Modeling the monkeypox infection using the Mittag–Leffler kernel

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 ℛ 0 < 1 {{\mathcal{ {\mathcal R} }}}_{0}\lt 1 , is given. The global asymptotical stability is given when ℛ 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.