Instituto Tecnológico de Tijuana, México
HIV mathematical model considering antiretroviral administration
In this work, we present a proposal of a mathematical model of four ordinary differential equations that describe the evolution of HIV in an HIV-positive individual and the effect of an antiretroviral in the process of virus replication in CD4⁺ T cells. In order to determine the long-term effectiveness of the drug, the cases with and without antiretroviral treatment are analyzed to observe the effect on the population of healthy and infected CD4⁺ T cells. With our mathematical model, we are able to obtain a case where the antiretroviral allows a clinically healthy concentration of uninfected CD4⁺ T cells. Additionally, by applying the Compact Invariant Sets method we determine maximum values for the concentration of free HIV and both cells populations, healthy and infected. Finally, we perform numerical simulations in order to illustrate our results in the temporal plane, we plot the solutions of the system and their corresponding upper bounds, the latter allow us to define the maximum values of the HIV concentration in the bloodstream and the infected and healthy cells populations.