An improved fractional-order transmission model of COVID-19 with vaccinated population in United States

In this paper, we propose a new fractional-order differential equation model with latent and vaccinated population to describe the dynamics of COVID-19. Firstly, the theoretical mathematical model is established based on the transmission mechanism of COVID-19 in the population. Then, the data of the infected, the recovered and the death are collected from big data report of Baidu's epidemic situation, and the parameters are estimated by piecewise fitting and nonlinear least square method based on collected data. The correlation coefficients between the infected and model simulation, between the recovered and model simulation, between the death and model simulation are 0.9868, 0.9948 and 0.9994, respectively and the accuracy of prediction are 96.05%, 99.33% and 99.88%, respectively. Additionally, the accuracy of prediction is compared between fractional-order differential equation model and integer-order differential equation model, and the results show fractional-order differential equation model can better predict the development trend of COVID-19. Finally, we analyze the sensitivity of the parameters through numerical simulations, and put forward the corresponding strategies to control the epidemic development according to the screened sensitive parameters.