Research On COVID-19 Infectious Disease Model With Controlled Intervention And Delay

This article mainly establishes two types of infectious disease models,analyzes the stability of the models,and discusses the estimation methods of parameters in the models.It is noted that the new type of coronavirus pneumonia(abbreviated as COVID-19),an acute respiratory infectious disease,is mainly spread through close contact and droplets,and it has erupted in many countries on a large scale,affecting people's normal life and global economic development.Therefore,this article takes COVID-19 as the research object,establishes an infectious disease dynamic model,studies its spreading rules,predicts the development trend of the epidemic,and analyzes the implementation effects of various control intervention measures.First of all,this article establishes a type of infectious disease dynamics model with control intervention measures,which considers prevention and control interventions such as quarantine isolation and confirmed isolation,as well as the difference between the infectivity of different sources of infection(infected during the incubation period,asymptomatic infection,symptomatic infection),gives the disease-free balance of the model and the threshold for determining whether the infectious disease is controlled--the basic reproduction number,and uses Liapunov's first method to obtain the condition of local asymptotic stability of the disease-free balance point of the model.Finally,the model is applied to the research and analysis of the COVID-19 epidemic in Italy.Through segmental fitting of the Italian epidemic data,the parameters of the model are estimated by the least square method to predict the development of the Italian epidemic in the later period,and the relative error of the prediction results is small.Secondly,this article establishes a type of infectious disease dynamics model with control intervention and delay,in which the impact of isolation measures and data delay is considered.Through analysis,the conditions for the stability of the model are obtained,and the parameter estimation method of the model based on the least square method is given.After that,the model is applied to analyze the domestic small-scale epidemic outbreak--the clustered COVID-19 epidemic in Beijing.Based on the official epidemic data,the parameters of the model fitting are obtained by using least square method to further verify the effectiveness of the model.Finally,the impact of changes in the isolation rate and infection rate in the model on the development of the epidemic is discussed.