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arXiv · 2206.00613

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

Alessandro Calvia·Fausto Gozzi·Francesco Lippi·Giovanni Zanco
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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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Alessandro Calvia, Fausto Gozzi, Francesco Lippi, Giovanni Zanco. 2022-06-01. A simple planning problem for COVID-19 lockdown: a dynamic programming approach. https://arxiv.org/abs/2206.00613

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