一类潜伏期具有传染性的随机SEI_(1)I_(2)RQ传染病模型  

A Stochastic SEI_(1)I_(2)RQ Epidemic Model with Infectious Latent Period

作　　者：曹欢 张太雷[1] 刘宗萱 蒋为平 CAO Huan;ZHANG Tailei;LIU Zongxuan;JIANG Weiping(School of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《山西大学学报（自然科学版）》2024年第4期704-716,共13页Journal of Shanxi University(Natural Science Edition)

基　　金：陕西省自然科学基础研究计划(2022JM-023)。

摘　　要：为了研究环境中的随机因素对传染病的影响,考虑了一类潜伏期传染的随机传染病模型。通过构造Lyapunov函数并结合伊藤公式等方法,首先证明了随机模型全局正解的存在唯一性。其次,分析了确定性模型和随机模型的解在无病平衡点和地方病平衡点附近的波动行为,得到了当基本再生数小于1时,确定性模型和随机模型的解均在无病平衡点附近波动,当基本再生数大于1时,确定模型和随机模型的解均在地方病平衡点附近波动,且随机模型解的波动幅度与干扰强度成正相关。再次,给出随机模型解的平均持续和灭绝性的充分条件。最后,对该模型做了相应的数值模拟,结果表明,当干扰强度足够大时,疾病将灭绝。In order to study the influence of random factors in the environment on infectious diseases,a random infectious disease model with infectious latent period is considered.By constructing Lyapunov function and combining with the Ito formula,the existence and uniqueness of the global positive solutions of the stochastic model is proved;Then,the fluctuation behavior of the solutions of the deterministic model and the stochastic model near the disease-free equilibrium point and the endemic equilibrium point are analyzed,and we obtained the solutions of the deterministic model and the stochastic model fluctuate near the disease-free equilibrium point when the basic reproduction number is less than 1,and the solution of the deterministic model and the stochastic model fluctuate near the endemic equilibrium point when the basic regeneration number is greater than 1.The fluctuation amplitude of the stochastic model solution is positively correlated with the interference intensity.The sufficient conditions for the average persistence and extinction of the stochastic model solution are also given.Finally,the corresponding numerical simulation of the model shows that the disease will become extinct when the disturbance is strong enough.

关 键 词：随机模型 平衡点 伊藤公式 波动行为 持久性 灭绝性 

分 类 号：O175.1[理学—数学]