Application Of Markov Chain Monte Carlo Method In Infectious Disease Model

The global pandemic of the novel coronavirus pneumonia(COVID-19)at the end of2019 has a great impact on our daily lives,and seriously threatened people’s lives and health.How to build an appropriate mathematical model and predict the development of the epidemic scientifically and effectively is very important for the prevention and control of the epidemic.First of all,based on the classical infectious disease model and considering the important factor that the immunity of the infected person may fade away after a few months.This paper introduce the immune failure rate of the infected person,and then establish a SIR infectious disease model in line with China’s prevention and control strategy for the spread of COVID-19.Next,based on the daily epidemic data provided by Wuhan Provincial Health Commission in the early stage of the outbreak of COVID-19,the Markov chain Monte Carlo method(MCMC method)was used to estimate the parameters of the established epidemic model.The estimated parameters were used to analyze and predict the initial outbreak of novel coronavirus pneumonia in Wuhan.The prediction result of the model was basically consistent with the actual development trend of the epidemic,which reflected that the estimated parameters were benign.Finally,by means of MCMC parameter estimation method,we introduce small parameters into the SIR infectious disease model,and obtain the singular perturbed infectious disease model.Using the qualitative and bifurcation theory of differential equations,we prove that it has a unique limit cycle under certain parameter conditions.These results indicate that when the novel coronavirus pneumonia is not completely eliminated,it will break out again in the future.Therefore,our results provide the theoretical basis for disease prevention and control strategy,and help government departments to make decisions.