Parameter Estimation And Dynamic Analysis Of A COVID-19 Transmission Model

Since the first case of novel coronavirus pneumonia was identified in Wuhan,Hubei in the Spring of 2020,COVID-19 has become a pandemic and has had a serious impact on people’s lives and socioeconomics worldwide.Therefore,the study of COVID-19 and the research on the characteristics of disease transmission is very timely and relevant.In the early stages of the COVID-19 outbreak,we can assume an almost exponential increase in the number of patients.In the first part of the study,we propose the SEIJHT model to simulate an epidemic in the exponential growth phase,based on the well-known SEIR model,considering infected individuals with mild symptoms(not hospitalized,I),infected individuals with severe symptoms(eventually hospitalized,J),hospitalized individuals(H)and diagnosed individuals(testing positive,T).The results show that to reliably estimate !," from the case count data,the fraction of patients showing severe symptom,the latent period,and the infectious period,must be independently estimated from other sources of data.In the second part of the study,for the omicron outbreak in Shanghai from March 2022 to June2022,we tabulated the published daily counts of confirmed cases and asymptomatic cases for each region in Shanghai.A two-region SEIRT model was constructed by classifying the population into susceptible(S),exposed(E),infected(I),self-recovered(R)and test-positive(T)according to the characteristics of the implementation of prevention and control measures in Shanghai.Parameter estimation was performed using the MCMC method.The results of the study show that the outbreak dies out because of only 27% of the population were active in disease transmission,possibly due to a combination of vaccination and lockdown.In the third part of the study,we construct two stochastic infectious disease model by adding noise terms to the first two parts of the deterministic model,considering the effect of environmental noise on the infectious disease model.And by constructing Lyapunov functions,we prove the uniqueness of the existence of global solutions to each of these two equations and obtain sufficient conditions for disease extinction for each.