具有双线性发生率的随机酗酒模型  

A Stochastic Binge Drinking Model with Bilinear Incidence Rate

作　　者：刘娟[1] 潘玉荣[1] 李娜[1] LIU Juan;PAN Yurong;LI Na(School of Mathematics and Physics,Bengbu University,Bengbu 233030,China)

机构地区：[1]蚌埠学院数理学院,安徽蚌埠233030

出　　处：《滨州学院学报》2024年第2期36-40,共5页Journal of Binzhou University

基　　金：国家自然科学基金项目(12061033);安徽省高校自然科学研究重点项目(KJ2021A1128);蚌埠学院自然科学研究项目(2021ZR08,2022ZR03)。

摘　　要：利用随机微分方程定性分析的方法,研究了一类具有双线性发生率的随机酗酒模型。将接触率系数的随机扰动引入确定型酗酒模型,研究了随机酗酒模型正解的存在性及唯一性。通过计算白噪声强度,得到了酗酒群体D(t)消失的充分性条件。研究结果显示,当外部干扰足够大时,酗酒群体、正在戒酒者、永久戒酒者都将消失。By using the method of qualitative analysis of stochastic differential equations,a stochastic binge drinking model with bilinear incidence is studied.Firstly,the random disturbance of the contact rate coefficient is introduced into the deterministic binge drinking model.On this basis,the existence and uniqueness of the positive solution of the random binge drinking model are discussed.Secondly,the sufficient conditions for the disappearance of the alcoholism population are obtained by calculating white noise intensity.The results show that when the external white noise is large enough,alcoholism population,population who are quitting alcohol and population who are permanently quitting will disappear.

关 键 词：白噪声 随机酗酒模型 ITO公式 强大数定律 正解 

分 类 号：O175[理学—数学]