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.
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
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\by N.~V.~Pertsev, B.~Yu.~Pichugin, K.~K.~Loginov
\paper Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 1
\pages 74--89
\mathnet{http://mi.mathnet.ru/sjim1034}
\crossref{https://doi.org/10.33048/sibjim.2018.22.108}
\elib{https://elibrary.ru/item.asp?id=38676770}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 1
\pages 103--117
\crossref{https://doi.org/10.1134/S1990478919010125}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064805257}
Linking options:
https://www.mathnet.ru/eng/sjim1034
https://www.mathnet.ru/eng/sjim/v22/i1/p74
This publication is cited in the following 9 articles:
N.V. Pertsev, G.A. Bocharov, K.K. Loginov, “Mathematical Modeling of the Initial Period of Spread of HIV-1 Infection in the Lymphatic Node”, Math.Biol.Bioinf., 19:1 (2024), 112
N. V. Pertsev, K. K. Loginov, “Stokhasticheskoe modelirovanie v immunologii na osnove stadiya-zavisimoi struktury s nemarkovskimi ogranicheniyami dlya dinamiki otdelnykh kletok i patogenov”, Matem. biologiya i bioinform., 18:2 (2023), 543–567
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Chislennoe stokhasticheskoe modelirovanie dinamiki vzaimodeistvuyuschikh populyatsii”, Sib. zhurn. industr. matem., 25:3 (2022), 135–153
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical Stochastic Modeling of Dynamics of Interacting Populations”, J. Appl. Ind. Math., 16:3 (2022), 524
N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Numerical modelling of the transition of infected cells and virions between two lymph nodes in a stochastic model of HIV-1 infection”, Russ. J. Numer. Anal. Math. Model, 36:5 (2021), 293–302
N. Pertsev, K. Loginov, G. Bocharov, “Nonlinear effects in the dynamics of hiv-1 infection predicted by mathematical model with multiple delays”, Discret. Contin. Dyn. Syst.-Ser. S, 13:9, SI (2020), 2365–2384
K. Loginov, N. Pertsev, “Stochastic compartmental model of hiv-1 infection”, International Conference Mathematical Modelling in Biomedicine 2019, Itm Web of Conferences, 31, eds. V. Volpert, F. Syomin, EDP Sciences, 2020, 02003
N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of a stage-dependent epidemic model based on a non-Markov random process”, J. Appl. Industr. Math., 14:3 (2020), 566–580
K. K. Loginov, N. V. Pertsev, V. A. Topchii, “Stokhasticheskoe modelirovanie kompartmentnykh sistem s trubkami”, Matem. biologiya i bioinform., 14:1 (2019), 188–203
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