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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 1, Pages 465–476
DOI: https://doi.org/10.33048/semi.2023.20.027 (Mi semr1591) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Probability theory and mathematical statistics

Critical Multitype Branching Processes on a Graph and the Model of the HIV Infection Development

V. A. Topchii, N. V. Pertsev

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2023.20.027
Abstract: We consider the Crump-Mode-Jagers branching process on an oriented graph in an application to modeling the development of HIV-1 infection in a human organism. For all particles of the same global type, located at each of the verteces or arcs of the graph, different types are assigned. Checking the criticality condition and searching for the eigenvectors of an offspring mean matrix in the critical case for the original process are reduced to an offspring mean matrix for some Galton-Watson process. The last has the types of particles corresponding only to the verteces of the graph.
Keywords: Crump-Mode-Jagers branching process on an oriented graph, Yaglom type limit theorem for critical branching process, eigenvectors for the mean matrix of high dimension, stochastic model of HIV-1 infection.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0003
The research was funded in accordance with the state task of the IM SB RAS, project FWNF-2022-0003.
Received September 13, 2022, published June 27, 2023
Document Type: Article
UDC: 519.218.2
MSC: 60J85,~60J80
Language: Russian
Citation: V. A. Topchii, N. V. Pertsev, “Critical Multitype Branching Processes on a Graph and the Model of the HIV Infection Development”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 465–476
Citation in format AMSBIB
\Bibitem{TopPer23}
\by V.~A.~Topchii, N.~V.~Pertsev
\paper Critical Multitype Branching Processes on a Graph and the Model of the HIV Infection Development
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 1
\pages 465--476
\mathnet{http://mi.mathnet.ru/semr1591}
\crossref{https://doi.org/10.33048/semi.2023.20.027}
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