具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1861-1872.

• 论文 • 上一篇

具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析

赵彦军¹, 孙晓辉¹, 苏丽¹, 李文轩²

1. 吉林外国语大学国际商学院, 长春 130117;
2. 吉林大学数学学院, 长春 130012

收稿日期:2021-12-03 修回日期:2022-05-30 发布日期:2022-12-16
通讯作者: 赵彦军,E-mail:zhaoyanjun@jisu.edu.cn E-mail:zhaoyanjun@jisu.edu.cn
基金资助:
国家自然科学基金(11271154)

Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate

Zhao Yanjun¹, Sun Xiaohui¹, Su Li¹, Li Wenxuan²

1. International Business School, Jilin International Studies University, Changchun 130117;
2. College of Mathematics, Jilin University, Changchun 130012

Received:2021-12-03 Revised:2022-05-30 Published:2022-12-16
Supported by:
Supported by the NSFC(11271154)

摘要/Abstract

摘要： 该文考虑了一类受环境噪声影响,具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型.通过构造Lyapunov函数并利用$\rm It\hat{o}$公式,证明了全局正解的存在唯一性,得到了决定疾病灭绝或持久的充分条件.最后,利用Matlab进行了数值模拟来说明理论结果的正确性.

关键词: SIRS传染病模型, Logistic增长, Beddington-DeAngelis发生率, 灭绝性, 持久性

Abstract: In this paper, we considered a class of stochastic SIRS epidemic model with logistic growth and Beddington-DeAngelis incidence rate by white noise in the environment. By constructing Lyapunov function and applying $\rm It\hat{o}$ formula, the global existence and uniqueness of positive solution are proved, the sufficient conditions which determines disease extinction and permanence are obtained. Finally, matlab is used for numerical simulation to illustrate the correctness of the theoretical results.

Key words: SIRS epidemic model, Logistic growth, Beddington-DeAngelis incidence rate, Extinction, Permanence

中图分类号:

O211.6

赵彦军, 孙晓辉, 苏丽, 李文轩. 具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析[J]. 数学物理学报, 2022, 42(6): 1861-1872.

Zhao Yanjun, Sun Xiaohui, Su Li, Li Wenxuan. Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1861-1872.

参考文献

[1] Kermack W O, McKendrick A G. Contributions to the mathematical theory of epidemics. Part I. Proc R Soc Lond, 1927, 115:701-721
[2] Zhu Q X. pth moment exponential stability of impulsive stochastic functional differential equations with markovian switching. J Franklin Inst, 2014, 351:3965-3986
[3] Cai Y L, Kang Y, Banerjee M, Wang W M. A stochastic SIRS epidemic model with infectious force under intervention strategies. J Differ Equ, 2015, 259:7463-7502
[4] Zhu Q X, Song S Y, Tang T R. Mean square exponential stability of stochastic nonlinear delay systems. Int J Control, 2017, 90:2384-2393
[5] Pitchaimani M, Rajasekar S P. Global analysis of stochastic SIR model with variable diffusion rates. Tamkang J Math, 2018, 49:155-182
[6] Zhu Q X, Song S Y, Shi P. Effect of noise on the solutions of non-linear delay systems. IET Control Theory Appl, 2018, 12:1822-1829
[7] Wang B, Zhu Q X. Stability analysis of semi-Markov switched stochastic systems. Automatica, 2018, 94:72-80
[8] Pitchaimani M, Rajasekar S P, Zhu Q X. Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function. Physica A, 2019, 535:122300
[9] Zhu Q X. Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Automat Contr, 2019, 64:3764-3771
[10] Hu W, Zhu Q X, Hamid R K. Some improved razumikhin stability criteria for impulsive stochastic delay differential systems. IEEE Trans Automat Contr, 2019, 64:5207-5213
[11] Rajasekar S P, Pitchaimani M. Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses. Chaos Solitons Fractals, 2019, 118:207-221
[12] Cai Y L, Kang Y, Wang W M. A stochastic SIRS epidemic model with nonlinear incidence rate. Appl Math Comput, 2017, 305:221-240
[13] Liu Q, Jiang D Q, Shi N Z, et al. Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence. Physica A, 2017, 469:510-517
[14] Capasso V, Serio G. A generalization of the Kermack-McKendrick deterministic epidemic model. Math Biosci, 1978, 42(1/2):43-61
[15] Xu R, Ma Z E. Global stability of a SIR epidemic model with nonlinear incidence rate and time delay. Nonlinear Analysis:Real World Applications, 2009, 10(5):3175-3189
[16] Xu R, Zhang S H, Zhang F Q. Global dynamics of a delayed SEIS infectious disease model with logistic growth and saturation incidence. Math Method Appl Sci, 2016, 39(12):3294-3308
[17] Miao A Q, Wang X Y, Zhang T Q, et al. Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. Advances in Difference Equations, 2017, 2017:Article number 226
[18] Li J J, Zhi X, Fu C. The stability of an SEIRS model with Beddington-DeAngelis incidence, vertical transmission and time delay. Journal of Anhui Normal University, 2016, 39(1):26-32
[19] Chen Y, Zhao W C. Asymptotic behavior and threshold of a stochastic SIQS epidemic model with vertical transmission and Beddington-DeAngelis incidence. Advances in Difference Equations, 2020, 2020:Article number 353
[20] Lin Y G, Wang L B, Dong X W. Long-time behavior of a regime-switching SIRS epidemic model with degenerate diffusion. Physica A, 2019, 529:121551
[21] Guo X X, Luo J W. Stationary distribution and extinction of SIR model with nonlinear incident rate under Markovian switching. Physica A, 2018, 505:471-481
[22] Liu Q, Jiang D Q. Stationary distribution of a stochastic SIS epidemic model with double diseases and the Beddington-DeAngelis incidence. Chaos, 2017, 27:083126
[23] Liu Q, Jiang D Q, Tasawar H, et al. A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate. Phys A:Statist Mech Appl, 2020, 551:124-152
[24] Liu Q, Jiang D Q, Shi N Z, et al. Dynamical behavior of a stochastic HBV infection model with logistic hepatocyte growth. Acta Mathematica Scientia, 2017, 37B(4):927-940
[25] Zhu L. The asymptotic behavior of a logistic SIR epidemic model with stochastic perturbation. Journal of University of Science and Technology of China, 2019, 49(11):910-919
[26] Arnold L, Horsthemke W, Stuxki J. The influence of external real and white noise the Lotka-Volterra model. Biometrical J, 1979, 21:541-471
[27] May R M. Stability and Complexity in Model Ecosystems. New Jersey:Princetion University Press, 2001
[28] Xu C. Global threshold dynamics of a stochastic differential equation SIS model. J Math Anal Appl, 2017, 477(2):736-757
[29] Gao N, Song Y, Wang X Z, Liu J X. Dynamics of a stochastic SIS epidemic model with nonlinear incidence rates. Advances in difference Equation, 2019, 41:1-19
[30] Wang Y M, Liu G R. Dynamics analysis of a stochastic SIRS epidemic model with nonlinear incidence rate and transfer from infectious to suceptible. Mathematical Biosciences and Engineering, 2019, 16(5):6047-6070

具有Logistic增长和Beddington-DeAngelis发生率的随机SIRS传染病模型定性分析

Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Beddington-DeAngelis Incidence Rate

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

Metrics

本文评价

推荐阅读 0

[1]	王长有,李楠,蒋涛,杨强. 一类具有时滞及反馈控制的非自治非线性比率依赖食物链模型[J]. 数学物理学报, 2022, 42(1): 245-268.
[2]	刘丽雅,蒋达清. 具有一般反应函数与贴壁生长现象的随机恒化器模型的全局动力学行为[J]. 数学物理学报, 2021, 41(6): 1912-1924.
[3]	王双明,樊馨蔓,张明军,梁俊荣. 具周期性潜伏期的SEIR传染病模型的动力学[J]. 数学物理学报, 2020, 40(2): 527-539.
[4]	曹忠威,文香丹,冯微,祖力. 一类具有随机扰动的非自治SIRI流行病模型的动力学行为[J]. 数学物理学报, 2020, 40(1): 221-233.
[5]	张静, 任艳霞. 具有奇异分枝机制的超扩散过程的性质[J]. 数学物理学报, 2010, 30(6): 1474-1484.
[6]	梁志清;陈兰荪. 离散Leslie捕食与被捕食系统周期解的稳定性[J]. 数学物理学报, 2006, 26(4): 634-640.