Ensembling Caputo, Caputo–Fabrizio and Atangana–Baleanu Fractional-Order Models to Study HIV Dynamics in Nigeria.

Abstract:

This study investigates HIV dynamics in Nigeria using fractional-order epidemic models formulated with Caputo, Caputo–Fabrizio, and Atangana–Baleanu fractional derivatives, together with an ensemble framework integrating their predictions. A five-compartment SEIDT model representing susceptible, exposed, infected, diagnosed, and treated populations is developed to incorporate memory effects inherent in HIV transmission and treatment. Numerical simulations covering 1990–2030 are conducted using parameter values from the literature and Nigerian demographic data. Results show that the Caputo–Fabrizio model produces rapid early responses, the Atangana–Baleanu model exhibits improved long-term stability, and the ensemble model provides conservative and robust forecasts. Sensitivity analysis confirms the stabilizing advantage of the ensemble approach. These findings highlight the relevance of fractional-order models for realistic HIV forecasting and public health planning in Nigeria.