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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (2): 295-309.doi: 10.3969/j.issn.1005-3085.2023.02.009

• • 上一篇    下一篇

具隔离和潜伏期传染性的随机SEIR模型的稳定性和灭绝性

秦闯亮1,   杜金姬1,   慧远先2   

  1. 1. 信阳学院数学与统计学院，河南 信阳 464000 
    2. 黄淮学院数学与统计学院，河南 驻马店 463000
  • 收稿日期:2020-12-09 接受日期:2022-04-29 出版日期:2023-04-15 发布日期:2023-06-20
  • 基金资助:
    国家自然科学基金 (11971127)；河南省高等学校重点项目 (23B110014).

Stabilization and Extinction of a Stochastic SEIR Model with Infectivity in Incubation Period and Homestead-isolation on the Susceptible

QIN Chuangliang1,   DU Jinji1,   HUI Yuanxian2   

  1. 1. School of Mathematics and Statistics, Xinyang College, Xinyang, Henan 464000 
    2. School of Mathematics and Statistics, Huanghuai University, Zhumadian, Henan 463003
  • Received:2020-12-09 Accepted:2022-04-29 Online:2023-04-15 Published:2023-06-20
  • Supported by:
    The National Natural Science Foundation of China (11971127); the Key Research Project of Universities and Colleges in Henan Province (23B110014).

PDF (PC)

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摘要：

考虑了随机扰动对流行病的影响，建立了具有疾病潜伏期传染性和易感者宅基地隔离的随机关联模型。首先证明了该模型整体正解的存在唯一性。其次，证明了传染病在某些条件下会消失。然后，在适当的条件下，利用随机李亚普诺夫函数方法，讨论了随机模型的解在相应的无病平衡点周围的渐近行为，并且该随机系统存在唯一的平稳分布。最后，通过数值模拟验证了理论分析的结果。

关键词: 随机SEIR传染病模型, 稳定性, 灭绝性

Abstract:

In this paper, we consider the influence of stochastic disturbances on epidemic, and establish a stochastic SEIR model with infectivity in incubation period and homestead-isolation on the susceptible. Firstly, the existence and uniqueness of the global positive solution of the model is proved. secondly, we show that the infectious disease will vanish under some conditions. Then, under appropriate conditions, by using the stochastic Lyapunov function method, we discuss the asymptotically behaviors of the solution of the stochastic model around the disease-free equilibrium point of the corresponding deterministic model and there is a unique stationary distribution for the stochastic system. Finally, numerical simulations are provided to illustrate our results.

Key words: stochastic SEIR epidemic model, stabilization, extinction

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