具有Lévy噪声的随机SIR模型的分析与滑模控制  

Analysis and Sliding Mode Control of Stochastic SIR Models with Lévy Noise

作　　者：王周源 张翼[1] 王莹莹 WANG Zhouyuan;ZHANG Yi;WANG Yingying(School of Science,Shenyang University of Technology,Shenyang 110870)

机构地区：[1]沈阳工业大学理学院,沈阳110870

出　　处：《系统科学与数学》2024年第11期3215-3227,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(62103289)资助课题。

摘　　要：针对考虑人口变动和受Lévy环境噪声影响的随机SIR传染病模型,通过It?公式和Lyapunov函数,证明了全局正解的存在唯一性,讨论了平衡点附近的渐近性质.在此基础上,利用滑模控制手段,将疫苗接种策略作为控制输入加入到传染病模型中,并设计了相应的非线性滑模面和对应的控制器,使模型在有限时间达到稳定,传染病的传播得到控制.最后通过仿真验证理论结果的有效性.Aiming at a stochastic SIR infectious disease model with population mobility and Lévy environmental noise,the existence and uniqueness of a global positive solution was obtained by using Itôformula and Lyapunov function,the asymptotic properties around the equilibrium point were discussed.In addition,the vaccination strategy was added to the infectious disease model as the control input by using sliding mode control,and the corresponding nonlinear sliding mode surface and controller were designed.The model would reach stability in a finite time,and the spread of infectious diseases was controlled.Finally,numerical simulation results were verified that the as-designed method is effective.

关 键 词：Lévy噪声 随机SIR模型 滑模控制 有限时间 

分 类 号：R181[医药卫生—流行病学] O175[医药卫生—公共卫生与预防医学]