Modeling the monkeypox infection using the Mittag–Leffler kernel

Author:

Khan Muhammad Altaf1,Meetei Mutum Zico2,Shah Kamal34,Abdeljawad Thabet3,Alshahrani Mohammad Y.5

Affiliation:

1. Faculty of Natural and Agricultural Sciences, University of the Free State , Bloemfontein , South Africa

2. Department of Mathematics, College of Science, Jazan University , Jazan 45142 , Saudi Arabia

3. Department of Mathematics and Sciences, Prince Sultan University , Riyadh 11586 , Saudi Arabia

4. Department of Mathematics, University of Malakand , Chakdara, Dir(L), KPK , Pakistan

5. Department of Clinical Laboratory Sciences, College of Applied Medical Sciences, King Khalid University , P.O. Box 61413 , Abha, 9088 , Saudi Arabia

Abstract

Abstract This article presents the mathematical formulation for the monkeypox infection using the Mittag–Leffler kernel. A detailed mathematical formulation of the fractional-order Atangana-Baleanu derivative is given. The existence and uniqueness results of the fractional-order system is established. The local asymptotical stability for the disease-free case, when 0 < 1 {{\mathcal{ {\mathcal R} }}}_{0}\lt 1 , is given. The global asymptotical stability is given when 0 > 1 {{\mathcal{ {\mathcal R} }}}_{0}\gt 1 . The backward bifurcation analysis for fractional system is shown. The authors give a numerical scheme, solve the model, and present the results graphically. Some graphical results are shown for disease curtailing in the USA.

Publisher

Walter de Gruyter GmbH

Subject

General Physics and Astronomy

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