Dynamically consistent discrete epidemic model with modified saturated incidence rate

被引：29
|
作者：
Suryanto, A. [1 ]
Kusumawinahyu, W. M. [1 ]
Darti, I. [1 ]
Yanti, I. [1 ]
机构：
[1] Brawijaya Univ, Dept Math, Fac Sci, Jl Veteran 65145, Malang, Indonesia
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2013年 / 32卷 / 02期
关键词：
Dynamically consistent; Nonstandard finite difference scheme; SIR epidemic model; Modified saturated incidence rate;
D O I：
10.1007/s40314-013-0026-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A nonstandard finite difference scheme is constructed to solve a SIR epidemic model with modified saturated incidence rate. The dynamical properties of the resulting discrete system are then analyzed. It is shown that the discrete system is dynamically consistent with the continuous model because it preserves essential properties of the considered model, such as positivity and boundedness of solutions, equilibrium points and their stability properties. These properties are confirmed by numerical simulations.
引用
收藏
页码：373 / 383
页数：11
相关论文
共 50 条
  • [31] Global attractivity of a discrete SIRS epidemic model with standard incidence rate
    Wang, Lei
    Teng, Zhidong
    Jiang, Haijun
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (05) : 601 - 619
  • [32] Stability analysis of a delayed sir epidemic model with diffusion and saturated incidence rate
    Abta, Abdelhadi
    Boutayeb, Salahaddine
    Laarabi, Hassan
    Rachik, Mostafa
    Alaoui, Hamad Talibi
    PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2020, 1 (04):
  • [33] A note on the stationary distribution of stochastic SEIR epidemic model with saturated incidence rate
    Qixing Han
    Liang Chen
    Daqing Jiang
    Scientific Reports, 7
  • [34] DYNAMICS OF SIS EPIDEMIC MODEL WITH THE STANDARD INCIDENCE RATE AND SATURATED TREATMENT FUNCTION
    Wei, Jingjing
    Cui, Jing-An
    INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2012, 5 (03)
  • [35] Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate
    Shatanawi, Wasfi
    Arif, Muhammad Shoaib
    Raza, Ali
    Rafiq, Muhammad
    Bibi, Mairaj
    Abbasi, Javeria Nawaz
    CMC-COMPUTERS MATERIALS & CONTINUA, 2020, 64 (02): : 797 - 811
  • [36] Asymptotic profile of endemic equilibrium to a diffusive epidemic model with saturated incidence rate
    Wang, Yan'e
    Wang, Zhiguo
    Lei, Chengxia
    MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2019, 16 (05) : 3885 - 3913
  • [37] A note on the stationary distribution of stochastic SEIR epidemic model with saturated incidence rate
    Han, Qixing
    Chen, Liang
    Jiang, Daqing
    SCIENTIFIC REPORTS, 2017, 7
  • [38] Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate
    Lu, Min
    Huang, Jicai
    Ruan, Shigui
    Yu, Pei
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (03) : 1859 - 1898
  • [39] On the nonstandard numerical discretization of SIR epidemic model with a saturated incidence rate and vaccination
    Suryanto, Agus
    Darti, Isnani
    AIMS MATHEMATICS, 2021, 6 (01): : 141 - 155
  • [40] Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate
    Sun, Deguo
    Li, Qing
    Zhao, Wencai
    FRACTAL AND FRACTIONAL, 2023, 7 (07)
12345