A simple planning problem for COVID-19 lockdown: a dynamic programming approach
Optimization and Control
2022-12-21 v2
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.
Cite
@article{arxiv.2206.00613,
title = {A simple planning problem for COVID-19 lockdown: a dynamic programming approach},
author = {Alessandro Calvia and Fausto Gozzi and Francesco Lippi and Giovanni Zanco},
journal= {arXiv preprint arXiv:2206.00613},
year = {2022}
}