¹Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
²Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia

Abstract. A continuously discrete stochastic model describing the dynamics of HIV-1 infection in the lymph node during the initial period of infection development is presented. The model uses two types of target cells for viral particles: CD4+ T lymphocytes and dendritic cells. The contacts of viral particles with CD4+ T lymphocytes lead to the absorption of viral particles and the transformation of CD4+ T lymphocytes into latently infected cells. Dendritic cells that capture viral particles go through an intermediate stage of development and turn into antigen-presenting cells capable of making contact with latently infected and uninfected CD4+ T lymphocytes. As a result of the contact interaction of these cells, complexes are formed that activate the proliferation of CD4+ T-lymphocytes, followed by the formation of productively infected cells. The Monte Carlo method was used to perform computational experiments with the model. The planning of computational experiments and preliminary calculations were carried out on the basis of a deterministic analogue of the model in the form of a nonlinear system of delay differential equations. The results of calculations for estimating model parameters when fitting solutions to real data on the number of viral particles in the blood in the acute phase of HIV-1 infection kinetics, including the eclipse phase, are presented. The conditions of development and attenuation of HIV-1 infection in the lymph node were studied depending on the parameters reflecting the competition of CD4+ T-lymphocytes and dendritic cells for contacts with viral particles, from the duration of the intermediate stage of formation of antigen-presenting dendritic cells and the average time to activation of reproduction of uninfected and latently infected CD4+ T-lymphocytes.

Key words: HIV-1 infection, lymph node, CD4+ T-lymphocytes, dendritic cells, stochastic model, delay differential equations, Monte Carlo method, computational experiment