A Mathematical Model Of Covid-19 Epidemic With Applications

Since the outbreak of the pandemics of Coronavirus Disease 19(COVID-19)two years ago,400 million people has been infected and more than 6 million died from COVID-19.The transmission and evolution of epidemics follows its own natural laws.So proper mathematical models in accordance with the characteristics of COVID-19 pandemics and related policies towards COVID-19 are especially useful in not only predicting the pandemics for reasonable decisions but also the retrospective study for analyzing mechanisms of the transmission and effects of various actions against COVID-19,and furthermore,for the preparation for the next epidemics.As COVID-19 has longer latent periods,more asymptomatic cases with much more strict policies of quarantine for containing the pandemics in the early stage of the pandemics worldwide,this thesis establishes an SEIR-QD model based on the classic SIER model of infectious diseases to characterize the dynamics of the COVID-19 within the period of one wave,with emphasis on the special policies against COVID-19 such as quarantines and protection of susceptible people due to closure of public spaces.The SEIR-QD model is verified by fitting and predicting the epidemic data of several regions in China as well as the first wave of epidemics in some hotspots worldwide.To further test the SEIR-QD model,we make a rational evaluation of 16 other epidemic dynamical models including explicit functions,statistical models and ordinary differential equations in terms of complexity,precision,the ability of forecast,robustness,etc.Akaike information criterion,root mean square errors and robust coefficients are employed to evaluate those models systematically.The results suggest none of the models are able to make reliable predictions given only the data of the early stage of the epidemics.The key to predict the epidemics reasonably is the inflection point.By comparison,we verify that the SEIR-QD model is a proper model to analyze and predict the COVID-19 epidemics.In addition,we also find that Logistic function and Gompertz’s function are always overestimate and underestimate the final size of the epidemics respectively.Sequential Bayesian method and effective reproduction number are probably the best two predictor given the data of late stage of the epidemics among the 17 models.Last but not least,we investigate effects of 15 policies in containing the pandemics via the dynamical model SEIR-QD.By clustering,we divide the countries and regions into four categories.For each category,a representative country is investigated via SEIR-QD model on the effects of lifting a policy on the epidemic dynamics.Our results show that the response of changing a policy may vary for different countries with different basal policies.While,more common effects are shared among the countries/regions.For example,protections of susceptible people,prevention of susceptible people from infectious ones are always needed for containing the epidemics.This thesis conducts a systematic study on the characteristics of the spread and prevention of the COVID-19 in the early stage,including establishing a mathematical model,rational evaluation of the models and applying the model to policy evaluations.The findings are not only significant for the prevention and control of COVID-19,but also provide potential suggestions for fighting with possible outbreaks in the future.