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<p>The human immunodeficiency virus (HIV) of type 1 hits the immune system and weakens the defense against other infections and some types of cancer that could be suppressed by the immune system of a healthy person. Using highly active antiretroviral therapy (HAART) still cannot completely eliminate HIV from the body of an infected person. However, due to wide access to the means of HIV prevention, diagnosis and treatment with HAART, HIV infection became one of controllable chronic diseases. Methods of mathematical modeling are actively used to study the kinetic mechanisms of HIV pathogenesis and to develop personalized approaches to treatment based on combined immunotherapy. One of the central problems 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. In this paper, we use a mathematical model of eight ordinary differential equations formulated by Bank et al.&#xa0;[<CitationRef CitationID="CR2">2</CitationRef>] to study the kinetics of the pathogenesis of HIV infection. This system of equations describes the change of size of four subpopulations of CD4+ T cells and two types of CD8+ T cells. This model considers 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. We study the inverse problem of identification of parameters based on the data of the acute phase of HIV infection. In particular, we analyse the identifiability of the parameters and their sensitivity from the input data. We reduce the inverse problem to the minimization problem using the evolutionary centers method.</p>

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DETERMINING PARAMETERS OF THE MATHEMATICAL MODEL OF THE IMMUNE RESPONSE TO HIV INFECTION

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • P. S. Surnin,
  • M. A. Shishlenin,
  • G. A. Bocharov

摘要

The human immunodeficiency virus (HIV) of type 1 hits the immune system and weakens the defense against other infections and some types of cancer that could be suppressed by the immune system of a healthy person. Using highly active antiretroviral therapy (HAART) still cannot completely eliminate HIV from the body of an infected person. However, due to wide access to the means of HIV prevention, diagnosis and treatment with HAART, HIV infection became one of controllable chronic diseases. Methods of mathematical modeling are actively used to study the kinetic mechanisms of HIV pathogenesis and to develop personalized approaches to treatment based on combined immunotherapy. One of the central problems 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. In this paper, we use a mathematical model of eight ordinary differential equations formulated by Bank et al. [2] to study the kinetics of the pathogenesis of HIV infection. This system of equations describes the change of size of four subpopulations of CD4+ T cells and two types of CD8+ T cells. This model considers 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. We study the inverse problem of identification of parameters based on the data of the acute phase of HIV infection. In particular, we analyse the identifiability of the parameters and their sensitivity from the input data. We reduce the inverse problem to the minimization problem using the evolutionary centers method.