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Direct Statistical Modeling of HIV-1 Infection Based on a Non-Markovian Stochastic Model

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Abstract

An approach to the numerical modeling of the dynamics of HIV-1 infection based on a non-Markovian stochastic model is presented. In the model, the population dynamics of cells and viral particles are described taking into account the prehistory of their development and transitions between two compartments. An algorithm for direct statistical modeling of the dynamics of the studied populations is developed. Results obtained by studying special cases of the constructed model, including its deterministic analogue, and published clinical data are used for specifying the details of numerical experiments. The eradication probability of HIV-1 infection and the dynamics of typical realizations of population sizes are examined in relation to the initial number of virus particles and parameters of the model.

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Funding

Bocharov’s research was supported by the Russian Science Foundation (project no. 18-11-00171) and the Moscow Center for Fundamental and Applied Mathematics (agreement no. 075-15-2019-1624 with the Ministry of Science and Higher Education of the Russian Federation). Pertsev acknowledges the support of the Russian Science Foundation (project no. 18-11-00171), and the work by Loginov and Topchii was performed within the state assignment at the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2019-0009).

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Authors and Affiliations

  1. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia

    G. A. Bocharov & N. V. Pertsev

  2. Moscow Center for Fundamental and Applied Mathematics, Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia

    G. A. Bocharov

  3. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    K. K. Loginov, N. V. Pertsev & V. A. Topchii

Authors
  1. G. A. Bocharov
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  2. K. K. Loginov
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  3. N. V. Pertsev
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  4. V. A. Topchii
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Corresponding authors

Correspondence to G. A. Bocharov, K. K. Loginov, N. V. Pertsev or V. A. Topchii.

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Translated by I. Ruzanova

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Bocharov, G.A., Loginov, K.K., Pertsev, N.V. et al. Direct Statistical Modeling of HIV-1 Infection Based on a Non-Markovian Stochastic Model. Comput. Math. and Math. Phys. 61, 1229–1251 (2021). https://doi.org/10.1134/S0965542521060026

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  • DOI: https://doi.org/10.1134/S0965542521060026

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