Cost effective reproduction number based strategies for reducing deaths from COVID-19

In epidemiology, the effective reproduction number [Formula: see text] is used to characterize the growth rate of an epidemic outbreak. If [Formula: see text] , the epidemic worsens, and if [Formula: see text] , then it subsides and eventually dies out. In this paper, we investigate properties of [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] to a given value are computed. We propose three types of heuristic strategies for mitigating COVID-19 that are targeted at reducing [Formula: see text] , 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 [Formula: see text] , 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 [Formula: see text] 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.