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

Christopher Thron; Vianney Mbazumutima; Luis V Tamayo; Léonard Todjihounde

doi:10.1186/s13362-021-00107-6

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

J Math Ind. 2021;11(1):11. doi: 10.1186/s13362-021-00107-6. Epub 2021 Jun 28.

Authors

Christopher Thron¹, Vianney Mbazumutima², Luis V Tamayo¹, Léonard Todjihounde²

Affiliations

¹ Department of Sciences and Mathematics, Texas A&M University-Central Texas, Killeen, TX 76549 USA.
² Institute of Mathematics and Physical Sciences, IMSP-Bénin, Abomey Calavi University, Porto-Novo, Bénin.

Abstract

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.

Keywords: At-risk subpopulation; Control strategies; Coronavirus 2019; Distancing; Effective reproduction number; Reproduction number; Spectral radius; Testing.