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The mobility patterns of individuals in China during the early outbreak ofthe COVID-19 pandemic exhibit reversible changes -- in many regions, themobility first decreased significantly and later restored. Based on thisobservation, here we study the classical SIR model on a particular type oftime-varying network where the links undergo a freeze-recovery process. Wefirst focus on an isolated network and find that the recovery mechanism couldlead to the resurgence of an epidemic. The influence of link freezing onepidemic dynamics is subtle. In particular, we show that there is an optimalvalue of the freezing rate for links which corresponds to the lowest prevalenceof the epidemic. This result challenges our conventional idea that stricterprevention measures (corresponding to a larger freezing rate) could always havea better inhibitory effect on epidemic spreading. We further investigate anopen system where a small fraction of nodes in the network may acquire thedisease from the "environment" (the outside infected nodes). In this case, thesecond wave would appear even if the number of infected nodes has declined tozero, which can not be explained by the isolated network model.

How the reversible change of contact network affects the epidemic spreading