Abstract

DELGADO-MOYA, Erick  and  PIETRUS, Alain. Fractional-order optimal control for a model of tuberculosis treatment efficacy in the presence of HIV/aids and diabetes. Rev. Mat [online]. 2022, vol.29, n.2, pp.177-223. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v29i2.50888.

In this paper, taking advantage of the use of fractional order derivatives in the Caputo sense, we present a study of optimal control of tuberculosis (TB) treatment efficacy in the presence of HIV/AIDS and diabetes. The mathematical model to which control is applied is found in (17) and studies the relationship between TB, HIV/AIDS and diabetes with respect to treatment efficacy and differentiates into multidrug-resistant TB (MDRTB), and extensively drug-resistant TB (XDR-TB). The definition of controls focuses on avoiding reinfection/reactivation, MDR-TB and XDR-TB in the different subpopulations (TB only, TB-HIV/AIDS and TB-Diabetes). The model which is divided into subpopulations allows us to differentiate transmission and resistance behaviors and to evaluate the different costs in the application of controls. We performed computational simulations with literature data to study our control problem in a specific scenario. We explored the behavior of the basic reproduction number by varying the effective contact rate and the parameters associated with the resistance for different values of α (fractional order). We studied different control strategies based on the activation of the controls and found that the most effective is when we activate all the controls. With this strategy, we reduce the number of resistant cases, mainly in XDR-TB in diabetics which has a strong impact on the dynamics of TB resistance and transmission. In addition, this strategy avoids future growth in the number of resistant cases.

Keywords : diabetes; HIV/AIDS; fractional derivatives in the Caputo sense; optimal control problem; tuberculosis..

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