Lockdown interventions in SIR models : Is the reproduction number the right control variable?
(2021) 60th IEEE Conference on Decision and Control, CDC 2021 In Proceedings of the IEEE Conference on Decision and Control 2021-December. p.4254-4259- Abstract
The recent COVID-19 pandemic highlighted the need of non-pharmaceutical interventions in the first stages of a pandemic. Among these, lockdown policies proved unavoidable yet extremely costly from an economic perspective. To better understand the tradeoffs between economic and epidemic costs of lockdown interventions, we here focus on a simple SIR epidemic model and study lockdowns as solutions to an optimal control problem. We first show numerically that the optimal lockdown policy exhibits a phase transition from suppression to mitigation as the time horizon grows, i.e., if the horizon is short the optimal strategy is to impose severe lockdown to avoid diffusion of the infection, whereas if the horizon is long the optimal control... (More)
The recent COVID-19 pandemic highlighted the need of non-pharmaceutical interventions in the first stages of a pandemic. Among these, lockdown policies proved unavoidable yet extremely costly from an economic perspective. To better understand the tradeoffs between economic and epidemic costs of lockdown interventions, we here focus on a simple SIR epidemic model and study lockdowns as solutions to an optimal control problem. We first show numerically that the optimal lockdown policy exhibits a phase transition from suppression to mitigation as the time horizon grows, i.e., if the horizon is short the optimal strategy is to impose severe lockdown to avoid diffusion of the infection, whereas if the horizon is long the optimal control steers the system to herd immunity to reduce economic loss. We then consider two alternative policies, motivated by government responses to the COVID19 pandemic, where lockdown levels are selected to either stabilize the reproduction number (i.e., "flatten the curve") or the fraction of infected (i.e., containing the number of hospitalizations). We compute analytically the performance of these two feedback policies and compare them to the optimal control. Interestingly, we show that in the limit of infinite horizon stabilizing the number of infected is preferable to controlling the reproduction number, and in fact yields close to optimal performance.
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- author
- Cianfanelli, Leonardo ; Parise, Francesca ; Acemoglu, Daron ; Como, Giacomo LU and Ozdaglar, Asuman
- organization
- publishing date
- 2021
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 60th IEEE Conference on Decision and Control, CDC 2021
- series title
- Proceedings of the IEEE Conference on Decision and Control
- volume
- 2021-December
- pages
- 6 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 60th IEEE Conference on Decision and Control, CDC 2021
- conference location
- Austin, United States
- conference dates
- 2021-12-13 - 2021-12-17
- external identifiers
-
- scopus:85126031656
- ISSN
- 2576-2370
- 0743-1546
- ISBN
- 9781665436595
- DOI
- 10.1109/CDC45484.2021.9682977
- project
- Dynamics of Complex Socio-Technological Network Systems
- language
- English
- LU publication?
- yes
- additional info
- Funding Information: ACKNOWLEDGEMENTS This research was carried on within the framework of the MIUR-funded Progetto di Eccellenza of the Dipartimento di Scienze Matematiche G.L. Lagrange, Politecnico di Torino, CUP: E11G18000350001. It received partial support from the Compagnia di San Paolo through a Joint Research Project. It was also supported by C3.ai Digital Transformation Institute award. Publisher Copyright: © 2021 IEEE.
- id
- 97e29104-176f-4077-96e9-b35aa3e19155
- date added to LUP
- 2022-09-06 16:37:43
- date last changed
- 2024-08-08 23:59:42
@inproceedings{97e29104-176f-4077-96e9-b35aa3e19155,
abstract = {{<p>The recent COVID-19 pandemic highlighted the need of non-pharmaceutical interventions in the first stages of a pandemic. Among these, lockdown policies proved unavoidable yet extremely costly from an economic perspective. To better understand the tradeoffs between economic and epidemic costs of lockdown interventions, we here focus on a simple SIR epidemic model and study lockdowns as solutions to an optimal control problem. We first show numerically that the optimal lockdown policy exhibits a phase transition from suppression to mitigation as the time horizon grows, i.e., if the horizon is short the optimal strategy is to impose severe lockdown to avoid diffusion of the infection, whereas if the horizon is long the optimal control steers the system to herd immunity to reduce economic loss. We then consider two alternative policies, motivated by government responses to the COVID19 pandemic, where lockdown levels are selected to either stabilize the reproduction number (i.e., "flatten the curve") or the fraction of infected (i.e., containing the number of hospitalizations). We compute analytically the performance of these two feedback policies and compare them to the optimal control. Interestingly, we show that in the limit of infinite horizon stabilizing the number of infected is preferable to controlling the reproduction number, and in fact yields close to optimal performance. </p>}},
author = {{Cianfanelli, Leonardo and Parise, Francesca and Acemoglu, Daron and Como, Giacomo and Ozdaglar, Asuman}},
booktitle = {{60th IEEE Conference on Decision and Control, CDC 2021}},
isbn = {{9781665436595}},
issn = {{2576-2370}},
language = {{eng}},
pages = {{4254--4259}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{Proceedings of the IEEE Conference on Decision and Control}},
title = {{Lockdown interventions in SIR models : Is the reproduction number the right control variable?}},
url = {{http://dx.doi.org/10.1109/CDC45484.2021.9682977}},
doi = {{10.1109/CDC45484.2021.9682977}},
volume = {{2021-December}},
year = {{2021}},
}