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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (5): 10-17.doi: 10.6040/j.issn.1671-9352.0.2016.531

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一类具有不同发生率的双疾病随机SIS传染病模型的动力学研究

张道祥1,2,胡伟1,陶龙1,周文1   

  1. 1.安徽师范大学数学计算机科学学院, 安徽 芜湖 241002;2.赫尔辛基大学数理统计学院, 芬兰 赫尔辛基 00014
  • 收稿日期:2016-11-18 出版日期:2017-05-20 发布日期:2017-05-15
  • 作者简介:张道祥(1979— ),男,博士,副教授,研究方向为微分方程理论及其应用. E-mail:18955302433@163.com
  • 基金资助:
    国家自然科学基金青年项目(11302002)

Dynamics of a stochastic SIS epidemic model with different incidences and double epidemic hypothesis

ZHANG Dao-xiang1,2, HU Wei1, TAO Long1, ZHOU Wen1   

  1. 1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China;
    2. Department of Mathematics and Statistics, University of Helsinki, Helsinki 00014, Finland
  • Received:2016-11-18 Online:2017-05-20 Published:2017-05-15

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摘要： 提出了一类新的具有不同发生率的双疾病随机SIS传染病模型。 借助Lyapunov函数和伊藤公式, 获得了模型中疾病的灭绝以及系统持久性的充分条件。 结果表明不仅强噪声能够使得传染病灭绝,而且弱噪声在一定条件下也能使传染病灭绝。

关键词: 随机传染病模型, 阈值, 持久性, 灭绝性

Abstract: We propose a new mathematical model with two different incidence rates and double epidemic hypothesis. By the Lyapunov function and Itôs formula, we explore and obtain the threshold of a stochastic SIS system for the extinction and thepermanence in mean of two epidemic diseases. The results show that not only a large stochastic disturbance but also a small stochastic disturbance can cause infectious diseases to go to extinction.

Key words: stochastic epidemic model, extinction, threshold, permanence

中图分类号: 

  • Q332
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