Geodesic
Mathematical model of economic dynamics in an epidemic
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 797-813.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2023_20_2_a54,
     author = {A. Boranbayev and N. Obrosova and A. Shananin},
     title = {Mathematical model of economic dynamics in an epidemic},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {797--813},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a54/}
}
TY  - JOUR
AU  - A. Boranbayev
AU  - N. Obrosova
AU  - A. Shananin
TI  - Mathematical model of economic dynamics in an epidemic
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2023
SP  - 797
EP  - 813
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a54/
LA  - en
ID  - SEMR_2023_20_2_a54
ER  - 
%0 Journal Article
%A A. Boranbayev
%A N. Obrosova
%A A. Shananin
%T Mathematical model of economic dynamics in an epidemic
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2023
%P 797-813
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a54/
%G en
%F SEMR_2023_20_2_a54
A. Boranbayev; N. Obrosova; A. Shananin. Mathematical model of economic dynamics in an epidemic. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 797-813. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a54/

[1] J. Fernández-Villaverde, C.I. Jones, “Macroeconomic outcomes and COVID-19: A progress report”, Brookings Papers on Economic Activity, 2020:3 (2020), 111–166 | DOI

[2] V. Guerrieri, G. Lorenzoni, L. Straub, I. Werning, Macroeconomic implications of COVID-19: Can negative supply shocks cause demand shortages?, SSRN Electronic Journal, 2020

[3] R. Chetty, J.N. Friedman, M. Stepner, The economic impacts of COVID-19: Evidence from a new public database built using private sector data, Working Paper, No 27431, National Bureau of Economic Research, Cambridge, 2020

[4] D. Acemoglu, V. Chernozhukov, I Werning, M.D. Whinston, A multi-risk SIR model with optimally targeted lockdown, Working Paper, No 27102, National Bureau of Economic Research, Cambridge, 2020

[5] F.E. Alvarez, D. Argente, F. Lippi, A simple planning problem for Covid-19 lockdown, Working Paper, No 26981, National Bureau of Economic Research, 2020

[6] M.S Eichenbaum, S. Rebelo, M. Trabandt, “The macroeconomics of epidemics”, The Review of Financial Studies, 34:11 (2021), 5149–5187 | DOI

[7] A. Goenka, L. Liu, M.-H. Nguyen, “SIR economic epidemiological models with disease induced mortality”, J. Math. Econ., 93 (2021), 102476 | DOI | MR | Zbl

[8] D. Krüger, H. Uhlig, T. Xie, Macroeconomic dynamics and reallocation in an epidemic: Evaluating the «Swedish Solution», NBER Working Paper Series, Working Paper, No 27047, 2021

[9] S. Aseev, A. Kryazhimskiy, “The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons”, SIAM J. Control Optim., 43:3 (2004), 1094–1119 | DOI | MR | Zbl

[10] M. Bardi, I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, Birkhäuser, Boston, 1997 | MR | Zbl

[11] F. van der Ploeg, A. de Zeeuw, “Pricing carbon and adjusting capital to fend off climate catastrophes”, Environ. Resource Econ., 72 (2019), 29–50 | DOI