Investigation the epidemiological transition of ebola virus under contagious population with sustainable extended fractional operator.

The Ebola outbreak represents one of the most severe global health crises in recent history. In this study, we develop and analyze a new fractional-order mathematical model for the transmission dynamics of the Ebola virus, incorporating an extended Atangana-Baleanu Caputo fractional operator. The model's foundational properties-such as existence, uniqueness, positivity, and well-posedness of solutions are established through fixed point theorems. A detailed investigation of the basic reproduction number is carried out, accompanied by a sensitivity analysis to highlight influential parameters affecting disease spread. To ensure the stability of the system, chaos control methods and Lyapunov functions are employed, alongside first and second derivative tests, to demonstrate global stability. Additionally, the convergence and uniqueness of the models solution are explored. For the numerical approximation, we apply Lagranges interpolation polynomials method, known for its effectiveness in generating accurate and convergent solutions. This approach offers a novel analytical framework for fractional-order epidemiological models. The findings demonstrate that fractional order derivatives are more dependable and efficient than classical orders when it comes to explaining biological processes.