一类反应扩散SIQR传染病模型的最优控制  

Optimal Control of a Class of Reaction-diffusion SIQR Epidemic Models

作　　者：毛金凤 周敏 MAO Jinfeng;ZHOU Min(School of Mathematics and Statistics,Hubei Minzu University,Enshi 445000,China)

机构地区：[1]湖北民族大学数学与统计学院,湖北恩施445000

出　　处：《湖北民族大学学报（自然科学版）》2024年第1期127-136,143,共11页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(11961023);湖北民族大学研究生教育创新项目(MYK2023041)。

摘　　要：为探究疾病发生时如何更快地控制疾病、避免疾病的扩散和流行,研究了一类反应扩散的易感-感染-隔离-恢复(susceptible-infectious-quarantined-recovered,SIQR)传染病模型的最优控制问题。首先利用截断方法证明状态方程解y=(S,I,Q,R)^(T)的存在性,其次利用极小化序列证明最优控制对(S^(*),I^(*),Q^(*),R^(*),u^(*))的存在性,最后利用拉格朗日方法得到一阶必要条件以及最优控制u^(*)的表达形式。结果表明:当控制u=u^(*)为最优控制时,给定的目标泛函达到最小值。该研究在偏微分方程传染病模型的最优控制方面具有重要意义。In order to investigate how to control the disease faster when it occurs and to avoid spreading and epidemics,this paper investigated the optimal control problem for a class of susceptible-infectious-quarantined-recovered(SIQR)reaction-diffusion epidemic models.Firstly,the truncation method was used to prove the existence of the solution y=(S,I,Q,R)^(T) of the state equation.Secondly,the minimisation sequence was used to prove the existence of the optimal control pair(S^(*),I^(*),Q^(*),R^(*),u^(*)).Finally,the Lagrange method was used to obtain the first-order necessary condition and the expression of the optimal control u^(*).The results showed that when the control u=u^(*)was optimal,the given objective function was minimised.This study is of great significance to the problem of optimal control of infectious disease models with partial differential equations.

关 键 词：传染病模型 反应扩散方程 解的存在唯一性 最优控制 一阶必要条件 

分 类 号：O175[理学—数学]