Parameter Estimation And Prediction Of The Conformable Fractional Stochastic Infectious Disease Model

On the basis of the classical SIR model,the Conformable fractional SIR model and the fractional stochastic SIR model are given,and the numerical solution of fractional SIR model is solved by the second-order Adams-Bashforth method,and the relationship between fractional stochastic SIR model and fractional SIR model is discussed by using probability generation function.The Gillespie stochastic simulation algorithm was used to obtain the simulation values of the susceptible population,infected number and recovered number of fractional stochastic SIR model,and the maximum likelihood estimation of the fractional stochastic SIR model and the parameter estimation results of MCWM algorithm were given.Finally,the parameter estimation results of fractional stochastic SIR model and integer stochastic SIR model were compared by using influenza data from British boarding schools and SARS data from Hong Kong region,the results show that when the order of the fractional stochastic SIR model is taken within a certain range,the fitting effect of the original data is better than that of the integer stochastic SIR model,and the error of parameter estimation is smaller.Based on the classical SIRD model,the Conformable fractional stochastic SIRD model and the Conformable fractional time-varying stochastic SIRD model are given.Then,the data of COVID-19 in India and Maryland are used to analyze and compare the differences between the fractional stochastic SIRD model and the integer stochastic SIRD model.The results show that when the order of the fractional stochastic SIRD model is in a certain interval,the root mean square error between the simulated value and the real value of the number of infected people is smaller than that of the integer stochastic SIRD model.The maximum likelihood estimation of the parameters of the fractional stochastic SIRD model is carried out,and compared with the maximum likelihood estimation of the parameters of the integer stochastic SIRD model,it can be seen that the root mean square error of the fractional stochastic SIRD model is smaller when the fractional order is valued in a certain interval.Finally,the fractional time-varying stochastic SIRD model is used to predict the development of COVID-19 in India and Maryland,and the results show that reasonable selection of the order of the fractional model is conducive to improving the prediction effect.