Spatiotemporal dynamics of a novel hybrid modified ABC fractional monkeypox virus involving environmental disturbance and their stability analysis

Abstract

This research explores the epidemiology of widespread monkeypox virus (MPV) transmission using a modified Atanagana-Baleanu-Caputo (mABC) fractional derivative mathematical model in the sense of a generalized Mittag-Leffler kernel. The stability of the disease-free equilibrium in the fractional MPV model is provided, demonstrating the result for $R_0<1$. The Jacobian matrix technique shows the global stability of model equilibrium. We conduct sensitivity evaluations to find important factors affecting illness eradication and provide the results. Moreover, we investigate the existence, uniqueness, and Hyers-Ulam (HU) stability of the generalized fractional order nonlinear framework for the MPV model. The solution's uniqueness and stability are demonstrated using fixed point theory and within the HU context. We provide numerical representations for analysis employing Lagrange polynomials. The optimality criteria are produced by applying Pontryagin's maximal argument to prove the validity of the most effective control. Experiments show the approach's usefulness, predictive capabilities, and confirmation of mABC fractional orders.