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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 8, Pages 1245–1268
DOI: https://doi.org/10.31857/S0044466921060028 (Mi zvmmf11273) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Ordinary differential equations

Direct statistical modeling of HIV-1 infection based on a non-Markovian stochastic model

G. A. Bocharovab, K. K. Loginovc, N. V. Pertsevac, V. A. Topchiic

a Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
b Moscow Center for Fundamental and Applied Mathematics, Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
c Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
Citations (6)
DOI: https://doi.org/10.31857/S0044466921060028
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.
Key words: non-Markov model of HIV-1 infection, branching process, delay differential equations, Monte Carlo method, numerical experiment, eradication of HIV-1.
Funding agency Grant number
Russian Science Foundation 18-11-00171
18-11-00171
Moscow Center of Fundamental and Applied Mathematics 075-15-2019-1624
Ministry of Education and Science of the Russian Federation 0314-2019-0009
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).
Received: 05.06.2020
Revised: 23.12.2020
Accepted: 11.02.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 8, Pages 1229–1251
DOI: https://doi.org/10.1134/S0965542521060026
Bibliographic databases:
Document Type: Article
UDC: 519.248:57
Language: Russian
Citation: G. A. Bocharov, K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Direct statistical modeling of HIV-1 infection based on a non-Markovian stochastic model”, Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021), 1245–1268; Comput. Math. Math. Phys., 61:8 (2021), 1229–1251
Citation in format AMSBIB
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