A Caputo fractional-order SEIHRD model for Ebola: theoretical analysis, sensitivity, bifurcation, and numerical simulations

Abstract This study develops and analyzes a Caputo fractional-order SEIHRD model to investigate the transmission dynamics and control of Ebola virus disease. The model ensures positivity, boundedness, and invariance of feasible regions for all solutions. Rigorous analysis establishes local and global existence, uniqueness, and well-posedness of the system. The basic reproduction number $$R_0$$ is derived, with stability analysis of disease-free and endemic equilibria revealing a forward transcritical bifurcation at $$R_0 = 1$$ . Sensitivity analysis identifies key parameters significantly influencing $$R_0$$ and endemic infection levels. Numerical simulations using both the Fractional Runge-Kutta scheme and the Fractional Differential Transform Method demonstrate the pronounced impact of the fractional order on system stability and persistence, with the Runge–Kutta method providing superior accuracy. These results highlight the critical role of fractional-order modeling in capturing memory effects in epidemic processes and suggest the efficacy of fractional calculus in enhancing epidemic predictions. The results show that fractional-order dynamics capture Ebola’s persistence and memory effects, providing a framework for control strategies. This also points toward incorporating fuzzy fractional approaches to better address parameter uncertainty, offering a robust framework for future extensions in epidemic modeling and control strategies.