In epidemiology, the effective reproduction number $R_e $is used to characterize the growth rate of an epidemic outbreak . 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 . 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.