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

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

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.

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.