一类具有非线性发生率的随机SIS传染病模型阈值动力学行为研究

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 197-208.

• 论文 • 上一篇

一类具有非线性发生率的随机SIS传染病模型阈值动力学行为研究

张丽萍¹, 赵瑜², 原三领¹

1. 上海理工大学理学院上海 200093;
2. 宁夏医科大学公共卫生与管理学院银川 750004

收稿日期:2016-11-15 修回日期:2017-06-08 出版日期:2018-02-26 发布日期:2018-02-26
通讯作者: 原三领 E-mail:sanling@usst.edu.cn
基金资助:
国家自然科学基金（11271260，11671260，11601250）、沪江基金（B14005）、上海市一流学科建设资助项目（XTKX2012）和宁夏医科大学校级科研项目（XT2017002）

Threshold Dynamical Behaviors of a Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

Zhang Liping¹, Zhao Yu², Yuan Sanling¹

1. Business School, University of Shanghai for Science and Technology, Shanghai 200093;
2. School of Public Health and Management, Ningxia Medical University, Yinchuan 750004

Received:2016-11-15 Revised:2017-06-08 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (11271260, 11671260, 11601250), the Hujiang Foundation of China (B14005), the Shanghai Leading Academic Discipline Project(XTKX2012) and the Ningxia Medical University Research Project (XT2017002)

摘要/Abstract

摘要： 考虑到环境波动对传染病传播过程的影响，该文研究了一类具有非线性发生率的SIS随机传染病动力学模型的阈值动力学行为.利用Feller检测和随机比较原理得到了决定疾病绝灭或持久的随机基本再生数R₀^s，即当R₀^s<1时，疾病将趋于绝灭；当R₀^s=1时，疾病也将趋于绝灭，这一结论补充了已有随机阈值结果；当R₀^s>1时，疾病将随机持续下去，并给出了最终传染规模的范围估计.最后，利用数值仿真验证了文中所得出的结论并根据实际生物参数说明了环境波动对不同大小尺度群体中SIS传染病传播的影响.

关键词: 随机SIS传染病模型, 随机基本再生数, Feller检测, 阈值动力学行为

Abstract: In this paper, a stochastic susceptible-infected-susceptible (SIS) epidemic model with nonlinear incidence rate is considered to investigate the effect of environment fluctuation on the transmission threshold dynamical behaviors. By using Feller's test and stochastic comparison principle, we obtain the stochastic basic reproduction number R₀^s, which determined whether the disease persistent or not. If R₀^s<1, the disease will go to extinction. If R₀^s=1, the disease will also go to extinction in probability, which has not been reported in the known literatures. In addition, if R₀^s>1, the disease will stochastic persistence and the scale range estimation of spread is presented eventually. Finally, numerical simulations are carried out to support the theoretical results. According to the actual parameter, it illustrated the environmental fluctuation have different effect on different size of group.

Key words: Stochastic SIS epidemic model, Feller's test, Basic reproduction number, Threshold dynamical behaviors

中图分类号:

O211.6

张丽萍, 赵瑜, 原三领. 一类具有非线性发生率的随机SIS传染病模型阈值动力学行为研究[J]. 数学物理学报, 2018, 38(1): 197-208.

Zhang Liping, Zhao Yu, Yuan Sanling. Threshold Dynamical Behaviors of a Stochastic SIS Epidemic Model with Nonlinear Incidence Rate[J]. Acta mathematica scientia,Series A, 2018, 38(1): 197-208.

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一类具有非线性发生率的随机SIS传染病模型阈值动力学行为研究

Threshold Dynamical Behaviors of a Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

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