  In this manuscript we present several possible ways of modeling human capital
accumulation during the spread of a disease following an agent based approach,
where agents behave maximizing their intertemporal utility. We assume that the
interaction between agents is of mean field type, yielding a Mean Field Game
description of the problem. We discuss how the analysis of a model including
both the mechanism of change of species from one epidemiological state to the
other and an optimization problem for each agent leads to an aggregate behavior
that is not easy to describe, and that sometimes exhibits structural problems.
Therefore we eventually propose and study numerically a SEIRD model in which
the rate of infection depends on the distribution of the population, given
exogenously as the solution to the the Mean Field Game system arising as the
macroscopic description of the discrete multi-agent economic model for the
accumulation of human capital. Such model arises in fact as a simplified but
tractable version of the initial one.
