一类具有无症状感染和隔离的 SIAQR 传播模型动力学分析和最优控制

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1914-1928.

一类具有无症状感染和隔离的 SIAQR 传播模型动力学分析和最优控制

钟毅¹(),王毅^1,^*(),蒋添合²

¹中国地质大学 (武汉) 数学与物理学院武汉 430074
²广西民族大学数学与物理学院南宁 530006

收稿日期:2022-07-03 修回日期:2023-08-16 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *王毅，E-mail: yiwang@cug.edu.cn
作者简介:钟毅，E-mail: qydzwuhan@foxmail.com
基金资助:
国家自然科学基金(12171443);国家自然科学基金(11801532);中央高校基本科研业务费专项资金: 中国地质大学(武汉)(CUGQT2023001)

Dynamic Analysis and Optimal Control of an SIAQR Transmission Model with Asymptomatic Infection and Isolation

Zhong Yi¹(),Wang Yi^1,^*(),Jiang Tianhe²

¹School of Mathematics and Physics, China University of Geosciences Wuhan, Wuhan 430074
²School of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006

Received:2022-07-03 Revised:2023-08-16 Online:2023-12-26 Published:2023-11-16
Supported by:
National Natural Science Foundation of China(12171443);National Natural Science Foundation of China(11801532);Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)(CUGQT2023001)

摘要/Abstract

摘要：

该文以新型冠状病毒肺炎 (COVID-19) 的群体传播为背景, 提出了一个具有无症状感染和隔离的传染病模型. 研究了模型的基本再生数, 最终暴发规模, 以及最终暴发规模方程解的存在唯一性与可解性等问题. 在此基础上, 考虑了两种可能的控制策略, 采用 Filippov-Cesari 存在性定理和 Pontryagin 极值原理分析最优控制的存在性. 选取浙江省新冠肺炎感染的历史数据, 采用马尔可夫链蒙特卡洛方法对模型参数进行估计. 数值模拟结果显示采取控制策略可以降低 33.92% 的隔离峰值、76.54% 的最终暴发规模. 说明降低传染率、为易感者接种疫苗仍是控制新冠肺炎疫情发展的有效手段, 对控制新冠肺炎疫情和应对新发传染病给出建议.

关键词: 无症状感染, 隔离, 基本再生数, 最终规模方程, 最优控制

Abstract:

This paper presents an epidemic model with asymptomatic infection and isolation in the context of population transmission of a Corona Virus Disease 2019 (COVID-19), we analyze the basic reproduction number of the model, the final epidemic size, the existence and uniqueness and solvability of the solution for the implicit final size equation. On this basis, we consider two possible control strategies and analyze the existence of optimal control by using the Filippov-Cesari existence theorem and Pontryagin extreme principle. Base on the historical data of COVID-19 infection in Zhejiang Province, the model parameters are estimated using the Markov Chain Monte Carlo method. The numerical simulation results show that the control strategy can reduce the peak isolation rate by 33.92% and final epidemic size by 76.54%. This suggests that reducing transmission rates and vaccinating susceptible individuals are still effective means of controlling the development of COVID-19 outbreaks, and provides recommendations for controlling COVID-19 outbreaks and responding to emerging infectious diseases.

Key words: Asymptomatic infection, Isolation, Basic reproduction number, Final size equation, Optimal control

中图分类号:

O175

钟毅, 王毅, 蒋添合. 一类具有无症状感染和隔离的 SIAQR 传播模型动力学分析和最优控制[J]. 数学物理学报, 2023, 43(6): 1914-1928.

Zhong Yi, Wang Yi, Jiang Tianhe. Dynamic Analysis and Optimal Control of an SIAQR Transmission Model with Asymptomatic Infection and Isolation[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1914-1928.

图/表 5

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