The economic cost of social distancing during a pandemic: an optimal control approach in the SVIR model

Alessandro Ramponi () and M. Elisabetta Tessitore ()
Additional contact information
Alessandro Ramponi: University of Rome Tor Vergata
M. Elisabetta Tessitore: University of Rome Tor Vergata

Decisions in Economics and Finance, 2025, vol. 48, issue 1, No 23, 485-516

Abstract: Abstract We devise a theoretical model for the optimal dynamical control of an infectious disease whose diffusion is described by the SVIR compartmental model. The control is realized through implementing social rules to reduce the disease’s spread, which often implies substantial economic and social costs. We model this trade-off by introducing a functional depending on three terms: a social cost function, the cost supported by the healthcare system for the infected population, and the cost of the vaccination campaign. Using Pontryagin’s Maximum Principle, we are able to characterize the optimal control strategy in three instances of the social cost function, the linear, quadratic, and exponential models, respectively. Finally, we present a set of results on the numerical solution of the optimally controlled system by using Italian data from the recent COVID-19 pandemics for the model calibration.

Keywords: Optimal control; Social distancing; SVIR epidemic model; Pontryagin’s maximum principle (search for similar items in EconPapers)
JEL-codes: C61 C63 I12 I15 I18 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10203-023-00406-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:decfin:v:48:y:2025:i:1:d:10.1007_s10203-023-00406-0

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10203/PS2

DOI: 10.1007/s10203-023-00406-0

Access Statistics for this article

Decisions in Economics and Finance is currently edited by Paolo Ghirardato

More articles in Decisions in Economics and Finance from Springer, Associazione per la Matematica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().