  Evolution of disease in a large population is a function of the top-down
policy measures from a centralized planner, as well as the self-interested
decisions (to be socially active) of individual agents in a large heterogeneous
population. This paper is concerned with understanding the latter based on a
mean-field type optimal control model. Specifically, the model is used to
investigate the role of partial information on an agent's decision-making, and
study the impact of such decisions by a large number of agents on the spread of
the virus in the population. The motivation comes from the presymptomatic and
asymptomatic spread of the COVID-19 virus where an agent unwittingly spreads
the virus. We show that even in a setting with fully rational agents, limited
information on the viral state can result in an epidemic growth.
