Determination of the parameters of the mathematical model of the immune response to HIV

Human immunodeficiency virus of type 1 (HIV) attacks the immune system and thereby weakens the defense against other infections and some types of cancer that the immune system of a healthy person can cope with. Despite the use of highly active antiretroviral therapy (HAART), there are no methods yet to completely eliminate HIV from the body of an infected person. However, due to the expansion of access to HIV prevention, diagnosis and treatment with HAART, HIV infection has moved into the category of controllable chronic diseases. Mathematical modeling methods are actively used to study the kinetic mechanisms of HIV pathogenesis and the development of personalized approaches to treatment based on combined immunotherapy. One of the central tasks of HIV infection modeling is to determine the individual parameters of the immune system response during the acute phase of HIV infection by solving inverse problems.
To study the kinetics of the pathogenesis of HIV infection, a mathematical model of eight ordinary differential equations formulated by Bank et al. [5] was used. The system of equations of the model describes the change in the number of four subpopulations of CD4+ T cells and two types of CD8+ T cells. A feature of this model is the consideration of latently infected CD4+ T cells, which serve as the main reservoir of the viral population. The viral load on the human body is determined by the combination of populations of infectious and noninfectious viral particles.
The inverse problem of parameter identification based on the data of the acute phase of HIV infection was studied. In particular, the identifiability of the parameters was studied and sensitivity analysis from the input data was performed. The inverse problem was reduced to a minimization problem using the evolutionary centers method.