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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Fractional-Order VSEITR Model with Caputo Derivative for Analyzing Tuberculosis Dynamics and Control Strategies in Algeria

Journal of Applied Nonlinear Dynamics 15(4) (2026) 765--787 | DOI:10.5890/JAND.2026.12.001

Rayane Boucherma, Mohammed Salah Abdelouahab, René Lozi

Laboratoire de Mathématiques Appliquées et Didactique, Ecole Normale Supérieure de Constantine, Constantine, Algeria

Laboratory of Mathematics and their interactions, University Centre Abdelhafid Boussouf, Mila, 43000, Algeria

Laboratoire J. A. Dieudonne, CNRS, Université Côte d'Azur, 06108 Nice, France

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Abstract

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, $\mathcal{R}_0$, 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.

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