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The importance of a strict quarantine has been widely debated during theCOVID-19 epidemic even from the purely epidemiological point of view. Oneargument against strict lockdown measures is that once the strict quarantine islifted, the epidemic comes back, and so the cumulative number of infectedindividuals during the entire epidemic will stay the same. We consider an SIRmodel on a network and follow the disease dynamics, modeling the phases ofquarantine by changing the node degree distribution. We show that the systemreaches different steady states based on the history: the outcome of theepidemic is path-dependent despite the same final node degree distribution. Theresults indicate that two-phase route to the final node degree distribution (astrict phase followed by a soft phase) are always better than one phase (thesame soft one) unless all the individuals have the same number of connectionsat the end (the same degree); in the latter case, the overall number ofinfected is indeed history-independent. The modeling also suggests that theoptimal procedure of lifting the quarantine consists of releasing nodes in theorder of their degree - highest first.

Path-dependent course of epidemic: are two phases of quarantine better than one?