  Recent wide spreading of Ransomware has created new challenges for
cybersecurity over large-scale networks. The densely connected networks can
exacerbate the spreading and makes the containment and control of the malware
more challenging. In this work, we propose an impulse optimal control framework
for epidemics over networks. The hybrid nature of discrete-time control policy
of continuous-time epidemic dynamics together with the network structure poses
a challenging optimal control problem. We leverage the Pontryagin's minimum
principle for impulsive systems to obtain an optimal structure of the
controller and use numerical experiments to corroborate our results.
