  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.
