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Grass D, Wrzaczek S, Caulkins JP, Feichtinger G, Hartl RF, Kort PM, Kuhn M, Prskawetz A, Sanchez-Romero M, Seidl A. Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses. Theor Popul Biol 2024; 156:46-65. [PMID: 38310975 DOI: 10.1016/j.tpb.2024.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Revised: 01/30/2024] [Accepted: 02/01/2024] [Indexed: 02/06/2024]
Abstract
Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.
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Affiliation(s)
- D Grass
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria
| | - S Wrzaczek
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria.
| | - J P Caulkins
- Heinz College, Carnegie Mellon University, Pittsburgh, USA
| | - G Feichtinger
- Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria; Research Group Variational Analysis, Dynamics & Operations Research, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria
| | - R F Hartl
- Department of Business Decisions and Analytics, University of Vienna, Vienna, Austria
| | - P M Kort
- Tilburg School of Economics and Management, Tilburg University, Tilburg, Netherlands
| | - M Kuhn
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria
| | - A Prskawetz
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria; Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria
| | - M Sanchez-Romero
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria; Vienna Institute of Demography (VID), Austrian Academy of Sciences (OeAW), Vienna, Austria
| | - A Seidl
- Department of Business Decisions and Analytics, University of Vienna, Vienna, Austria; Faculty of Management, Seeburg Castle University, Seekirchen am Wallersee, Austria
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Calvia A, Gozzi F, Lippi F, Zanco G. A simple planning problem for COVID-19 lockdown: a dynamic programming approach. ECONOMIC THEORY 2023:1-28. [PMID: 37360773 PMCID: PMC10105532 DOI: 10.1007/s00199-023-01493-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Accepted: 03/15/2023] [Indexed: 05/31/2023]
Abstract
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.
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Affiliation(s)
- Alessandro Calvia
- Dipartimento di Economia e Finanza, LUISS University, Viale Romania 32, 00197 Rome, Italy
| | - Fausto Gozzi
- Dipartimento di Economia e Finanza, LUISS University, Viale Romania 32, 00197 Rome, Italy
| | - Francesco Lippi
- Dipartimento di Economia e Finanza, LUISS University, Viale Romania 32, 00197 Rome, Italy
- Einaudi Institute for Economics and Finance, Via Sallustiana 62, 00187 Rome, Italy
| | - Giovanni Zanco
- Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena, Via Roma 56, 53100 Siena, Italy
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