On modeling of coronavirus-19 disease under Mittag-Leffler power law

Abstract

Abstract This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as ( ABC ) $(\mathcal{ABC})$ . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

Keywords

• Coronavirus disease model
• ( ABC ) $(\mathcal{ABC})$ derivative
• Stability results
• Fractional Adams–Bashforth (AB) method
• Numerical simulations