In the context of the recent COVID-19 outbreak, quarantine has been used to "flatten the curve" and slow the spread of the disease. In this paper, we show that this is not the only benefit of quarantine for the mitigation of an SIR epidemic spreading on a graph. Indeed, we theoretically prove that nodes of high-degree  are disproportionately in the Removed state after a first wave of infection, which has very positive consequences. In particular, powerlaw graphs do not retain their structure after a few waves of infection, which implies second and third waves may be of much smaller amplitude than the first wave. We propose an opening and closing strategy aiming at immunizing the graph while infecting the minimum number of individuals, while guaranteeing the population is now robust to future infections. We experimentally verify our results on simulated  networks.
In the context of the recent COVID-19 outbreak, quarantine has been used to "flatten the curve" and slow the spread of the disease. In this paper, we show that this is not the only benefit of quarantine for the mitigation of an SIR epidemic spreading on a graph. Indeed, human contact networks exhibit a powerlaw structure, which means immunizing nodes at random is extremely ineffective at slowing the epidemic, while immunizing high-degree nodes can efficiently guarantee herd immunity. We theoretically prove that if quarantines are declared at the right moment, high-degree nodes are disproportionately in the Removed state , which is a form of targeted immunization. Even if quarantines are declared too early, subsequent waves of infection spread slower than the first waves. This leads us to propose an opening and closing strategy aiming at immunizing the graph while infecting the minimum number of individuals, guaranteeing the population is now robust to future infections. To the best of our knowledge, this is the only strategy that guarantees herd immunity without requiring vaccines. We extensively verify our results on simulated and real-life networks.
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To the best of our knowledge, this is the only strategy that guarantees herd immunity without requiring vaccines. We extensively
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