Extending the SIR epidemic model

被引:111
|
作者
Satsuma, J
Willox, R
Ramani, A
Grammaticos, B
Carstea, AS
机构
[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan
[2] Ecole Polytech, CNRS, UMR 7644, F-91128 Palaiseau, France
[3] Univ Paris 07, GMPIB, F-75251 Paris, France
[4] Inst Phys & Nucl Engn, Bucharest, Romania
基金
日本学术振兴会;
关键词
population dynamics; epidemic; discrete-time; cellular automaton;
D O I
10.1016/j.physa.2003.12.035
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We investigate possible extensions of the susceptible-infective-removed (SIR) epidemic model. We show that there exists a large class of functions representing interaction between the susceptible and infective populations for which the model has a realistic behaviour and preserves the essential features of the classical SIR model. We also present a new discretisation of the SIR model which has the advantage of possessing a conserved quantity, thus making possible the estimation of the non-infected population at the end of the epidemic. A cellular automaton SIR is also constructed on the basis of the discrete-time system. (C) 2003 Elsevier B.V. All rights reserved.
引用
收藏
页码:369 / 375
页数:7
相关论文
共 50 条
  • [1] The effect of impulsive vaccination on an SIR epidemic model
    Shi, Ruiqing
    Jiang, Xiaowu
    Chen, Lansun
    APPLIED MATHEMATICS AND COMPUTATION, 2009, 212 (02) : 305 - 311
  • [2] 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
  • [3] Bifurcations for a deterministic SIR epidemic model in discrete time
    Xiaoliang Zhou
    Xiaopei Li
    Wu-Sheng Wang
    Advances in Difference Equations, 2014
  • [4] Global dynamics of an SIR epidemic model with nonlocal diffusion
    Kuniya, Toshikazu
    Wang, Jinliang
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 43 : 262 - 282
  • [5] Bifurcations for a deterministic SIR epidemic model in discrete time
    Zhou, Xiaoliang
    Li, Xiaopei
    Wang, Wu-Sheng
    ADVANCES IN DIFFERENCE EQUATIONS, 2014,
  • [6] A susceptible-infected removal (SIR) epidemic model
    Das, PK
    De, SS
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2000, 31 (07): : 783 - 795
  • [7] Qualitative analysis of an SIR epidemic model with stage structure
    Jia Jianwen
    Li Qiuying
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (01) : 106 - 115
  • [8] Numerical Approaching of SIR Epidemic Model for Propagation of Computer Worms
    Valdez, J. S.
    Guevara, P.
    Audelo, J.
    Delgado, G.
    IEEE LATIN AMERICA TRANSACTIONS, 2015, 13 (10) : 3452 - 3460
  • [9] Explicit formulae for the peak time of an epidemic from the SIR model
    Turkyilmazoglu, Mustafa
    PHYSICA D-NONLINEAR PHENOMENA, 2021, 422
  • [10] SI and SIR epidemic models
    Allen, LJS
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2001, 7 (05) : 759 - 761