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.

A simple planning problem for COVID-19 lockdown: a dynamic programming approach / Calvia, Alessandro; Gozzi, Fausto; Lippi, Francesco; Zanco, Giovanni Alessandro. - In: ECONOMIC THEORY. - ISSN 0938-2259. - 77:1-2(2024), pp. 169-196. [10.1007/s00199-023-01493-1]

A simple planning problem for COVID-19 lockdown: a dynamic programming approach

Calvia, Alessandro;Gozzi, Fausto;Lippi, Francesco;Zanco, Giovanni
2024

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.
2024
Controlled SIRD model, Optimal control with state space constraints, Optimal lockdown policies, Optimality conditions, Viscosity solutions
A simple planning problem for COVID-19 lockdown: a dynamic programming approach / Calvia, Alessandro; Gozzi, Fausto; Lippi, Francesco; Zanco, Giovanni Alessandro. - In: ECONOMIC THEORY. - ISSN 0938-2259. - 77:1-2(2024), pp. 169-196. [10.1007/s00199-023-01493-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/234281
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