Abstract
In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray–Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik–Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.
Highlights
Corona virus or severe acute respiratory syndrome corona virus 2 (SARS-CoV-2) is a virus that attacks the respiratory system
The ICTV corona virus disease study group stated that this virus is a species associated with the severe acute respiratory syndrome
COVID-19 was first discovered in humans in December 2019
Summary
Corona virus or severe acute respiratory syndrome corona virus 2 (SARS-CoV-2) is a virus that attacks the respiratory system. Theorem 1 The COVID-19 free equilibrium (CFE) point E0 of the proposed fractional order SEQIR pandemic model (2) is locally asymptotically stable if R0 < 1. A sufficient condition for the local asymptotic stability of the equilibrium points is that the eigenvalues ωi, i = 1, 2, 3, 4, 5, of the Jacobian matrix J(E0) satisfy the condition This confirms that fractional order differential equations are, at least, as stable as their integer order counterparts. A sufficient condition for the local asymptotic stability of the equilibrium points is that the eigenvalues ωi, i = 1, 2, 3, 4, 5, of the Jacobian matrix J|∗|(E∗) satisfy the condition. The pandemic equilibrium point E∗ is locally asymptotically stable
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