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20 October 2026

45 Pages

Optimal Control Approach for Modeling the Introduction of Sterilizing Treatment for Tuberculosis in Low- and Middle-Income Countries

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1
Department of Basic Sciences, Universidad Nacional de Colombia, Palmira 763533, Colombia
2
Department of Mathematics, Universidad Autonoma de Occidente, Cali 760032, Colombia
3
Institute of Mathematics, Brandenburg University of Technology, 03046 Cottbus, Germany
4
Department of Mathematics, Universidad del Valle, Cali 760031, Colombia

Abstract

This study presents a mathematical modeling framework to analyze the impact of integrating sterilizing treatment into tuberculosis (TB) control strategies, particularly in resource-limited settings. The numerical analysis of the proposed mathematical framework indicates that while sterilizing treatment alone is highly effective in reducing TB incidence and mortality, its widespread implementation requires significant financial investment. The optimal control approach demonstrates that a mixed strategy, combining sterilizing and non-sterilizing treatments, can achieve comparable public health benefits at a lower cost, especially in medium-term planning. From a long-term perspective, however, our results suggest that exclusively sterilizing treatment ultimately leads to greater reductions in TB incidence, prevalence, and mortality, justifying its higher initial cost. This is primarily due to the ability of sterilizing drugs to eliminate latent TB infections, prevent future active infections and disease-induced deaths, and avoid a considerable number of treatments. Additionally, under scenarios where the cost of sterilizing drugs decreases over time, a swift transition to a solely sterilizing treatment could result in both epidemiological and economic advantages for healthcare systems.

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