Screening multi-dimensional heterogeneous populations for infectious diseases under scarce testing resources, with application to COVID-19

Abstract

Testing provides essential information for managing infectious disease outbreaks, such as the COVID-19 pandemic. When testing resources are scarce, an important managerial decision is who to test. This decision is compounded by the fact that potential testing subjects are heterogeneous in multiple dimensions that are important to consider, including their likelihood of being disease-positive, and how much potential harm would be averted through testing and the subsequent interventions. To increase testing coverage, pooled testing can be utilized, but this comes at a cost of increased false-negatives when the test is imperfect. Then, the decision problem is to partition the heterogeneous testing population into three mutually exclusive sets: those to be individually tested, those to be pool tested, and those not to be tested. Additionally, the subjects to be pool tested must be further partitioned into testing pools, potentially containing different numbers of subjects. The objectives include the minimization of harm (through detection and mitigation) or maximization of testing coverage. We develop data-driven optimization models and algorithms to design pooled testing strategies, and show, via a COVID-19 contact tracing case study, that the proposed testing strategies can substantially outperform the current practice used for COVID-19 contact tracing (individually testing those contacts with symptoms). Our results demonstrate the substantial benefits of optimizing the testing design, while considering the multiple dimensions of population heterogeneity and the limited testing capacity.

Keywords: COVID‐19 testing; heterogeneous population; partition problem; pooled testing; resource allocation under limited resources.

FIGURE 1

(A) The coverage (C) and (B) expected harm (E[H]) for CP, HP, and SI strategies over a 12‐week testing period

FIGURE 2

The distribution of expected harm (E[H]) for CP, HI, HP, HP(risk), and SI strategies over a 1‐week testing period

FIGURE 3

The number of subjects in the individual testing, pooled testing, and no testing sets (|Ω _I  | , | Ω _P  | , | Ω₀|), for each subject category in Table 1, for CP, HI, HP, HP(risk), and SI strategies over a 1‐week testing period. (A) Household contacts. (B) Other contacts