This paper aims to suggest a time-fractional model of the COVID-19 pandemic disease in the sense of the Atangana-Baleanu-Caputo operator. The proposed model consists of six compartments: susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized and recovered population. We prove the existence and uniqueness of solutions to the proposed model via fixed point theory. Furthermore, a stability analysis in the context of Ulam-Hyers and the generalized Ulam-Hyers criterion is also discussed. For the approximate solution of the suggested model, we use a well-known and efficient numerical technique, namely the Toufik-Atangana numerical scheme, which validates the importance of arbitrary order derivative and our obtained theoretical results. Finally, a concise analysis of the simulation is proposed to explain the spread of the infection in society.
Keywords: Banach contraction mapping principle; COVID-19; Fractional calculus; Schauder fixed point theorem.
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