Data-driven COVID-19 Epidemic Modeling And Application Research

Since its outbreak at the end of 2019,the COVID-19 epidemic has had a great impact on the production and life of people all over the world.At the same time,various types of COVID-19-related data are constantly emerging.The analysis of these COVID-19-related data through mathematical methods is of great significance for the control and treatment of COVID-19.This paper studies the COVID-19 data based on mathematical modeling and MCMC methods to recognize the transmission risk of the COVID-19,study the specific transmission law and development process of the COVID-19,and analyze the relevant changes and differences in COVID-19 patients,so as to provide theoretical support for the control and treatment of COVID-19.The research contents are as follows:（1）In order to make a quick and rough judgment on the transmission risk of COVID-19,this paper proposed an improved effective reproduction number estimation method based on the SEIR model.According to the linear relationship between the growth rate of the number of potentially infected individuals and the effective reproduction number in the SEIR model,this paper constructed two state space models,and combined Kalman filter with Gibbs sampling algorithm to calculate them,by inputting the existing cases data to estimate the effective reproduction number.The verification on simulation data and actual data showed that the estimation method proposed in this paper can obtain a reasonable estimate of the effective reproduction number,and has the advantages of real-time estimation and no hysteresis.This method can help to recognize the transmission risk of COVID-19 and evaluate the effectiveness of interventions.（2）In order to simulate the specific transmission process of the COVID-19 epidemic and analyze the impact of control measures,this paper proposed a SEIAHRD transmission dynamic model that considers asymptomatic patients and self-healing populations,and a complete parameter estimation method for the infectious disease model based on the MCMC method.The model parameters were estimated based on the second wave epidemic data in Delhi,India,and subsequent sensitivity analysis and numerical simulation were conducted based on the parameter estimates.The main results were as follows:The estimated parameter values could make the model fit the actual data very well,and the maximum prediction error was about 0.8%;the lockdown reduced the infection rate to 0.66 and the effective reproduction number to 1.173;infection rate and asymptomatic proportional factor were the main parameters affecting the scale of cumulative confirmed cases,and the partial rank correlation coefficients were all greater than 0.9;the lockdown on April 19 reduced the number of confirmed cases by 38.37%,but extended the duration of the epidemic from 134days to 151 days.According to the results,the prevention and control suggestions are as follows:The best time for lockdown is at the beginning of the outbreak,which can effectively reduce the scale of the epidemic and ensure the effect of lockdown is significant enough;the prevention and control of the epidemic cannot rely on the lockdown alone,but also needs to be combined with other measures to shorten the duration of the epidemic（3）In order to study the within-host dynamics of COVID-19 patients and analyze the differences between critical patients and severe patients,this paper proposed a new TCL-IR model by extending the idea of infectious disease dynamic modeling to the microscopic level.The TCL-IR model was constructed by considering the immune response into the target cell limited model and the expression of within-host reproduction number of this model was derived;then some parameters in the model were determined based on existing studies,and the remaining unknown parameters were estimated by using the actual data and the Adaptive Metropolis algorithm;finally,the differences between critical patients and severe patients were analyzed according to the obtained results.The results showed that there were some differences in immune response and viral load between critical patients and severe patients:T cell proliferation coefficient and immune apoptosis rate of critical patients were 0.652 and4.137×10^-6 respectively,and the T cell proliferation coefficient and immune apoptosis rate of severe patients were 0.266 and3.283×10^-6 respectively;the viral load in critical patients peaked around 35 days,at about7.2×10⁴ copies/m L;the viral load in severe patients peaked around 28 days,at about1.38×10⁵ copies/m L,which was higher than critical patients.Based on results analysis and literature verification,the study found that the severity of some critical patients was not due to high viral load,but to their own excessive immune response.The conclusion suggests that immunomodulatory strategies should be considered in the treatment of critical patients.This research topic ranged from the rough estimation of the COVID-19 transmission risk by using the SEIR model,to the simulation of the COVID-19 specific transmission process by using the SEIAHRD transmission dynamic model,to the analysis of the changes and differences in COVID-19 patients by using the TCL-IR within-host dynamic model,and achieved the purpose of modeling and application research on COVID-19,which was multi-angle and multi-scale.This research can provide some help and reference for the control and treatment of COVID-19.