Modeling the initial period of HIV-1 infection spread in the lymph node based on delay differential equations

Pertsev N.V., Loginov K.K.
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A mathematical model describing the dynamics of HIV-1 infection in a single lymph node during the initial period of infection development is presented. Within the framework of the model, the infection of an individual is set by a nonnegative finite function describing the rate of entry of the initial viral particles into the lymph node. The equations of the model are derived with consideration of two factors: 1) the interaction of viral particles with naive CD4+ T lymphocytes in various phases of the cell cycle; 2) contact interaction between multiplying naive CD4+ T lymphocytes and infected CD4+ T lymphocytes producing viral particles. The specific feature of intercellular contact interactions is the formation of complexes consisting of pairs of these cells. The duration of the complexes’ existence is determined by the distribution functions over finite time intervals. The model is presented as a high-dimensional system of nonlinear delay differential equations, including two equations with distributed delay, and is supplemented with non-negative initial data. In the absence of HIV-1 infection, the model is reduced to four delay differential equations describing the number of naive CD4+ T-lymphocytes in different phases of the cell cycle. The global solvability of the model (the existence and uniqueness of the solution on the semi-axis) is determined, and the non-negativity of the solution components is established. To carry out computational experiments with the model, an algorithm for numerically solving the used system of differential equations are developed based on the semi-implicit Euler scheme for the case of uniform distribution of durations of the complexes existence. The results of computational experiments aimed at approximation the numerical solution of the model to describing the kinetics of HIV-1 infection spread in its acute phase, including the eclipse phase, are presented. The variable used as the observable is the variable describing the number of viral particles per milliliter of blood on days 10–12 after the onset of acute infection. The dynamics of the observable variable is numerically studied depending on the variation of the model parameters reflecting the patterns of complex formation and the formation of cells producing viral particles. The possibility of attenuation of HIV-1 infection in the lymph node at certain values of some of the model parameters is shown.

Keywords: HIV-1 infection, lymph node, naive CD4+ T lymphocytes, delay differential equations, computational experiment
Citation in English: Pertsev N.V., Loginov K.K. Modeling the initial period of HIV-1 infection spread in the lymph node based on delay differential equations // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1181-1203
Citation in English: Pertsev N.V., Loginov K.K. Modeling the initial period of HIV-1 infection spread in the lymph node based on delay differential equations // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1181-1203
DOI: 10.20537/2076-7633-2025-17-6-1181-1203
URL: http://crm-en.ics.org.ru/journal/article/3673/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2025 Pertsev N.V., Loginov K.K.

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