Mathematical Analysis and Optimal Control of a Tuberculosis Model with Early Diagnosed Latent Infections

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DOI: https://doi.org/10.28924/2291-8639-24-2026-260
Published: Aug 24, 2026
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Abdelfatah Abasher, Yasser Salah S. Abougamea, Elsiddeg Ali, Ibrahim Bashir, Mathematical Analysis and Optimal Control of a Tuberculosis Model with Early Diagnosed Latent Infections, Int. J. Anal. Appl., 24 (2026), 260.

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Abdelfatah Abasher, Yasser Salah S. Abougamea, Elsiddeg Ali, Ibrahim Bashir

Abstract

Tuberculosis (TB) remains one of the most dangerous infections disease and a major public health problem. This study develops an SEIR model for TB transmission, taking into account the early diagnosed latent infections. The model is used to derive the basic reproductive number \(\mathcal{R}_0\), study equilibrium points, and identify the most influential parameters through sensitivity analysis on \(\mathcal{R}_0\). An optimal control is formulated using four interventions: transmission reduction, early diagnosed latent TB, treatment, and vaccination. Different strategies are compared using infection averted, total cost, the average cost effectiveness ratio (ACER) and incremental cost effectiveness ratio (ICER). The results show that combined strategy which involve all interventions reduce the total cost, while transmission reduction only strategy gives the greatest reduction in infected individuals.

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