Evaluación teórica de estrategias óptimas y sub-óptimas de terapia antirretroviral para el control de la infección por VIH

Abstract

HIV interaction with the immune response is modeled mathematically. Initially, a detailed model is proposed that consists of a system of differential equations including immune cells (antigen presenting cells, T latent infected cells, T actively infected cells, resting T cells, helper T cells, inactive cytotoxic cells and active cytotoxic cells) and viral particles. Then, stability conditions are given from the basic reproduction number and numerical simulations are performed. From this it is possible to conclude what are the most influential parameters to reduce infection. From the initial model, a control problem is formulated in order to determine the most appropriate type of intervention to ensure high levels of activated T cells and immune response. Five different control strategies based on antiretroviral are evaluated to conclude that a strategy of constant control, obtained as the average value of optimal control, provides satisfactory results.

HIV Propagation in a Population Group Considering Infection in the Immune System Of Each Infected Individual

“…Also the equilibrium values are in the interval of (500, 2000), which means there is an infection outbreak (in those cases simulated R 0 was greater than 1). In spite of having varied the effectiveness of PI (u 2 ), the results for the infected cells T * were also quite similar, almost equal to those obtained in the previous simulation (Figure 4), when using values of u 2 ≤ 0.6, T * tends to stabilize in the interval (5,30) cell/mm 3 . and the active CD8 T cells stabilize in the interval (13,17).…”

“…The R 0 is important given that "theoretically" it determines if there will be a peak in viral production (R 0 > 1), on the contrary, there will be no increase of the viral particles when R 0 < 1, which means that the infection is not established and manages to disappear, as established in the following results [28][29][30].…”

Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation

“…A wide variety of mathematical models have been formulated to study HIV infection at the cellular level [2,3,18,20,21,23,24,26,28,[31][32][33][34][35]37,38,40,[46][47][48] as well as its spread in susceptible populations [7,10,22,39,44,45]. Such models approach the study of infection from different perspectives, and have made it possible to evaluate the effect that preventive measures or prophylaxis and diagnosis may have in reducing transmission [10,11,17,39,41,43], the effectiveness of antiretrovirals in controlling viral loads, in this case, optimal control models have been very important tools [20,23,31,[41][42][43][44]46]. Finally, any study must begin from the knowledge of the virus and how it interacts with the host's immune system, in particular, a more relevant topic is latent infection in people who are unaware of its serological status.…”

Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation

“…A wide variety of mathematical models has been formulated to study HIV infection at cellular level [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], as well as its spread in uninfected populations [28][29][30][31][32][33]. Such models address the study of infection from different perspectives and have made it possible to evaluate the possible effect of preventive measures or prophylaxis and diagnosis on reducing transmission [29,31,[34][35][36][37]. Concerning the effectiveness of antiretroviral medications in controlling viral loads, optimal control models have been very important tools [11,13,17,25,32,[36][37][38].…”

“…Such models address the study of infection from different perspectives and have made it possible to evaluate the possible effect of preventive measures or prophylaxis and diagnosis on reducing transmission [29,31,[34][35][36][37]. Concerning the effectiveness of antiretroviral medications in controlling viral loads, optimal control models have been very important tools [11,13,17,25,32,[36][37][38]. Finally, any study must begin with knowledge of the virus and how it interacts with the host's immune system.…”