Modeling and stability analysis of a fractional-order tuberculosisvmodel with different exposed populations progressing to infection

Muhammad Farman; Kottakkaran Sooppy Nisar

doi:10.46481/jnsps.2026.3502

Authors

Muhammad Farman
Faculty of Arts and Sciences, Department of Mathematics, Near East University, Mersin 10, Nicosia 99138, Turkey;

Faculty of Medicine, Department of Biostatistics and Medical Informatics, Karadeniz Technical University, Trabzon, Turkey;

International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore, Pakistan
Kottakkaran Sooppy Nisar
[email protected]

Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Keywords:

Tuberculosis model, Well-posedness, Basic reproduction number, Lyapunov stability, Simulation

Abstract

This study develops a fractional-order mathematical model based on the Atangana--Baleanu--Caputo (ABC) operator to investigate the transmission dynamics of tuberculosis (TB). The framework incorporates memory and nonlocal effects to represent the spread and progression of TB within a population. The first derivative of a Lyapunov function is used to evaluate the infection locally and globally within the fractional-order model. The model satisfies the essential mathematical properties of positivity, boundedness, existence, and uniqueness of solutions, thereby establishing its biological and mathematical well-posedness. Fixed-point theory is used to analyze the model and bound its solution. The analysis establishes local and global stability conditions and identifies the parameters that most strongly affect disease transmission. An advanced numerical method is used to obtain approximate solutions of the fractional-order system and evaluate the effect of the fractional-order parameter. Numerical simulations show that decreasing the fractional-order parameter enhances memory effects and produces smoother convergence toward equilibrium states than the classical integer-order model. The results indicate that the fractional-order framework provides a useful representation of TB dynamics and may support the understanding and control of TB transmission.

Dimensions

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