Abstract

ARIAS-CASTRO, Juddy-Heliana; GIRON-CARABALI, Tatiana  and  MARTINEZ-ROMERO, Héctor-Jairo. Mathematical Model for the Dynamics of Tuberculosis Considering Low-Risk Latents. Rev. Cient. [online]. 2023, n.47, pp.138-154.  Epub Sep 22, 2023. ISSN 0124-2253.  https://doi.org/10.14483/23448350.20549.

This work proposes a model for the dynamics of tuberculosis, which considers a latent low-risk population, with the aim of evaluating the importance of including it in the model and determining whether it is necessary to treat and/or control it. To this effect, a qualitative analysis of the model was carried out, determining which parameters are most relevant in the initial transmission of the disease and calculating the average number of new infections produced by an infectious individual. An optimal control problem was formulated and numerically solved, which seeks to minimize both the infected and the economic costs generated by the implementation of controls in the proposed dynamics of tuberculosis. Numerical simulations were used to analyze the effects of implementing the controls obtained. Finally, simulations are carried out for Cali (Colombia), establishing a methodology for the design of control strategies aimed at reducing the transmission of tuberculosis in the city.

Keywords : control methodology; mathematical modeling; numerical simulations; optimal control; qualitative analysis; tuberculosis..

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