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

Abstract

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 results, numerical simulations are performed using the Adams–Bashforth approximation method, alongside the development of an interpolation-based numerical scheme to enhance computational 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.