Effectiveness of Quarantine in Worm Epidemics

Quarantine is a natural concept borrowed from human disease control to slow down worm outbreaks. We study the effectiveness of partial quarantine for simple epidemics (without removals) and find that the optimal quarantine strategy is not as simple as expected. The strategy depends on which networks are most important to protect. We also investigate the effectiveness of quarantine for general epidemics (with removals) and derive the critical threshold for networks to have herd immunity. We show that, given a limited capability to quarantine a given number of networks, the optimal quarantine strategy is to isolate the networks small enough to have herd immunity, and then divide the remaining networks as evenly as possible.