  In this survey we report some recent results in the mathematical modeling of
epidemic phenomena through the use of kinetic equations. We initially consider
models of interaction between agents in which social characteristics play a key
role in the spread of an epidemic, such as the age of individuals, the number
of social contacts, and their economic wealth. Subsequently, for such models,
we discuss the possibility of containing the epidemic through an appropriate
optimal control formulation based on the policy maker's perception of the
progress of the epidemic. The role of uncertainty in the data is also discussed
and addressed. Finally, the kinetic modeling is extended to spatially dependent
settings using multiscale transport models that can characterize the impact of
movement dynamics on epidemic advancement on both one-dimensional networks and
realistic two-dimensional geographic settings.
