单纯复形上的随机 SIS 传染病模型

数学物理学报 ›› 2024, Vol. 44 ›› Issue (5): 1392-1399.

单纯复形上的随机 SIS 传染病模型

杨红^1,^*(),张晓光²

¹太原师范学院数学与统计学院山西晋中 030619
²山西大学数学科学学院太原 030006

收稿日期:2023-10-19 修回日期:2023-12-26 出版日期:2024-10-26 发布日期:2024-10-16
通讯作者: *杨红, E-mail: yanghong_9002@163.com
基金资助:
国家自然科学基金(12231012);山西省自然科学基金(20210302123441);山西省自然科学基金(202303021212249);博士科研启动经费(410220139)

A Stochastic SIS Epidemic Model on Simplex Complexes

Yang Hong^1,^*(),Zhang Xiaoguang²

¹Department of Mathematics and Statistics, Taiyuan Normal University, Shanxi Jinzhong 030619
²School of Mathematical Sciences, Shanxi University, Taiyuan 030006

Received:2023-10-19 Revised:2023-12-26 Online:2024-10-26 Published:2024-10-16
Supported by:
National Natural Science Foundation of China(12231012);Shanxi Province Natural Science Research General Project(20210302123441);Shanxi Province Natural Science Research General Project(202303021212249);Start-up Funding for Doctoral Research at Taiyuan Normal University(410220139)

摘要/Abstract

摘要：

该文考虑了噪声影响下单纯复形上的随机 SIS 传染病模型, 比较了 1 单形传染强度 ($\lambda$) 或 2 单形传染强度 ($\lambda_{\triangle}$) 受噪声扰动后的模型在随机稳定性和随机分岔方面的区别. 结果表明: 对于随机模型而言, 噪声作用于 $\lambda$ 所在的低次项后传染病依概率 1 灭绝的阈值与噪声强度有关, 反之作用于 $\lambda_{\triangle}$ 所在的高次项则对阈值无影响; 增大 $\lambda_{\triangle}$, 会使稳态概率密度函数靠近 1 处出现峰值、峰值变大或峰值趋近于 1, 即: 增大 $\lambda_{\triangle}$, 会促进疾病的传播.

关键词: 单纯复形, SIS 传染病模型, 随机稳定性, 随机分岔

Abstract:

This paper considers the SIS stochastic epidemic model on the simplex complex under the influence of noise, the difference in stochastic stability and stochastic bifurcation of models with 1 simplex contagion strength ($\lambda$) or 2 simplex contagion strength ($\lambda_{\triangle}$) perturbed by noise is compared. The results show that the threshold of the stochastic model infectious disease extinction with probability 1 after the noise acts on the low-order term where $\lambda$ is located is related to the noise intensity, and vice versa when it acts on the high-order term where $\lambda_{\triangle}$ is located has no effect; increasing $\lambda_{\triangle}$ causes the point near 1 of the steady-state probability density function appearing peak, larger the pear value or nearing the 1 point, that is, increasing $\lambda_{\triangle}$ promotes the outbreak of the disease.

Key words: Simplex complexes, SIS epidemic model, Stochastic stability, Stochastic bifurcation

中图分类号:

O211.63

杨红, 张晓光. 单纯复形上的随机 SIS 传染病模型[J]. 数学物理学报, 2024, 44(5): 1392-1399.

Yang Hong, Zhang Xiaoguang. A Stochastic SIS Epidemic Model on Simplex Complexes[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1392-1399.

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