Abstract
The COVID-19 virus continues to circulate in many countries, despite successful attempts to curb previous waves, and hence the issue of effective control both of the epidemic and its economic consequences remains a matter of lively debate. Although the estimated development time for an effective vaccine proved to be relatively accurate, many governments were still unable to devise a clear and coherent control policy during the pre-vaccination period. Policy responses often vacillated between two seemingly conflicting strategies—protecting the economy versus containing the spread of the epidemic by all available means, including mobility restrictions and social and economic lockdown. In the setup of a multidimensional and non-linear optimal control model, we describe the performance of a capital accumulation-based economy in which the revenue generated from production relies on both capital and labor. Using analytical means, we characterize intertemporal policies that ensure an optimal tradeoff between: (i) the level of lockdown, the purpose of which is to contain the epidemic and prevent the national health system from becoming overwhelmed; (ii) the level of investment in treatments; (iii) the level of consumption; and (iv) consequential impacts on labor availability and capital accumulation. We show that the fear of infection alone can be highly capital-destructive. Finally, given an incompressible consumption level, we identify thresholds for the initial endowment in capital below which the stock of capital decreases over time and can eventually become fully depleted.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Acemoglu, D., Chernozhukov, V., Werning, I., Whinston, M.D.: Optimal targeted lockdowns in a multigroup SIR model. Am. Econ. Rev. Insights 3(4), 487–502 (2021)
Alvarez, F., Argente, D., Lippi, F.: A simple planning problem for COVID-19 lockdown, testing, and tracing. Am. Econ. Rev. Insights 3(3), 367–382 (2021)
Arrow, K.J.: Aspects of the Theory of Risk Bearing. Yrjö Jahnssonin Säätiö, Helsinki (1965)
Atolia, M., Papageorgiou, C., Turnosky, S.: Re-opening after the lockdown: long-run aggregate and distributional consequences of COVID-19. J. Math. Econ. 93, 102481 (2021)
Berkowitz, M.K., Qiu, J.: A further look at household portfolio choice and health status. J. Bank. Finance 30(4), 1201–1217 (2006)
Boucekkine, R., Carvajal, A., Chakraborty, S., Goenka, A.: The economics of epidemics and contagious diseases: an introduction. J. Math. Econ. 93, 102498 (2021)
Calvia, A., Gozzi, F., Lippi, F., Zanco, G.: A simple planning problem for COVID-19 lockdown: a dynamic programming approach. Econ. Theor. (2023). https://doi.org/10.1007/s00199-023-01493-1
Casey, B.H.: Covid-19: Is there a trade-off between economic damage and loss of life? The London School of Economics (2020). https://blogs.lse.ac.uk/europpblog/2020/12/18/covid-19-is-there-a-trade-off-between-economic-damage-and-loss-of-life/
Caulkins, J.P., Grass, D., Feichtinger, G., Hartl, R.F., Kort, P.M., Prskawetz, A., Seidl, A., Wrzaczek, S.: The optimal lockdown intensity for COVID-19. J. Math. Econ. 93, 102489 (2021)
Dobson, A., Ricci, C., Boucekkine, R., Gozzi, F., Fabbri, G., Loch-Temzelides, T., Pascual, M.: Balancing economic and epidemiological interventions in the early stages of pathogen emergence. Sci. Adv. 9(21), 1–15 (2023). https://doi.org/10.1126/sciadv.ade6169
Eichenbaum, M.S., Rebelo, S., Trabandt, M.: Economic activity and the spread of viral diseases: evidence from high frequency data. Rev. Financ. Stud. 34(11), 5149–5187 (2021)
El Ouardighi, F., Khmelnitsky, E., Sethi, S.P.: Epidemic control with endogenous treatment capability under popular discontent and social fatigue. Prod. Oper. Manag. 31 (4), 1734–1752 (2022)
Fabbri, G., Federico, S., Fiaschi, D., Gozzi, F.: Mobility decisions, economic dynamics and epidemic. Econ. Theor. (2023). https://doi.org/10.1007/s00199-023-01485-1
Financial Times: China insists it will stick with zero-Covid strategy. October 22 (2022). https://www.ft.com/content/885865b1-2320-43c0-b41e-10c1d026202a
Flaxman, S., Mishra, S., Gandy, A., Unwin, H.J.T., Coupland, H., Mellan, T.A., Bhatt, S.: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries. Nature (2020). https://doi.org/10.1038/s41586-020-2405-7
Goenka, A., Lui, L., Nguyen, M.-H.: SIR economic epidemiological models with disease induced mortality. J. Math. Econ. 93, 102476 (2021)
Goldsztejn, U., Schwartzman, D., Nehorai, A.: Public policy and economic dynamics of COVID-19 spread: a mathematical modeling study. PLoS ONE (2020). https://doi.org/10.1371/journal.pone.0244174
Grass D., Caulkins J.P., Feichtinger G., Tragler G., Behrens D.A.: Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror. Springer, Berlin (2008)
Hritonenko, N., Yatsenko, Y.: Analysis of optimal lockdown in integral economic–epidemic model. Econ. Theor. (2022). https://doi.org/10.1007/s00199-022-01469-7
Iboi, E.A., Sharomi, O., Ngonghala, C.N., Gumel, A.B.: Mathematical modeling and analysis of COVID-19 pandemic in Nigeria. Math. Biosci. Eng.Biosci. Eng. 17(6), 7192–7220 (2020). https://doi.org/10.3934/mbe.2020369
Kajitani, Y., Hatayama, M.: Explaining the effective reproduction number of covid-19 through mobility and enterprise statistics: evidence from the first wave in japan. PLoS One 16, e0247186 (2021). https://doi.org/10.1371/journal.pone
Keller, W.W., Lowi, T.J., Gendlin, G.: Negative capital and the wealth of nations. Int. Stud. Perspect.Perspect. 1(1), 75–87 (2000)
Kermack, W., McKendrick, O.: Contributions to the mathematical theory of epidemics—I. Bull. Math. Biol. 53(1–2), 33–55 (1991a)
Kermack, W., McKendrick, O.: Contributions to the mathematical theory of epidemics—II. The problem of endemicity. Bull. Math. Biol. 53(1–2), 57–87 (1991b)
Kermack, W., McKendrick, O.: Contributions to the mathematical theory of epidemics—III. Further studies of the problem of endemicity. Bull. Math. Biol. 53(1–2), 89–118 (1991c)
Kim, B.N., Kim, E., Lee, S., Oh, C.: Mathematical model of COVID-19 transmission dynamics in South Korea: the impacts of travel restrictions, social distancing, and early detection. Processes 8(10), 1304 (2020). https://doi.org/10.3390/pr8101304
Li, X., Rudolph, A.E., Mennis, J.: Association between population mobility reductions and new COVID-19 diagnoses in the United States along the urban-rural gradient. Prev. Chronic Dis. 17, 200–241 (2020). https://doi.org/10.5888/pcd17.200241externalicon
Mussio, I., Sosa Andrés, M., Kidwai, A.: Higher order risk attitudes in the time of COVID-19: an experimental study. Oxf. Econ. Pap.. Econ. Pap. (2022). https://doi.org/10.1093/oep/gpac007
Nhamo, G., Dube, K., Chikodzi, D.: Impact of COVID-19 on the global network of airports. In: Nhamo, G., Dube, K., Chikodzi, D. (eds.) Counting the cost of COVID-19 on the global tourism industry, pp. 109–133. Springer, Cham (2020a)
Nhamo, G., Dube, K., Chikodzi, D.: Implications of Covid-19 on gaming, leisure and entertainment industry. In: Nhamo, G., Dube, K., Chikodzi, D. (eds.) Counting the cost of COVID-19 on the global tourism industry, pp. 273–275. Springer, Cham (2020b)
Pachetti, M., Marini, B., Giudici, F., et al.: Impact of lockdown on Covid-19 case fatality rate and viral mutations spread in 7 countries in Europe and North America. J. Transnatl. Med. 18, 338 (2020). https://doi.org/10.1186/s12967-020-02501-x
Pratt, J.W., Zeckhauser, R.J.: Proper risk aversion. Econometrica 55(1), 143–154 (1987)
Smithson, M.: Data from 45 countries show containing COVID vs saving the economy is a false dichotomy. The Conversation, November (2020). https://theconversation.com/data-from-45-countries-show-containing-covid-vs-saving-the-economy-is-a-false-dichotomy-150533
South China Morning Post: ‘Stealth Omicron’: How dangerous is the pandemic’s new highly infectious strain of Covid 19? March 10 (2022). https://www.scmp.com/video/coronavirus/3169970/stealth-omicron-how-dangerous-pandemics-new-highly-infectious-strain
Worldometer: COVID-19 coronavirus (2021). www.worldometers.info/coronavirus/?utm_campaign=homeAdUOA?Si%23countries
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kogan, K., El Ouardighi, F. & Herbon, A. The economic impact of lockdown and bounded treatment capability for an epidemic without vaccine. Econ Theory 77, 283–306 (2024). https://doi.org/10.1007/s00199-023-01531-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-023-01531-y