一类潜伏期与染病期均具有传染性的随机传染病模型  

A stochastic epidemic model with infectivity in both incubation period and infection period

作　　者：胡瑞 黄立冬[1] 李荣庭 徐权峰 HU Rui;HUANG Li-dong;LI Rong-ting;XU Quan-feng(School of Mathematics and Computer Science,Yunnan Minzu University,Kunming 650500,China)

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650500

出　　处：《云南民族大学学报（自然科学版）》2022年第2期213-220,234,共9页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(12061088);云南民族大学研究生科研项目(SJXY2020-102;SJXY2020-107).

摘　　要：考虑在环境白噪音扰动下建立一类潜伏期和染病期均具有传染性的随机SEIQR模型.首先利用Lyapunov函数和Ito公式证明随机SEIQR传染病模型存在唯一的全局正解.其次讨论当基本再生数不大于1时,给出相应确定性模型的无病平衡点渐近稳定的充分条件,当白噪声较小时,疾病将灭绝;当基本再生数大于1时,给出相应确定性模型的地方病平衡点渐近稳定的充分条件,反应了在一定条件下,疾病将流行.A stochastic SEIQR model with infectivity in both incubation period and infection period is established under the disturbance of environmental white noise.Firstly,by using Lyapunov function andformula,it is proved that there is a unique global positive solution for the stochastic SEIQR epidemic model.Secondly,when the basic reproduction number is not greater than 1,the sufficient conditions for the asymptotic stability of the disease-free equilibrium of the corresponding deterministic model are given.When the white noise is small,the disease will become extinct;When the basic reproduction number is greater than 1,then a sufficient condition for the asymptotic stability of the endemic equilibrium of the corresponding deterministic model is given,which reflects that the disease will be epidemic under certain conditions.

关 键 词：传染病模型 随机微分方程 LYAPUNOV函数 ITO公式 渐近稳定性 

分 类 号：O211.63[理学—概率论与数理统计]