A mathematical model for the study of latent tuberculosis under 3HP and 1HP regimens

Erick M. D. Moya; Diego Samuel Rodrigues; Erick M. D. Moya; Diego Samuel Rodrigues

doi:10.3934/mmc.2024032

Mathematical Modelling and Control

2024, Volume 4, Issue 4: 400-416. doi: 10.3934/mmc.2024032

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Research article

A mathematical model for the study of latent tuberculosis under 3HP and 1HP regimens

School of Technology, Universidade Estadual de Campinas (UNICAMP), Limeira 13484332, SP, Brazil

Received: 09 October 2023 Revised: 20 May 2024 Accepted: 28 June 2024 Published: 19 November 2024

In this paper, we proposed a mathematical model for the study of tuberculosis treatment with latent treatment, taking into account the 3HP and 1HP. The model is constructed using a fractional order derivative in the Caputo sense to take advantage of the memory effect. The aim is to compare the impact on tuberculosis, whether we keep the therapies that are applied to latent tuberculosis, use of once-weekly isoniazid-rifapentine for 12 weeks (3HP), or use of isoniazid and rifapentine once a day for 28 days (1HP). We presented the basic properties of the model and found the basic reproduction number. We performed computational simulations with different fractional orders to study the behavior of the model. We studied the variation of parameters associated with new latent therapies and different treatments for active tuberculosis in the basic reproduction number. We found that the implementations have a positive impact, as the basic reproduction number remains less than unity. We showed that both implementations enable positive results because they reduce active tuberculosis in the population. The 1HP results were better and showed that the duration of treatment positively influences adherence to therapy.
- fractional derivative,
- latent,
- tuberculosis,
- therapies
Citation: Erick M. D. Moya, Diego Samuel Rodrigues. A mathematical model for the study of latent tuberculosis under 3HP and 1HP regimens[J]. Mathematical Modelling and Control, 2024, 4(4): 400-416. doi: 10.3934/mmc.2024032

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Abstract

In this paper, we proposed a mathematical model for the study of tuberculosis treatment with latent treatment, taking into account the 3HP and 1HP. The model is constructed using a fractional order derivative in the Caputo sense to take advantage of the memory effect. The aim is to compare the impact on tuberculosis, whether we keep the therapies that are applied to latent tuberculosis, use of once-weekly isoniazid-rifapentine for 12 weeks (3HP), or use of isoniazid and rifapentine once a day for 28 days (1HP). We presented the basic properties of the model and found the basic reproduction number. We performed computational simulations with different fractional orders to study the behavior of the model. We studied the variation of parameters associated with new latent therapies and different treatments for active tuberculosis in the basic reproduction number. We found that the implementations have a positive impact, as the basic reproduction number remains less than unity. We showed that both implementations enable positive results because they reduce active tuberculosis in the population. The 1HP results were better and showed that the duration of treatment positively influences adherence to therapy.

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