Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2021.tde-14012022-171117
Document
Author
Full name
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2021
Supervisor
Committee
Oliva Filho, Sergio Muniz (President)
Kuhl, Nelson Mugayar
Rodrigues, Diego Samuel
Sartori, Larissa Marques
Severo, Aymée de Los Ángeles Marrero
Title in English
Mathematical models for the study of adherence to tuberculosis treatment taking into account the effects of HIV/AIDS and diabetes
Keywords in English
Diabetes
Fractional derivatives in the Caputo sense
HIV/AIDS
Model
Optimal control
Tuberculosis
Abstract in English
In this work, we propose a new mathematical model for the study of the effectiveness of TB treatment taking into account the vulnerable subpopulations, HIV/AIDS and diabetic patients. Our model studies the different types of treatment resistance, multidrug-resistant (MDR TB) and extensively drug-resistant (XDRTB). We use two modeling techniques, ordinary differential equations (ODE) and fractional-order derivatives equations (FDE) in the Caputo sense. The main mathematical and epidemiological properties of the model are investigated. The basic reproduction number (0) in the different subpopulations (diabetics, HIV/AIDS, and those who do not suffer from these diseases) was studied. We present results that allow us to know how the basic reproductive number is affected when we vary the parameters of resistance and recovery together. We performed a sensitivity analysis of the parameters associated with TB. We proved the persistence of tuberculosis in a subpopulation showing the need to apply a control strategy. We formulated and studied an optimal control problem with the objective of reducing resistance to tuberculosis treatment. The controls are focused on reinfection/reactivation, MDR-TB and XDR-TB differentiated into subpopulations. We use the models with ODE and FDE in the formulation of the control problems. In order to study our models, we performed computational simulations. Among the results obtained, we have that drug-sensitive TB reported a greater number of cases with respect to MDR-TB and XDR-TB cases, and MDR-TB cases surpass XDR-TB cases, except in the diabetes subpopulation, which has a growth of XDR-TB cases that surpasses the other compartments of resistant of all the subpopulations. We show the need to pay differentiated attention to these vulnerable subpopulations due to the behavior of resistant cases. Regarding the control study, we obtained that the most effective strategy is to activate all controls and start with a high control. With this strategy we reduced the number of resistant cases significantly and prevented the growth of cases. This work helps health policies on how to act in this disease and these ideas can be applied to other epidemics of respiratory transmission.
Title in Portuguese
Modelos matemáticos para o estudo da aderência ao tratamento da tuberculose levando em conta os efeitos do HIV/AIDS e diabetes
Keywords in Portuguese
Controle ótimo
Derivadas fracionárias no sentido de Caputo
Diabetes
HIV/AIDS
Modelo
Tuberculose
Abstract in Portuguese