On the fractional SIRD mathematical model and control for the transmission of COVID-19: The first and the second waves of the disease in Iran and Japan

In this paper, a fractional-order SIRD mathematical model is presented with Caputo derivative for the transmission of COVID-19 between humans. We calculate the steady-states of the system and discuss their stability. We also discuss the existence and uniqueness of a non-negative solution for the system under study. Additionally, we obtain an approximate response by implementing the fractional Euler method. Next, we investigate the first and the second waves of the disease in Iran and Japan; then we give a prediction concerning the second wave of the disease. We display the numerical simulations for different derivative orders in order to evaluate the efficacy of the fractional concept on the system behaviors. We also calculate the optimal control of the system and display its numerical simulations.