日期/Last Update: 2018-04-15