Parameter Estimation for a Class of Fractional Stochastic SIRD Models with Random Perturbations

Abstract

The classical SIRD model is extended to the conformable fractional stochastic SIRD model. The differences between the fractional stochastic SIRD model and the integer stochastic SIRD model are analyzed and compared using COVID-19 data from India. The results show that when the order of the fractional stochastic SIRD model is between $[0.93,0.99]$, the root mean square error between the simulated value and the real value of the number of infections is smaller than that of the integer stochastic SIRD model. Then, the maximum likelihood estimation of the parameters of the conformable fractional stochastic SIRD model is carried out, and compared with the maximum likelihood estimation results 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 between $[0.93,0.99]$.