首页|一类具有潜伏期检测和外源性再感染的随机结核病模型动力学分析

一类具有潜伏期检测和外源性再感染的随机结核病模型动力学分析

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为探究潜伏期检测、外源性再感染及环境噪声扰动等因素对结核病传播和控制的影响,研究了一类具有潜伏期检测和外源性再感染的结核病模型在随机扰动下的动力学行为.首先,通过构造合适的Lyapunov函数证明了该模型全局正解的存在唯一性,采用Has'minskii理论及一些不等式技巧给出了遍历平稳分布存在唯一性的充分条件;其次,证明了结核病的灭绝性;最后,通过数值模拟验证了理论结果的正确性.结果表明,增加潜伏期检测比例或降低外源性再次感染率可以减少发展为活动性结核病患者的数量,但环境噪声的存在会导致结核病的控制变得复杂.研究证实了在较大的噪声扰动下可以导致结核病的灭绝,从而有效控制结核病的流行.
Dynamic Analysis of a Stochastic Tuberculosis Model with Incubation Period Detectivity and Exogenous Reinfection
In order to explore the effects of incubation period detectivity,exogenous reinfection and environmental noise disturbance on tuberculosis transmission and control,the dynamics behavior of a tuberculosis model with incubation period detectivity and exogenous reinfection under random perturbations was studied in this paper.Firstly,the existence and uniqueness of the solution was verified by constructing appropriate Lyapunov function and the condition of existence of ergodic stationary distribution was obtained by applying the Has'minskii theory and some inequality techniques.Secondly,the extinction of the disease was proved.Finally,the correctness of the theoretical results was verified through numerical simulations.The results showed that increasing the proportion of incubation period detectivity or reducing the rate of exogenous reinfection could reduce the number of patients who progressed to active tuberculosis.However,the presence of environmental noise led to the complexity of tuberculosis control.The research revealed that the greater noise disturbance could lead to the extinction of tuberculosis and effectively control the epidemic of tuberculosis.

stochastic tuberculosis modelincubation period detectivityexogenous reinfectionLyapunov functionHas'minskii theorystationary distributionextinction

黄松、刘志军

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湖北民族大学 数学与统计学院,湖北 恩施 445000

随机结核病模型 潜伏期检测 外源性再感染 Lyapunov函数 Has'minskii理论 平稳分布 灭绝性

湖北省自然科学基金项目湖北民族大学研究生科研创新项目

2023AFB1095MYK2023043

2024

10.13501/j.cnki.42-1908/n.2024.03.018

湖北民族大学学报(自然科学版)
湖北民族学院

湖北民族大学学报(自然科学版)

影响因子：0.458
ISSN：2096-7594
年,卷(期)：2024.42(1)
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