具有非单调发生率的时滞随机传染病模型分析

数学物理学报 ›› 2017, Vol. 37 ›› Issue (6): 1162-1175.

具有非单调发生率的时滞随机传染病模型分析

孟笑莹

中南财经政法大学统计与数学学院武汉 430073

收稿日期:2016-10-21 修回日期:2017-03-25 出版日期:2017-12-26 发布日期:2017-12-26
作者简介:孟笑莹,E-mail:mxy922@163.com
基金资助:
国家自然科学基金（61503415）

Analysis of a Stochastic Delayed Epidemic Model with a Non-Monotonic Incidence Rate

Meng Xiaoying

The School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073

Received:2016-10-21 Revised:2017-03-25 Online:2017-12-26 Published:2017-12-26
Supported by:
Supported by the NSFC (61503415)

摘要/Abstract

摘要： 传染病模型易受外界随机因素的干扰.该文提出一类具有非单调发生率的时滞随机传染病模型.利用Lyapunov方法及伊藤公式，证明了该模型具有唯一一个正全局解和该模型的无病平衡点是随机稳定的，并且得到了相应的确定型模型地方病平衡点在随机扰动下的渐近性.最后，利用数值仿真图例对理论结果加以验证说明.

关键词: 随机传染病模型, 稳定性, 渐近性, Lyapunov函数, 伊藤公式

Abstract: Epidemic models are often subject to random perturbations. This article proposes a stochastic delayed epidemic model with a non-monotonic incidence rate. By the Lyapunov method and Itô's formula, the existence of a unique global positive solution of the model and the stability of the disease-free equilibrium of the model are proved. The asymptotic behavior around the endemic equilibrium of the associated definite model is obtained. Finally, numerical simulations are presented to illustrate the results.

Key words: Stochastic epidemic model, Stability, Asymptotic behavior, Lyapunov function, Itô's formula

中图分类号:

O175.1

孟笑莹. 具有非单调发生率的时滞随机传染病模型分析[J]. 数学物理学报, 2017, 37(6): 1162-1175.

Meng Xiaoying. Analysis of a Stochastic Delayed Epidemic Model with a Non-Monotonic Incidence Rate[J]. Acta mathematica scientia,Series A, 2017, 37(6): 1162-1175.

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