In epidemiology, the effective reproduction number $R_{e}$ is used to characterize the growth rate of an epidemic outbreak. If $R_{e} >1$ , the epidemic worsens, and if $R_{e}< 1$ , then it subsides and eventually dies out. In this paper, we investigate properties of $R_{e}$ for a modified SEIR model of COVID-19 in the city of Houston, TX USA, in which the population is divided into low-risk and high-risk subpopulations. The response of $R_{e}$ to two types of control measures (testing and distancing) applied to the two different subpopulations is characterized. A nonlinear cost model is used for control measures, to include the effects of diminishing returns. Lowest-cost control combinations for reducing instantaneous $R_{e}$ to a given value are computed. We propose three types of heuristic strategies for mitigating COVID-19 that are targeted at reducing $R_{e}$ , and we exhibit the tradeoffs between strategy implementation costs and number of deaths. We also consider two variants of each type of strategy: basic strategies, which consider only the effects of controls on $R_{e}$ , without regard to subpopulation; and high-risk prioritizing strategies, which maximize control of the high-risk subpopulation. Results showed that of the three heuristic strategy types, the most cost-effective involved setting a target value for $R_{e}$ and applying sufficient controls to attain that target value. This heuristic led to strategies that begin with strict distancing of the entire population, later followed by increased testing. Strategies that maximize control on high-risk individuals were less cost-effective than basic strategies that emphasize reduction of the rate of spreading of the disease. The model shows that delaying the start of control measures past a certain point greatly worsens strategy outcomes. We conclude that the effective reproduction can be a valuable real-time indicator in determining cost-effective control strategies.

中文翻译：

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基于成本有效的再生数的减少 COVID-19 死亡人数的策略


在流行病学中，有效繁殖数$R_{e}$用于表征流行病爆发的增长率。如果 $R_{e} >1$ ，则疫情恶化，如果 $R_{e}< 1$ ，则疫情消退并最终消失。在本文中，我们研究了美国德克萨斯州休斯顿市经过修改的 COVID-19 SEIR 模型的 $R_{e}$ 的属性，其中将人群分为低风险和高风险亚人群。描述了 $R_{e}$ 对应用于两个不同亚群的两种控制措施（测试和疏远）的反应。非线性成本模型用于控制措施，以包括收益递减的影响。计算将瞬时 $R_{e}$ 降低至给定值的最低成本控制组合。我们提出了三种缓解 COVID-19 的启发式策略，旨在减少 $R_{e}$ ，并展示了策略实施成本和死亡人数之间的权衡。我们还考虑每种策略的两种变体：基本策略，仅考虑控制对 $R_{e}$ 的影响，而不考虑子群体；以及高风险优先策略，最大限度地控制高风险人群。结果表明，在三种启发式策略类型中，最具成本效益的涉及为 $R_{e}$ 设置目标值并应用足够的控制来实现该目标值。这种启发导致了一系列策略，首先是对整个人群进行严格的疏远，然后是增加测试。最大限度地控制高风险个体的策略的成本效益低于强调降低疾病传播率的基本策略。 该模型表明，将控制措施的启动延迟到某一点之后会大大恶化战略结果。我们的结论是，有效繁殖可以成为确定具有成本效益的控制策略的一个有价值的实时指标。