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时滞随机SIS传染病模型

黄佩,周少波   

  1. 1. 华中科技大学数学与统计学院, 武汉 430074; 2. 华中科技大学 数学与统计学院湖北省工程模型与科学计算重点实验室, 武汉 430074
  • 出版日期:2021-03-25 发布日期:2021-06-22

黄佩, 周少波. 时滞随机SIS传染病模型[J]. 系统科学与数学, 2021, 41(3): 615-626.

HUANG Pei, ZHOU Shaobo. A Stochastic SIS Epidemic Model with Time Delay[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(3): 615-626.

A Stochastic SIS Epidemic Model with Time Delay

HUANG Pei, ZHOU Shaobo   

  1. 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074; 2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074
  • Online:2021-03-25 Published:2021-06-22
考虑了时滞随机SIS (susceptible-infected-susceptible)传染病模型, 研究了系统解的存在唯一性, 灭绝性及持久性, 证明了在一定条件下, 减少有利疾病扩散的随机干扰, 或者增加有利于减少感染的随机干扰, 都可使得疾病消亡, 并且研究了使疾病持久存在的因素. 最后, 用计算机仿真证实了文章所得的结论.
In this paper, we have considered a stochastic SIS (susceptible-infected-susceptible) epidemic models with time delay. We first prove the existence and uniqueness, extinction and persistent of the system. Then we prove that it is able to make the disease die out by reducing the stochastic disturbance that is favorable to the spread of the disease, or increasing the stochastic disturbance that is beneficial to reduce the infection. Moreover, we study the factors that make the disease last for a long time. Finally, we support our analytical results with numerical simulations.
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