Mathematical analysis of an extended SEIR model of COVID-19 using the ABC-fractional operator.

ABSTRACT

This paper aims to suggest a time-fractional S P E P I P A I P S P H P R P 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 ϑ and our obtained theoretical results. Finally, a concise analysis of the simulation is proposed to explain the spread of the infection in society.