Application Of Fractional Calculus In A COVID-19 Epidemic Model

COVID-19 is an epidemic caused by the severe acute respiratory syndrome coronavirus 2,which has seriously harmed the world’s public health and economic development since the end of 2019.In order to effectively control the spread of COVID-19,it is necessary to establish appropriate COVID-19 epidemic models to study its transmission dynamics according to different conditions.Due to the memory effect of the fractional calculus,consider the Caputo fractional derivative about time t.In view of the domestic epidemic data report,based on the SEIARQ model of COVID-19 epidemic,εA,the change of asymptomatic infected persons into infected people,and θI,the change of death due to COVID-19 epidemic,were introduced to study the transmission pattern of the disease in the population.The main research content of the article includes three parts.Chapter 2 establishes a fractional SEIARQ model for the COVID-19 epidemic based on the spread of domestic epidemics and reporting data.We first prove the boundedness of the solution of the discussed model.Then we calculate the disease-free equilibrium point and the endemic equilibrium point of the model and find the basic reproduction number R0 by using the classical next-generation matrix method.Finally,we discuss the stability of the diseasefree cquilibrium point,namely,if R0<1 and a1a2a3-a12a4-a32>0 the disease-free equilibrium point M0 is locally asymptotically stable;if D(f)<0,a1>0,a2>0,a3>0 and a<1/2,the disease-free equilibrium point M0 is locally asymptotically stable.Chapter 3 introduces the fractional Predictor-corrector,using mathematical software to simulate the numerical solution of the discussed model,and compare with the numerical simulation results of the infectious disease model based on Atangana-Baleanu fractional derivative.Chapter 4 introduces the combination of mixed simplex method and particle swarm optimization,and then sets the different fractional derivatives of each differential equar tion in the model.Using this parameter estimation method,according to the epidemic data published by the government,the six fractional derivatives and the two parameters proposed in this paper are fitted to simulate the spread of the epidemic.In this paper,a targeted mathematical model based on the SEIARQ model of COVID-19 epidemic is established,which can well simulate the domestic epidemic data report.