一类具有随机扰动的水源性传染病模型的动力学行为  

Dynamic Analysis of a Stochastic Water-borne Epidemic Model

作　　者：廖书[1] 张雨 杨炜明[2] LIAO SHU;ZHANG YU;YANG WEIMING(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing Key Laboratory of Statistical Intelligent Computing and Monitorin,Chongqing 400067,China;School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,统计智能计算与监测重庆市重点实验室,重庆400067 [2]重庆工商大学数学与统计学院,重庆400067

出　　处：《应用数学学报》2025年第2期208-229,共22页Acta Mathematicae Applicatae Sinica

基　　金：重庆市教委人文社科研究项目(批准号:23SKJD106)资助项目。

摘　　要：本文研究一类具有多种传播途径的随机霍乱传染病模型,首先通过构造适当的Lyapunov函数,证明该模型唯一正解的全局存在性和疾病的灭绝性.其次利用遍历性理论,得出了系统存在平稳分布且具有遍历性.最后利用数值模拟验证了所得理论结果的正确性,随机噪声对传染病的传播有很大的影响,较大的噪声有利于控制传染病的爆发和传播.In this paper,we study a water-borne epidemic model with multiple trans-mission ways.Firstly,we show the existence and uniqueness of global positive solution of the stochastic model by using suitable Lyapunov function.Moreover,by applying the Has'minskii theory,we obtain the existence of a ergodic stationary distribution of the positive solution of the model system under certain sufficient conditions.At last,we carry out numerical simulations to verify the analytical results.The results show that Random noise has a great infuence on the spread of infectious diseases,and larger noise is beneficial to control the outbreak and spread of infectious diseases.

关 键 词：随机模型 霍乱 灭绝性 遍历性 

分 类 号：O29[理学—应用数学]