Verification Results for Age-Structured Models of Economic-Epidemics Dynamics

TL;DR

This paper develops an age-structured macro-dynamic model for economic-epidemic interactions, reformulates the optimal control problem in an infinite-dimensional space, and provides a verification theorem for optimal strategies.

Contribution

It introduces a novel continuous-time, age-structured framework for analyzing economic-epidemic dynamics and derives a verification theorem for optimal control strategies within this setting.

Findings

Verification theorem for optimal strategies

Framework for analyzing policy implications

Reformulation in infinite-dimensional Hilbert space

Abstract

In this paper we propose a macro-dynamic age-structured set-up for the analysis of epidemics/economic dynamics in continuous time. The resulting optimal control problem is reformulated in an infinite dimensional Hilbert space framework where we perform the basic steps of dynamic programming approach. Our main result is a verification theorem which allows to guess the feedback form of optimal strategies. This will be a departure point to discuss the behavior of the models of the family we introduce and their policy implications.