A Fractional-Order VSEITR Model with Caputo Derivative for Analyzing Tuberculosis Dynamics and Control Strategies in Algeria - Boucherma, Rayane; Abdelouahab, Mohammed Salah; Lozi, René (Journal of Applied Nonlinear Dynamics, 2026)
This paper presents a novel VSEITR fractional-order model to investigate the dynamics and control strategies of tuberculosis (TB) in Algeria. The model incorporates the Caputo fractional derivative, offering a more precise representation of TB transmission dynamics by integrating memory effects and long-term dependencies. Using TB data reported from 1990 to 2023, the model parameters were carefully calibrated, demonstrating a strong alignment with real-world data. Key analyses include the computation of the basic reproduction number, R_0, and the examination of equilibrium states. Stability of both disease-free and endemic equilibria are rigorously analysed within the fractional model. Numerical simulations highlight the advantages of the proposed fractional-order model in capturing complex disease behaviour, with implications for public health strategies.