一类具有潜伏期的随机禽流感模型的渐近性分析  

Asymptotic Analysis of a Stochastic Viral Infection Model with a Latent Period

作　　者：谭杨[1] 郭子君[2] 杨林 王海扬[1] TAN Yang;GUO Zi-jun;YANG Lin;WANG Hai-yang(College of Information Engineering,Tongren Polytechnic College,Tongren 554300,China;Institute of Applied Mathematics,South China Agricultural University,Guangzhou 510642,China)

机构地区：[1]铜仁职业技术学院信息工程学院,贵州铜仁554300 [2]华南农业大学应用数学研究所,广东广州510642

出　　处：《中北大学学报（自然科学版）》2020年第2期110-115,共6页Journal of North University of China(Natural Science Edition)

基　　金：广东省自然科学基金资助项目(2015A030310065);铜仁市科技计划项目(铜市科研(2017)47-99号)。

摘　　要：研究了一类禽类患病系统具有潜伏期而人类染病系统受到随机白噪声干扰的随机禽流感模型的渐近性质.首先通过构造停时和Lyapunov函数及伊藤引理的方法得到了随机模型全局正解的存在唯一性.其次证明了在禽类患病种群灭绝的情形下,人类患病种群必将灭绝的结果;再次得到了禽类患病种群长期存在的前提下,由于随机因素的干扰,人类患病种群终将趋于灭绝的充分条件.最后通过数值模拟比较了人类染病种群在确定性和随机性系统中的发展趋势.Asymptotic analysis of an avian influenza model with a latent period and human infection system disturbed by random white noise was investigated.Firstly,the existence and uniqueness of global positive solutions was proved by constructing stopping time,Lyapunov functions and Ito’s lemma.Then,it was proved that the human infected population would be extinct in the case of avian infected population going extinction.Even though the avian disease population existed in a long time,the human infected population would be extinct due to the random disturbances,and the sufficient conditions were obtained.Finally,development tendency of the human infected population in determinate and random system was compared by simulations.

关 键 词：禽流感模型 潜伏期 停时 随机干扰 灭绝 

分 类 号：O211.63[理学—概率论与数理统计]