CHAOS ANALYSIS AND CONTROL FOR A CLASS OF SIR EPIDEMIC MODEL WITH SEASONAL FLUCTUATION

被引：10
|
作者：
Zhang, Yi [1 ,2 ]
Zhang, Qingling [1 ]
Zhang, Fuzhen [3 ]
Bai, Fenglan [4 ]
机构：
[1] Northeastern Univ, Inst Syst Sci, Shenyang 110819, Liaoning, Peoples R China
[2] Shenyang Univ Technol, Sch Sci, Shenyang 110870, Peoples R China
[3] Nova SE Univ, Div Math Sci & Technol, Ft Lauderdale, FL 33314 USA
[4] Dalian Jiaotong Univ, Sch Sci, Dalian 116028, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIOMATHEMATICS | 2013年 / 6卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Epidemic model; differential-algebraic system; seasonal fluctuation; chaos; tracking control; NONLINEAR INCIDENCE; GLOBAL STABILITY; PULSE;
D O I：
10.1142/S1793524512500635
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, the problems of chaos and chaos control for a class of susceptible-infected-removed (SIR) epidemic model with seasonal fluctuation are investigated. The seasonality in outbreak is natural among infectious diseases, as the common influenza, A type H1N1 influenza and so on. It is shown that there exist chaotic phenomena in the epidemic model. Furthermore, the tracking control method is used to control chaotic motions in the epidemic model. A feedback controller is designed to achieve tracking of an ideal output. Thus, the density of infected individuals can converge to zero, in other words, the disease can be disappeared. Finally, numerical simulations illustrate that the controller is effective.
引用
收藏
页数：11
相关论文
共 50 条
  • [21] Optimal control for a SIR epidemic model with limited quarantine
    Rocío Balderrama
    Javier Peressutti
    Juan Pablo Pinasco
    Federico Vazquez
    Constanza Sánchez de la Vega
    Scientific Reports, 12
  • [22] Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model
    Mandal, P. S.
    Banerjee, M.
    MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2012, 7 (03) : 99 - 116
  • [23] Traveling Wave Solutions for a Class of Discrete Diffusive SIR Epidemic Model
    Zhang, Ran
    Wang, Jinliang
    Liu, Shengqiang
    JOURNAL OF NONLINEAR SCIENCE, 2021, 31 (01)
  • [24] Traveling Wave Solutions for a Class of Discrete Diffusive SIR Epidemic Model
    Ran Zhang
    Jinliang Wang
    Shengqiang Liu
    Journal of Nonlinear Science, 2021, 31
  • [25] On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach
    Zakary O.
    Rachik M.
    Elmouki I.
    International Journal of Dynamics and Control, 2017, 5 (3) : 917 - 930
  • [26] Analysis of a delayed SIR epidemic model with pulse vaccination
    Gao, Shujing
    Teng, Zhidong
    Xie, Dehui
    CHAOS SOLITONS & FRACTALS, 2009, 40 (02) : 1004 - 1011
  • [27] Analysis of SIR epidemic model with information spreading of awareness
    Kabir, K. M. Ariful
    Kuga, Kazuki
    Tanimoto, Jun
    CHAOS SOLITONS & FRACTALS, 2019, 119 : 118 - 125
  • [28] Stability and bifurcation analysis in a discrete SIR epidemic model
    Hu, Zengyun
    Teng, Zhidong
    Zhang, Long
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2014, 97 : 80 - 93
  • [29] Stability analysis and optimal vaccination of an SIR epidemic model
    Zaman, Gul
    Kang, Yong Han
    Jung, Il Hyo
    BIOSYSTEMS, 2008, 93 (03) : 240 - 249
  • [30] Qualitative analysis of an SIR epidemic model with stage structure
    Jia Jianwen
    Li Qiuying
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (01) : 106 - 115
12345