广西师范大学学报（自然科学版） ›› 2020, Vol. 38 ›› Issue (2): 144-155.doi: 10.16088/j.issn.1001-6600.2020.02.017

• CCIR2019 • 上一篇    下一篇

具有双疾病的随机SIRS传染病模型的灭绝性与持久性分析

李海燕, 韦煜明*, 彭华勤   

  1. 广西师范大学数学与统计学院,广西桂林541006
  • 收稿日期:2018-12-27 发布日期:2020-04-02
  • 通讯作者: 韦煜明(1974—), 男, 广西桂平人, 广西师范大学教授, 博士。 E-mail: ymwei@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11771104); 广西自然科学基金(2018GXNSFAA294084,2018GXNSFBA281140); 广西研究生教育创新计划项目(XYCSZ2019083,JGY2019030)

Persistence and Extinction of a Stochastic SIRS EpidemicModel with Double Epidemic Hypothesis

LI Haiyan, WEI Yuming*, PENG Huaqin   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2018-12-27 Published:2020-04-02

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摘要： 本文研究了一类具有饱和发生率的双疾病随机SIRS传染病模型, 通过构造合适的Lyapunov函数, 运用Itô公式, 证明了全局正解的存在唯一性;得到了在某些条件下决定疾病灭绝和持久的随机基本再生数; 探讨了环境变化对疾病的影响。结果表明, 白噪声强度在一定条件下会抑制疾病的爆发。通过数值模拟验证结论的正确性。

关键词: 随机基本再生数, 双疾病, 灭绝性, 持久性

Abstract: In this paper, a stochastic SIRS epidemic model with saturated incidence rate and double epidemic hypothesis is investigated. By constructing suitable Lyapunov function and applying Itô formula, the global existence and uniqueness of positive solution are proved, and the random basic reproductive number which determines disease extinction and persistence under certain conditions is obtained. The influence of disease is also discussed when the environment changes. The results show that the intensity of white noise suppresses the outbreak of the disease under certain conditions.The conclusions are simulated through the numerical method.

Key words: stochasticbasicreproductionnumber, doubleepidemichypothesis, extinction, persistence

中图分类号: 

  • O211.63
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