Novel Coronavirus Pneumonia Modeling Analysis And Bayesian Parameter Estimation

The prevention and control of the new crown epidemic plays an important role in the steady development of our country.Especially in the early stage of the epidemic,the use of mathematical models to evaluate the effectiveness of prevention and control measures has very important practical significance.In this paper,we improve the parameter estimation method and perform parameter estimation for the innovative COVID-19 model,and then analyzed the impact of different control measures and virus variation on epidemic.The main research contents are as follows:(1)Approximate Bayesian method is the most commonly used method for infectious disease model parameter estimation,but its efficiency is relatively low.Therefore,an improved Approximate Bayesian algorithm is proposed in this paper,and the rationality of this algorithm is proved theoretically.In this algorithm,a posterior re-adjustment algorithm is used to readjust the samples to reduce the influence of tolerance,and the tolerance sequence is adaptive.Compared with the Approximate Bayesian Computation Sequence Monte Carlo algorithm,the improved algorithm not only guarantees the accuracy of the results,but also increases the calculation efficiency by more than 30%;(2)In the early stages of the epidemic,we focused on analyzing the impact of exposure rates,virus detection capabilities,hospitalization rates of patients with mild illness,and time taken to implement control measures on the epidemic.The challenge is how to couple these measures into traditional infectious disease models.Since the intensity of prevention and control measures will change with time,this paper converts these factors into functions that change with time and improves the model.Then,the improved parameter estimation method in(1)was used to estimate the parameters of the model.Finally,the sensitivity analysis of each prevention and control measure shows that the contact rate is the most critical for the control of the epidemic;(3)The COVID-19 is a single-stranded RNA,so it is easily mutated.The infectious characteristics of the mutated new coronavirus will also change.Therefore,it is necessary to study the impact of the mutated virus on the epidemic.Firstly,we combine the incubation period and infectious power into the traditional infectious disease model,and transform it into an age structure model and a time lag model,and then estimate and analyze the sensitivity of the model's parameters.Finally,the analysis shows that the infectivity and incubation period of the virus play a key role in the development of the epidemic.