  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.
