We consider a susceptible, infected, removed (SIR) system where the transmission rate may be temporarily reduced for a fixed amount of time. We show that in order to minimize the total number of fatalities, the transmission rate should be reduced on a single contiguous time interval, and we characterize this interval via an integral condition. We conclude with a few numerical simulations showing the actual reduction obtained.

中文翻译：

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安排固定长度的隔离，以尽量减少流行期间的死亡总数

我们考虑一个易感、受感染、已移除 (SIR) 系统，其中传输速率可能会在固定时间内暂时降低。我们表明，为了最大限度地减少死亡总数，应该在单个连续时间间隔内降低传输速率，并且我们通过积分条件来表征该间隔。我们以一些数值模拟结束，显示了实际减少的情况。