An Atangana–Baleanu derivative-based fractal-fractional order model for the monkey pox virus: A case study of USA

Abstract

In this study, we apply both classical and fractional-order differential equations to construct a deterministic mathematical model of the monkeypox virus. The model accounts for every conceivable interaction that may play a role in the propagation of the disease throughout the population. In the current study, we investigate the monkeypox outbreak using an Atangana–Baleanu fractal-fractional derivative with an exponentially decaying type kernel to examine the impact of vaccination and isolation. We thoroughly investigate the model’s fundamental mathematical characteristics. We calculate the basic reproduction number and equilibrium points, as well as identify the feasible region for the model. We prove the existence and stability of the model using the Banach fixed-point theory and Picard’s successive approximation method. We establish the existence and uniqueness of the model’s solution under appropriate conditions. Additionally, we explore the asymptotically local and global stability of the disease-free equilibrium states and endemic equilibrium states. We also explore the Hyers-Ulam and Hyers-Ulam-Rassias consistency of the obsessive solution. To design effective infection control measures, we study the dynamic behavior of the system. We explore the complex dynamics of monkeypox infection under the influence of different system input factors through extensive numerical simulations of the proposed monkeypox model with varying input parameters. In this way, people can learn about the role that control parameters play in efforts to eradicate monkeypox. To design effective infection control measures, we study the dynamical behavior of the system. We present a number of different parameters to the decision-makers in the community to control monkeypox.

Keywords

• Mathematical modeling
• Monkeypox
• Vaccination
• Isolation
• Hyers-ulam stability
• Analysis