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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 797–813
DOI: https://doi.org/10.33048/semi.2023.20.047 (Mi semr1610) 		 
Computational mathematics

Mathematical model of economic dynamics in an epidemic

A. Boranbayeva, N. Obrosovabc, A. Shananindcb

a Nazarbayev University, 53 Kabanbay Batyr Ave., 010000, Astana, Kazakhstan
b Federal Research Center «Computer Science and Control» of Russian Academy of Sciences, Vavilov Street 44/2, 119333, Moscow, Russian Federation
c Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, 119991, Moscow, Russian Federation
d Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, 141701, Dolgoprudny, Moscow region, Russian Federation
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DOI: https://doi.org/10.33048/semi.2023.20.047
Abstract: The paper proposes a model of economic growth in an epidemic. It takes into account the dependence of the labor force on the parameters of the epidemic and the contacts restrictions, built on the base of the stable equilibrium in the corresponding SIR model, which evolves in a faster time compared to the main model. The model is formalized as an optimal control problem on an infinite horizon. The verification theorem is proved and the turnpike for the growth model without the epidemic is found. The study of a non-trivial stationary regime in a growth model during an epidemic makes it possible to analyze the dependence of the main macroeconomic indicators on the model parameters. Examples of calculations are presented that confirm the adequacy of the developed model.
Keywords: optimal control problem, Hamilton-Jacobi-Bellman equation, SIR model, economic growth model, epidemic, lockdown.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP09261118
This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP09261118).
Received June 26, 2023, published September 25, 2023
Document Type: Article
UDC: 519.86
MSC: 46N10
Language: English
Citation: A. Boranbayev, N. Obrosova, A. Shananin, “Mathematical model of economic dynamics in an epidemic”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 797–813
Citation in format AMSBIB
\Bibitem{BorObrSha23}
\by A.~Boranbayev, N.~Obrosova, A.~Shananin
\paper Mathematical model of economic dynamics in an epidemic
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 797--813
\mathnet{http://mi.mathnet.ru/semr1610}
\crossref{https://doi.org/10.33048/semi.2023.20.047}
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