Global Dynamics and Optimal Control Analysis of Tuberculosis Transmission Model With Incomplete Treatment

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DOI: https://doi.org/10.28924/2291-8639-24-2026-113
Published: Apr 20, 2026
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Ratchada Viriyapong, Suthidarat Duangchit, Global Dynamics and Optimal Control Analysis of Tuberculosis Transmission Model With Incomplete Treatment, Int. J. Anal. Appl., 24 (2026), 113.

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Ratchada Viriyapong, Suthidarat Duangchit

Abstract

A mathematical model of tuberculosis (TB) with incomplete treatment is proposed. Two classes of treated individuals including treated latent and treated active TB are considered and both classes may reenter due to an incomplete treatment. Our model therefore consists of six classes which are susceptible, latent, active TB, treated latent, treated active TB, and recovered individuals. The model solutions are proved to be nonnegative and bounded. We calculate two equilibrium points (disease-free and endemic) and their stability conditions are analyzed locally and globally. The basic reproduction number is computed and it is obtained that when it is less than a unity, a global asymptotic stability is observed for disease-free equilibrium point. And when it is greater than a unity, an endemic equilibrium point exists and stable under some certain conditions. Furthermore, a model is extended to include optimal control problem by considering four control variables which are preventive control, the screening and put under treatment control, the treatment effort for active TB and the campaign to make sure patients obtain complete treatment. Numerical simulations are performed and the results show that single control could reduce patients with TB infection for some certain amount, however, a combination of four controls give the most promising in reducing TB patients and increasing recovered ones. These results can benefit in providing information for public health authorities to take further action.

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