Advanced Mathematical Analysis of Ebola Virus Transmission Through Fractal Fractional Order Models

This study presents an advanced mathematical framework for analyzing the intricate dynamics of Ebola virus transmission, utilizing a fractal-fractional order model to encapsulate the complex geometric characteristics of the underlying dynamical system. The existence and uniqueness of solutions are established through a rigorous fixed-point theorem approach, while Ulam-Hyers stability is meticulously investigated. Fundamental epidemiological insights are derived, including the establishment of non-negative solutions, computation of the basic reproduction number, sensitivity analysis, and identification of equilibrium points. To corroborate the theoretical re- sults, numerical simulations are performed using the Adams-Bashforth approximation method, alongside the development of an interpolation-based numerical scheme to enhance computa- tional efficiency. The findings are illustrated through comprehensive graphical representations, highlighting the robustness and applicability of the proposed model in elucidating and predicting the transmission dynamics of the Ebola virus.