Analytical and Numerical investigation of a Mathematical Model for Ebola Virus Dynamics

Ebola Virus Disease (EVD) remains a major global health concern due to its high fatality rate and rapid transmission, particularly in resource limited regions. In this study, we investigate the dynamics of EVD transmission using a fractional-order SIRD model incorporating the Atangana–Baleanu–Caputo (ABC) derivative to capture memory-dependent behaviors inherent in infectious processes. The defined model based on fractional calculus provide a more accurate description of temporal dynamics by integrating nonlocal and nonsingular kernels. That model is biologically more realistic than classical integer-order formulations. We use the Homotopy Perturbation Method (HPM) to provide a reliable and efficient means to handle the nonlinear structure. Theoretical analysis of the model includes existence and uniqueness of the solution using fixed point theory. Furthermore, the basic reproduction number is derived through the next-generation matrix approach to assess threshold behavior and local stability of the disease free equilibrium. We use graphical simulations in Mathematica, based on varying fractional orders and key epidemiological parameters, offer insights into the impact of memory effects on disease progression. The suggested model architecture allows better forecasting for managing the Ebola outbreak and exhibits increased analytical integrity.