Department of Mathematics, Pennsylvania State University, State College, PA, 16802, USA.
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA.
J Math Biol. 2021 Jun 8;82(7):69. doi: 10.1007/s00285-021-01615-0.
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.
我们考虑一个易感染、感染、移除（SIR）系统，其中传播率可能在固定时间段内暂时降低。我们表明，为了使总死亡人数最小化，传播率应该在单个连续的时间间隔内降低，我们通过一个积分条件来刻画这个间隔。最后，我们通过一些数值模拟来展示实际获得的降低效果。
