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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

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

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.

• Q332
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