  The new cyber attack pattern of advanced persistent threat (APT) has posed a
serious threat to modern society. This paper addresses the APT defense problem,
i.e., the problem of how to effectively defend against an APT campaign. Based
on a novel APT attack-defense model, the effectiveness of an APT defense
strategy is quantified. Thereby, the APT defense problem is modeled as an
optimal control problem, in which an optimal control stands for a most
effective APT defense strategy. The existence of an optimal control is proved,
and an optimality system is derived. Consequently, an optimal control can be
figured out by solving the optimality system. Some examples of the optimal
control are given. Finally, the influence of some factors on the effectiveness
of an optimal control is examined through computer experiments. These findings
help organizations to work out policies of defending against APTs.
