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

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  • Alessandro Ramponi
  • Maria Elisabetta Tessitore

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 the Pontryagin's Maximum Principle, we give conditions for the existence of the optimal policy, which we characterize explicitly 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 pandemic for the model calibration.

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  • Alessandro Ramponi & Maria Elisabetta Tessitore, 2022. "The economic cost of social distancing during a pandemic: an optimal control approach in the SVIR model," Papers 2208.04908, arXiv.org.
  • Handle: RePEc:arx:papers:2208.04908
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    References listed on IDEAS

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    1. Michael McAsey & Libin Mou & Weimin Han, 2012. "Convergence of the forward-backward sweep method in optimal control," Computational Optimization and Applications, Springer, vol. 53(1), pages 207-226, September.
    2. Federico, Salvatore & Ferrari, Giorgio, 2021. "Taming the spread of an epidemic by lockdown policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    3. Thomas Kruse & Philipp Strack, 2020. "Optimal Control of an Epidemic through Social Distancing," Cowles Foundation Discussion Papers 2229, Cowles Foundation for Research in Economics, Yale University.
    4. Fernando Alvarez & David Argente & Francesco Lippi, 2021. "A Simple Planning Problem for COVID-19 Lock-down, Testing, and Tracing," American Economic Review: Insights, American Economic Association, vol. 3(3), pages 367-382, September.
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