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

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.