Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model

In this paper, we present a fractional-order mathematical model in the Caputo sense to investigate the significance of vaccines in controlling COVID-19. The Banach contraction mapping principle is used to prove the existence and uniqueness of the solution. Based on the magnitude of the basic reproduction number, we show that the model consists of two equilibrium solutions that are stable. The disease-free and endemic equilibrium points are locally stably when R-0 < 1 and R-0 > 1 respectively. We perform numerical simulations, with the significance of the vaccine clearly shown. The changes that occur due to the variation of the fractional order (alpha) are also shown. The model has been validated by fitting it to four months of real COVID-19 infection data in Thailand. Predictions for a longer period are provided by the model, which provides a good fit for the data.

Automated summary

In this paper, a fractional-order mathematical model in the Caputo sense is proposed to investigate the significance of vaccines in controlling COVID-19. The existence and uniqueness of the solution are proven using the Banach contraction mapping principle. Based on the basic reproduction number, the model reveals two stable equilibrium solutions, which are locally stable under different conditions. Numerical simulations demonstrate the significance of vaccines and the effects of varying the fractional order (alpha). The model is validated by fitting it to four months of real COVID-19 infection data in Thailand, and provides good predictions for a longer period.