MATHEMATICAL MODEL OF ECONOMIC DYNAMICS IN AN EPIDEMIC
Boranbayev A. Obrosova N. Shananin A.
2023Sobolev Institute of Mathematics
Siberian Electronic Mathematical Reports
2023#20Issue 2797 - 813 pp.
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.
economic growth model , epidemic , Hamilton-Jacobi-Bellman equation , lockdown , optimal control problem , SIR model
Text of the article Перейти на текст статьи
Nazarbayev University, 53 Kabanbay Batyr Ave., Astana, 010000, Kazakhstan
Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russian Federation
Federal Research Center «Computer Science and Control» of Russian Academy of Sciences, Vavilov Street 44/2, Moscow, 119333, Russian Federation
Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Moscow region, Dolgoprudny, 141701, Russian Federation
Nazarbayev University
Moscow Center for Fundamental and Applied Mathematics
Federal Research Center «Computer Science and Control» of Russian Academy of Sciences
Moscow Institute of Physics and Technology (State University)
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026