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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 1, Pages 74–89
DOI: https://doi.org/10.33048/sibjim.2018.22.108 (Mi sjim1034) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations

N. V. Pertsevab, B. Yu. Pichuginb, K. K. Loginovb

a Marchuk Institute of Numerical Mathematics RAS, ul. Gubkina 8, 119333 Moscow
b Sobolev Institute of Mathematics RAS, Omsk Branch, ul. Pevtsova 13, 644043 Omsk
Full-text PDF (495 kB) Citations (9)
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DOI: https://doi.org/10.33048/sibjim.2018.22.108
Abstract: Some deterministic and stochastic models are constructed basing on the same assumptions about the dynamics of HIV-1 infection. The deterministic model has the form of a system of differential equations with three delays. The stochastic model is based on a branching process with the interaction of particles and takes into account the stages of maturation of cells and virions. The durations of these stages correspond to the parameters describing the delays in the deterministic model. The influence of discreteness of stochastic model variables on the dynamics of HIV-1 infection is demonstrated. We find the coinciding and significantly different conditions of HIV-1 infection elimination in the framework of deterministic and stochastic models.
Keywords: HIV-1 infection, delay differential equation, branching process with interaction and immigration of particles, Monte-Carlo method, basic reproductive number.
Funding agency Grant number
Russian Science Foundation 18-11-00171
Received: 03.09.2018
Revised: 03.09.2018
Accepted: 15.12.2018
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 1, Pages 103–117
DOI: https://doi.org/10.1134/S1990478919010125
Bibliographic databases:
Document Type: Article
UDC: 519.248:57
Language: Russian
Citation: N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations”, Sib. Zh. Ind. Mat., 22:1 (2019), 74–89; J. Appl. Industr. Math., 13:1 (2019), 103–117
Citation in format AMSBIB
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\paper Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations
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\vol 22
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\pages 74--89
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\jour J. Appl. Industr. Math.
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\pages 103--117
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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