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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 ›› 2022, Vol. 39 ›› Issue (5): 725-738.doi: 10.3969/j.issn.1005-3085.2022.05.004

• • 上一篇    下一篇

随机潜蚤病模型的动力学行为分析

孔丽丽,   李录苹,   陈慧琴,   康淑瑰   

  1. 山西大同大学数学与统计学院，大同  037009
  • 出版日期:2022-10-15 发布日期:2022-12-15
  • 基金资助:
    国家自然科学基金(11871314)；大同市平城区科技计划项目(202106)；山西大同大学产教融合科研项目(2019CXK9; 2019CXK11).

Dynamic Behavior Analysis of a Stochastic Tungiasis Epidemic Model

KONG Lili,   LI Luping,   CHEN Huiqin,   KANG Shugui   

  1. School of Mathematics and Statistics, Shanxi Datong University, Datong 037009
  • Online:2022-10-15 Published:2022-12-15
  • Supported by:
    The National Natural Science Foundation of China (11871314); the Science and Technology Project of Pingcheng District of Datong (202106); the Industry-education integration Scientific Research Project of Shanxi Datong University (2019CXK9; 2019CXK11).

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摘要： 潜蚤病是贫困地区的一种人畜共患病，其发病过程极易受到随机波动环境因素的影响。因此，建立并讨论了一类以正确卫生习惯为控制策略的随机潜蚤病模型。首先，通过构造恰当的Lyapunov函数并利用It$\hat{\rm o}$公式证明了随机系统全局正解的存在唯一性。其次，在一定的条件下证明了随机系统的正解围绕在确定性系统平衡点附近的振荡行为。最后，通过数值模拟验证了理论结果的正确性。数值结果表明，当随机干扰强度足够大时将会导致疾病灭绝。

关键词: 随机潜蚤病模型, 平衡点, 渐近行为, Lyapunov函数, It$\hat{\rm o}$公式

Abstract: Tungiasis is a zoonotic disease in poverty-stricken areas, and its pathogenesis is easily affected by random fluctuation environmental factors. Therefore, a class of stochastic tungiasis model with correct hygiene habits as a control strategy is established and discussed. Firstly, the existence and uniqueness of global positive solutions of stochastic systems are proved by proper Lyapunov functions and It$\hat{\rm o}$ formula. Secondly, under certain conditions, the oscillation behavior of the positive solution of the stochastic system around the equilibrium point of the deterministic system is proved. Finally, the correctness of the theoretical analysis is verified by the numerical simulation. The results indicate that the disease will become extinct when the intensity of random interference is high enough.

Key words: stochastic tungiasis model, equilibrium point, asymptotic behavior, Lyapunov function, It$\hat{\rm o}$ formula

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