Mathematical modeling of a novel fractional-order monkeypox model using the Atangana–Baleanu derivative

In this research endeavor, we undertake a comprehensive analysis of a compartmental model for the monkeypox disease, leveraging the Atangana–Baleanu fractional derivative framework. Our primary objective is to investigate the effectiveness of a range of control strategies in containing the transmission of this infectious ailment. The parameterization of the model is executed meticulously via the application of the maximum likelihood estimation technique. Our study involves a rigorous mathematical analysis of the considered model, which encompasses an exploration of the existence and uniqueness of solutions, as well as the establishment of conditions ensuring the compactness and continuity of these solutions. Subsequently, we embark on an extensive stability analysis of the model, complemented by the computation of both the effective and basic reproduction numbers. These calculations are instrumental in illuminating the long-term behavior of the epidemic. Additionally, we perform a sensitivity analysis of the basic reproduction number to discern the influence of various factors on disease transmission dynamics. To derive our numerical results, we implement the Adams–Bashforth predictor–corrector algorithm tailored for the Atangana–Baleanu fractional derivatives. We employ this numerical technique to facilitate the simulation of the model under a spectrum of fractional-order values, offering a visual representation of our findings. Our study underscores the pivotal roles of infection awareness, vaccination campaigns, and effective treatment in significantly curtailing disease transmission, thus contributing valuable insight to the field of epidemiology.