Stochastic SIR Model And Its Application In The US Covid-19 Pandemic

Today,more than two years after the outbreak of the Covid-19 pandemic,the global pandemic situation is still not optimistic.The outbreak and rebound of the pandemic in many countries have brought serious impact on social operation,economic development and people’s lives,and have caused a huge impact on human society on a global scale.In the United States,for example,as of March 4th,2022,there were 78428884 cumulative confirmed cases and 947625 cumulative deaths.Therefore,it is necessary to study the pattern of pandemic development for global pandemic prevention and control.In this thesis,deterministic SIR models and SIR stochastic differential equation models are chosen as tools to study the Covid-19 pandemic.In the theoretical introduction section,the proposal and development of SIR models are reviewed,the theoretical basis of stochastic processes and stochastic differential equations required for the models are introduced,and the definitions,characteristics and parameter estimation methods of deterministic SIR model and SIR stochastic differential equation model are highlighted.In the empirical part,the daily published data of the pandemic in the United States from July 1,2021 to February 26,2022 reported by Ding Xiang Yuan are divided into two phases as the object of the study,for which deterministic SIR model and SIR stochastic differential equation model are developed,respectively.In parameter estimation for the deterministic model,y was first estimated based on the definition of the move-out intensity,then fixed y for the estimation of the intensity of infection β and the initial number of susceptible persons S0,and then fixed S0 for β and γ.For parameter estimation in the stochastic differential equation model,the Gauss-Newton algorithm was used to update the parameters of β and γ.Afterwards,the fitted values were compared with the true values and both models had a good fit.Next,the models and parameters were analyzed and the basic production number for the two phases were 3.6 and 7.6,respectively,which were consistent with the context of the U.S.population activity and the different virus variants in the two phases.Finally,the effects of different epidemic prevention measures on the key parameters β and γ in the model are also discussed,and then the different effects of these measures on the development of the pandemic are discussed,and it is concluded that strengthening the enforcement of mask mandates,strict control of the isolation of infected persons,and increasing the vaccination rate are necessary to control the pandemic as soon as possible.