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Identifying optimal COVID-19 testing strategies for schools and businesses: Balancing testing frequency, individual test technology, and cost

Identifying optimal COVID-19 testing strategies: Balancing testing frequency, test technology, and cost

Lyng

Gregory D.

Conceptualization Data curation Formal analysis Investigation Methodology Writing – original draft Writing – review & editing ¹

https://orcid.org/0000-0002-0631-5834

Sheils

Natalie E.

Conceptualization Data curation Formal analysis Investigation Methodology Visualization Writing – original draft Writing – review & editing ¹ Kennedy

Caleb J.

Formal analysis Investigation Methodology Writing – original draft Writing – review & editing ¹

https://orcid.org/0000-0001-5853-6906

Griffin

Daniel O.

Conceptualization Investigation Methodology Writing – original draft Writing – review & editing ² ³

https://orcid.org/0000-0003-0805-8218

Berke

Ethan M.

Conceptualization Formal analysis Investigation Methodology Supervision Writing – original draft Writing – review & editing ¹ *

OptumLabs, UnitedHealth Group, Minnetonka, MN, United States of America

Division of Infectious Diseases, Department of Medicine, Columbia University, New York, NY, United States of America

ProHealth Care, Optum, Lake Success, NY, United States of America

Simuunza

Martin Chtolongo

Editor

University of Zambia, ZAMBIA

Authors [GL, NS, CK, DG, EB] are employees of UnitedHealth Group; GL, NS, CK, and EB own stock in the company. DG is employed as the Senior Infectious Disease Fellow at UnitedHealth Group, Inc and serves as the Chief of Infectious Diseases for ProHealth NY an Optum Company. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

* E-mail: ethan.berke@uhg.com

25 3 2021

2021

16 3

e0248783

18 11 2020 5 3 2021

2021

Lyng et al

This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Background

COVID-19 test sensitivity and specificity have been widely examined and discussed, yet optimal use of these tests will depend on the goals of testing, the population or setting, and the anticipated underlying disease prevalence. We model various combinations of key variables to identify and compare a range of effective and practical surveillance strategies for schools and businesses.

Methods

We coupled a simulated data set incorporating actual community prevalence and test performance characteristics to a susceptible, infectious, removed (SIR) compartmental model, modeling the impact of base and tunable variables including test sensitivity, testing frequency, results lag, sample pooling, disease prevalence, externally-acquired infections, symptom checking, and test cost on outcomes including case reduction and false positives.

Findings

Increasing testing frequency was associated with a non-linear positive effect on cases averted over 100 days. While precise reductions in cumulative number of infections depended on community disease prevalence, testing every 3 days versus every 14 days (even with a lower sensitivity test) reduces the disease burden substantially. Pooling provided cost savings and made a high-frequency approach practical; one high-performing strategy, testing every 3 days, yielded per person per day costs as low as $1.32.

Interpretation

A range of practically viable testing strategies emerged for schools and businesses. Key characteristics of these strategies include high frequency testing with a moderate or high sensitivity test and minimal results delay. Sample pooling allowed for operational efficiency and cost savings with minimal loss of model performance.

Authors [GL, NS, CK, DG, EB] are employees of UnitedHealth Group. Author [DG] also serves as the Chief of Infectious Disease for ProHealth NY, part of Optum. These funders provided support in the form of salaries for authors [GL, NS, CK, DG, EB], but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.

Data Availability

Mathematical code is available in the supplemental file submitted with the manuscript.

Outbreaks

COVID-19

Introduction

As schools and businesses re-open and attempt to stay open, promptly detecting people with infectious COVID-19 is essential, especially as the risk of transmission may be expected to increase as contact networks increase in size and complexity [1, 2]. Recommended actions to attenuate spread include symptom checking, monitoring underlying community prevalence, and responsive policy adjustment. In addition to robust public health measures, successful return to normalcy will be accelerated and hopefully sustained by optimal COVID-19 testing strategies. Despite being commonly recommended, little guidance suggests the right approach to testing and how best to balance cost, test selection, results delays, the value of sample pooling, and how changing local disease prevalence should inform strategy adjustments.

Throughout the pandemic the number and variety of tests for detecting active infection have steadily increased [3]. Current tests include nucleic acid amplification tests (NAATs) such as reverse-transcription or reverse transcription polymerase chain reaction (RT-PCR), template mediated amplification (TMA), nicking enzyme amplification reaction (NEAR), loop-mediated isothermal amplification (LAMP), nucleic acid hybridization, viral metagenomic sequencing, and CRISPR-based assays. Most Food and Drug Administration (FDA) Emergency Use Authorization (EUA) tests are approved for symptomatic patients, but not all are validated in an asymptomatic population [4]. Despite these scientific advancements, there is scant guidance on how to apply a specific technology in the context of the underlying population and the goal of testing, such as diagnosis of an individual versus surveillance of a group. Cost, turnaround time, accuracy, and convenience in sample collection all play a role in achieving a rate of testing that achieves a goal of detecting and preventing transmission in a cohort. A testing strategy is not feasible if the cost per test at the individual level is too high, or the time to obtain results is too long, resulting in possible transmission while positive test results are in transit or missing an opportunity to attend work or school if the result is negative. To increase test processing efficiency and reduce cost, pooling of samples is a potential solution provided there is minimal degradation in test performance due to dilution, but a strategy should be devised carefully. Successful pooling strategies rely on a clear understanding of the test’s limit of detection (LOD), sensitivity, specificity, and the prevalence of disease in the population being tested [5].

Testing in large cohort settings such as schools and businesses that require continued surveillance can ensure that facilities remain open safely for the greatest number of people. We model various scenarios of test sensitivity and specificity, testing frequency, cost, and pooling to illustrate the range of practical and sustainable surveillance strategies.

Methods

To compare the effects of test sensitivity and specificity, test frequency, and the impact of pooling we considered a classical epidemiological susceptible, infectious-asymptomatic, infectious-symptomatic, removed (SIR) compartmental model for the tested population. That is, individuals move from one compartment to another as they transition from susceptible to infectious to removed. To account for the introduction of infections from the surrounding community, we added a time-dependent term which represents the rate (in people/time) of infections from outside interactions continuously in time. With frequent testing, this external forcing drives the behavior of the model (Fig 1).

10.1371/journal.pone.0248783.g001

Fig 1 Schematic representation of the model.

The model simulates testing for a common group of people who mix continuously in an institution (i.e., in a school or office) and are subject to the introduction of infection from the surrounding unmonitored community. The framework couples regular testing, described by a handful of tunable parameters, to a disease model. The disease model is dynamic in time, and infections may originate both from inside-the-institution mixing and from the surrounding community at varying rates depending on prevalence.

We examine two scenarios for this forcing. The first is a relatively low and more-or-less constant rate of introduced infections, with data from the 7-day rolling average of the case count in Fayette County, Pennsylvania for the 100 days beginning March 26, 2020, as reported in the New York Times [6]. This low-growth profile is reported as panel (a) in Figs 2–4. The second scenario used for high-growth external community prevalence is the seven-day rolling average of daily case counts in Miami-Dade County, Florida, for the 100 days beginning June 16, 2020. This profile is shown in panel (b) in Figs 2–4. In both profiles, we scaled the cases given by the relative population in our model, which we chose to be 1,500. It should be noted that the case counts in Miami-Dade County over this time period are outliers compared to case counts in other counties across the US over the past ten months. These cases are chosen for illustration to show the widest array of possible scenarios. To model symptom checking we solve the forced SIR model each day, and, at the end of the day, we remove the appropriate fraction of individuals from the infectious-symptomatic compartment. To model pooled testing with symptom tracking, when τ divides the day, in addition to removal due to symptom tracking from the infectious-symptomatic compartment, there is removal from both infectious compartments due to positive tests. The initial test is on day zero. To account for possible delays in receiving test results due to laboratory processing, we also allow for a delay parameter, d. When pooling samples, we adjust for test sensitivity and applied a linear deduction for pooling of 0.00323, consistent with minimal sample dilution or degradation in a nasal or nasopharyngeal sample [7]. Other deductions may be more appropriate in different settings, such as saliva sampling [8]. Our model allows for a varied percent of those that are infected to choose to comply with isolation protocols; in the scenarios presented, we set this tunable assumption to be perfect compliance. We assume the basic reproduction number R₀ is 2.5 and the average period of infectiousness is 4.5 days [9–12].

10.1371/journal.pone.0248783.g002

Fig 2 Impact of testing frequency.

Two scenarios for community prevalence corresponding, relatively, to low and high rates of imported infections (Panels (a) and (b)). Testing with a test with 98% sensitivity with 0-day resulting delay amidst high and low community prevalence (Panels (c) and (d)). Testing with a test with 98% sensitivity with 2-day resulting delay amidst high and low community prevalence (Panels (e) and (f)). Testing with a test with 60% sensitivity with 0-day resulting delay amidst high and low community prevalence (Panels (g) and (h)). Purple (dash-dot-dot) corresponds to no testing, orange (solid) to testing every two weeks with daily symptom tracking, green for testing every week with daily symptom tracking (dash-dot), blue (dash) for testing every 3 days with daily symptom tracking, and red (dot) for daily testing and symptom tracking.

10.1371/journal.pone.0248783.g003

Fig 3 Effect of pool size.

Two scenarios for community prevalence corresponding, relatively, to low and high rates of imported infections (Panels (a) and (b)). Testing weekly with a test with 98% sensitivity with 0-day resulting delay with daily symptom tracking amidst high and low community prevalence (Panels (c) and (d)). Testing weekly with a test with 98% sensitivity with 2-day resulting delay with daily symptom tracking amidst high and low community prevalence (Panels (e) and (f)). Testing every 3 days with a test with 98% sensitivity with 2-day resulting delay with daily symptom tracking amidst high and low community prevalence (Panels (g) and (h)). Orange lines (solid) correspond to 30 samples pooled, green (dash-dot) to ten samples pooled, blue (dash) to five samples pooled, and red (dot) to 2 samples pooled.

10.1371/journal.pone.0248783.g004

Fig 4 Cost comparison map for various pooling and frequency scenarios with and without confirmatory testing.

Use case of a test with 98% sensitivity and 99.5% specificity with a 2-day result delay costing $100 and a 98% sensitive test with 99.5% specificity and a 0 day result delay costing $120 with free daily symptom tracking. In (c, d, g, h) every person in a positive pool is retested for confirmation and in (e, f) no confirmatory testing is done. We assume all confirmatory tests cost $100. Colors correspond to cost per person per day in dollars.

We do not include an “exposed” category as is often done for compartmental models but account for the shorter time a person is infectious rather than the longer period of time they are infected. Our model includes symptomatic and asymptomatic infectious individuals with daily symptom tracking. In the results that follow we assume 40% of infections are asymptomatic [13] and symptom tracking will catch 66% of symptomatic infections [14]. Individuals can move directly from asymptomatic to removed or from asymptomatic, to symptomatic to removed.

The initial conditions are chosen from the average of population-scaled new confirmed cases reported by the New York Times for September 23, 2020 in a sample of counties scaled by average number of infectious days. This results in a starting value of 0.675 infections for a population of size 1,500. We take the conservative approach of assuming no one in the population has immunity to the virus based on previous infection. In the tests that follow we vary the testing frequency (τ), delay in the return of results (d), number of samples pooled (m), sensitivity of the test on one sample, and specificity of the test. We computed the cost of each testing strategy at the per person per day level, over 100 days. When pooling (m>1), we assumed a simple 2-stage Dorfman testing process in which each individual in a positive pool is retested individually using a high-sensitivity diagnostic test at $100 per test. We then calculated the expected number of tests required to complete each round of testing. The complete scientific code is available as S1 File. All analysis was done using Julia v1.5.1 [15].

Results

Fig 2 demonstrates scenarios of testing frequency at sensitivities of 98% with a two-day delay in receiving results during which mixing continues (Fig 2C and 2D), 98% sensitivity with no delay in receiving results (Fig 2E and 2F), and 60% sensitivity with no delay (Fig 2G and 2H) to simulate testing by various technologies such as PCR with lags between sample collection and centralized laboratory testing, antigen detection, and LAMP. As there are little data on the performance of some tests in asymptomatic people, we used more conservative sensitivity estimates aligning to published LOD for specific devices from the FDA [16]. The sawtooth pattern is the result of removal of infected persons from the population.

Any testing strategy is better than none at all, and as expected, tests with increased sensitivities perform better for a given time frequency. At the most lenient frequency considered, every 14 days, the number of infections is reduced approximately 21–56% (Table 1) compared to no testing at all. Each scenario can be explored comparatively. For example, at a test sensitivity of 80%, testing every day reduces the number of cumulative infections relative to no testing by 95.9–99.9% while testing every 14 days reduced the number of cumulative infections at day 100 relative to no testing by only 26.0–27.1%. Increased testing frequency results in a nonlinear decrease in cumulative infections over time, with daily testing resulting in the fewest cumulative infections at 100 days after implementing the testing strategy at any of the sensitivities shown. Importantly, at sensitivities of 98% our models predict that a two-day delay in results (by send-out PCR, for example) will result in just a 31% reduction in infections experienced at a 14-day testing frequency; however, as the testing frequency is increased, even with the two-day delay, the number of missed infections goes down rapidly to a 99% reduction from no testing at all at a daily testing frequency.

10.1371/journal.pone.0248783.t001

Table 1 Selected testing strategies ranked by reduction in cumulative infections, with and without confirmatory testing, for scenarios costing less than $10 per person per day<xref ref-type="table-fn" rid="t001fn001">*</xref>.

Daily symptom tracking assumed.

Community Prevalence: Low
Sensitivity	Specificity	Delay (days)	Frequency (days)	Pool Size	Cumulative Infections Experienced (over 100 days)	Cumulative Infections Caught (over 100 days)	Cumulative False Positives (over 100 days)	Per Person, Per Day Cost Without Confirmatory Testing ($)	Per Person, Per Day Cost With Confirmatory Testing ($)	% Reduction in Cumulative Infections Experienced
0.98	0.995	0	3	5	2	5	255	$ 7.92	$ 8.78	99.8%
0.98	0.995	0	3	10	3	5	255	$ 3.96	$ 5.65	99.8%
0.98	0.995	0	3	30	5	8	255	$ 1.32	$ 6.20	99.7%
0.98	0.995	0	7	2	35	68	112	$ 8.40	$ 8.63	97.4%
0.98	0.995	0	7	5	100	180	112	$ 3.36	$ 4.21	92.6%
0.98	0.995	0	7	10	241	388	111	$ 1.68	$ 4.23	82.0%
0.98	0.995	0	7	30	515	628	110	$ 0.56	$ 6.58	61.5%
0.6	0.9	0	3	1	560	536	5034	$ 6.60	$ 10.22	58.2%
0.98	0.995	0	14	1	588	649	58	$ 8.40	$ 8.73	56.1%
0.98	0.995	2	3	5	666	446	246	$ 6.60	$ 8.96	50.3%
0.98	0.995	2	3	30	706	467	246	$ 1.10	$ 9.87	47.3%
0.8	0.9	0	7	1	712	675	2195	$ 7.00	$ 8.76	46.9%
0.98	0.995	2	7	2	877	542	104	$ 7.00	$ 7.66	34.5%
0.98	0.995	2	7	5	880	542	104	$ 2.80	$ 4.18	34.3%
0.98	0.995	2	7	10	884	543	104	$ 1.40	$ 3.61	34.0%
0.98	0.995	2	7	30	899	545	104	$ 0.47	$ 4.52	32.9%
0.6	0.9	0	7	1	916	638	2198	$ 2.80	$ 4.47	31.6%
0.98	0.995	2	14	1	924	551	51	$ 7.00	$ 7.26	31.1%
0.8	0.9	0	14	1	977	631	1171	$ 3.50	$ 4.44	27.1%
0.6	0.9	0	14	1	1050	603	1171	$ 1.40	$ 2.30	21.6%
Community Prevalence: High
Sensitivity	Specificity	Delay (days)	Frequency (days)	Pool Size	Cumulative Infections Experienced (over 100 days)	Cumulative Infections Caught (over 100 days)	Cumulative False Positives (over 100 days)	Per Person, Per Day Cost Without Confirmatory Testing	Per Person, Per Day Cost With Confirmatory Testing	% Reduction in Cumulative Infections Experienced
0.98	0.995	0	3	5	97	267	254	$ 7.92	$ 9.56	93.2%
0.98	0.995	0	3	10	112	283	254	$ 3.96	$ 7.23	92.2%
0.98	0.995	0	3	30	187	366	253	$ 1.32	$ 11.01	87.0%
0.98	0.995	0	7	2	442	723	109	$ 8.40	$ 9.31	69.2%
0.98	0.995	0	7	5	480	749	109	$ 3.36	$ 5.50	66.5%
0.98	0.995	0	7	10	538	781	109	$ 1.68	$ 5.50	62.5%
0.98	0.995	0	7	30	704	823	109	$ 0.56	$ 7.51	50.9%
0.6	0.9	0	3	1	733	698	5015	$ 6.60	$ 10.28	48.9%
0.98	0.995	0	14	1	853	845	57	$ 8.40	$ 8.79	40.5%
0.8	0.9	0	7	1	859	799	2186	$ 7.00	$ 8.80	40.1%
0.98	0.995	2	3	5	863	578	246	$ 6.60	$ 9.43	39.9%
0.98	0.995	2	3	30	892	590	245	$ 1.10	$ 11.70	37.8%
0.98	0.995	2	7	2	1006	624	103	$ 7.00	$ 7.72	29.9%
0.98	0.995	2	7	5	1008	624	103	$ 2.80	$ 4.33	29.7%
0.98	0.995	2	7	10	1013	625	103	$ 1.40	$ 3.90	29.4%
0.98	0.995	2	7	30	1031	627	103	$ 0.47	$ 5.24	28.1%
0.6	0.9	0	7	1	1038	720	2191	$ 2.80	$ 4.50	27.7%
0.8	0.9	0	14	1	1062	750	1158	$ 3.50	$ 4.50	26.0%
0.98	0.995	2	14	1	1080	645	51	$ 7.00	$ 7.26	24.7%
0.6	0.9	0	14	1	1134	681	1161	$ 1.40	$ 2.33	21.0%

* Cost calculation assumes a test with a 98% sensitivity and 0-day delay in returning results costs $120, a 98% sensitive test with a 2-day delay in results costs $100, an 80% sensitive test costs $50, and a 60% sensitive test costs $20. All (true and false) positive tests are confirmed using a $100 test. The distribution of positive tests among pooled samples is uniform as is consistent with the homogeneous mixing assumptions of the SIR model, and we assume everyone in a pool that is positive will undergo a confirmatory test.

Next we looked at testing strategies that incorporate pooling. Fig 3 combines a weekly and every 3 day testing strategy with 98% sensitive tests with varying time delay, and pooling tests in samples of 2, 5, 10, and 30. Pooling potentially reduces the sensitivity of the tests, resulting in more missed infections. This can be overcome by an increase in test frequency, allowed by the cost savings of pooling. Fig 4 weighs cost against testing frequency and pooling size, both with confirmatory and without confirmatory testing of positive pools. Without confirmatory testing, the cost per person decreases dramatically.

Discussion

Our findings demonstrate that it is not only critical to choose the right test in terms of performance in asymptomatic individuals, but to use the test in the defined population at the optimal frequency to reduce the risk of case escalation. Optimization is further enhanced at the population level by understanding of underlying disease prevalence and utilization of pooling to reduce cost and increase efficiency. The “ideal” test strategy must be balanced with the practicalities of cost per person to ensure sustainability. For example, daily testing with a 60% sensitive test attenuates community spread, but at a cost of $30.11 per person per day with confirmatory testing, or $20.00 without, may not be possible. Using a 60% sensitive test less frequently reduces expense but sacrifices significant performance. A 98% sensitive test with no delay in results administered every 3 days with pools of 30 people, and no confirmatory test offered by the institution costs less than $1.50 per person per day, with high performance. Even with a highly specific (99.5%) test such as a PCR, in a low prevalence community with large pools, false positives may still become an issue. The previous example results in 253 false positives over 100 days, highlighting the importance of confirmatory testing. The model demonstrates that frequency of testing, test sensitivity, turn-around time, and the external community prevalence are all important factors to consider, and there is often more than one testing strategy to achieve the desired level of performance. The computational code is available as an on line supplement, and an easy-to-use web-based simulator to test various scenarios is available at https://calculator.unitedinresearch.com/. The ability to test different strategies under a variety of assumptions is especially important as we learn more about the performance of tests in asymptomatic populations over time.

With these scenarios in hand, institutions can make an informed operational choice, devise pods or cohorts to be tested by pooling and potentially isolated if positive, and create clear communication about a surveillance rationale. Acknowledging a dynamic community prevalence, the model can be re-run, and the testing strategy can be optimized to maximize benefit at the lost cost and least amount of disruption.

The frequency of test usage to minimize amplification of infection and allow schools and worksites to remain open is an important factor. Given the cost of high frequency testing, we demonstrate the value of pooling of samples to increase efficiency, particularly in areas with lower population prevalence. As background prevalence increases, the value of pooling diminishes as the likelihood of a positive pool will rise, but even a pool of two to three samples results in a dramatic reduction in the need for individual sample analysis. As noted above, with an extremely low prevalence, even in the case of a 99.5% specific test, false positives are much more likely than true positives and confirmatory testing may be necessary. A 90% specificity test would result in an untenable number of false positives over the course of 100 days without confirmatory testing. As shown in Fig 4, in order to achieve a minimal cost approach that includes confirmatory testing, one must balance pool size with frequency. Without confirmatory testing, costs drop dramatically (Fig 4G and 4H). The Dorfman protocol for pooled testing we use is suboptimal compared to a sequential split-pool strategy [17]. More sophisticated confirmatory testing strategies exist that would further lower costs and reduce the likelihood that uninfected individuals are sent home, such as sub-pooling of positive pools without individual level testing, each with benefits and disadvantages [18, 19].

This study confirms and extends previous work. Paltiel et al. [20] considered a compartment-based model simulating an abbreviated 80-day semester in a highly-residential college-campus-type setting. Across all scenarios considered, test frequency was more associated with cumulative infection than test sensitivity. That modeling exercise also suggested that symptom-based screening alone is insufficient to contain an outbreak under any of the scenarios considered. Using a model for viral loads in individuals, Larremore et al. [21] studied surveillance effectiveness using an agent-based modeling framework which accounts for test sensitivities, frequency, and sample-to-answer reporting time. The results indicate that frequency of testing and the speed of reporting are the principal contributors to surveillance effectiveness. The results also suggest that the impact of high sensitivity on surveillance effectiveness is relatively small.

Populations housed in long-term care facilities are especially vulnerable to COVID-19; surveillance programs designed for these settings may have different goals and tolerances for infection risk than those designed to maintain functionality for other institutions. Smith and colleagues [7] built a complex modeling framework for long-term care facilities including simulations of the detailed inter-individual contact networks describing patient-staff interactions in such settings. This work showed that symptom-based screening by itself had limited effectiveness. Testing upon admission detected most asymptomatic cases upon entry but missed potential introductions from staff. Random daily testing was determined to be, overall, an inefficient use of resources. This points to the opportunity for pooled testing as an effective and efficient COVID-19 surveillance strategy for long-term care facilities with limited resources.

Since our work focuses on screening and not performing diagnostic testing, the actual sensitivity of the various available COVID tests for this purpose is not entirely clear. The original testing approaches for COVID-19 focused on the high sensitivity required for diagnosis by clinicians in all stages of the acute period of COVID-19 through detection of SARS-CoV-2 RNA performed on patients with a high pretest probability of disease. This paradigm focused on high sensitivity tests with the performance feature of very low NAAT detectable units/mL (NDU/mL) with a goal of diagnosing patients even if past the contagious period. These tests were not optimized nor validated in terms of sensitivity for the detection of infectious individuals that might spread disease in schools, the workplace or other social situations.

Several studies looking at the ability to culture virus from samples collected from infected individuals have established that RNA copy numbers of 1,000,000 RNA copies/ml or higher are required for any consistent success in viral culture [22–26]. Based on contact tracing, this defined window of elevated RNA copy numbers starting 2–3 days prior to onset of symptoms and ending 5–9 days after symptom onset corresponds to most if not all cases of transmission. Studies of asymptomatic spreading suggests a very similar window of transmissibility during this period of time when RNA copy numbers are 1,000,000 copies/ml or higher [12, 27, 28]. Given that RT-PCR testing can have a sensitivity or LOD as low as <1,000 RNA copies/mL (1,000 NDU), there should ample performance in testing technology to leverage high-volume, high-frequency pooling, provided samples are not diluted by storage or buffering media beyond the minimum LOD when employed to detected asymptomatic but infectious individuals [29].

Our work has a number of limitations. The SIR compartmental model provides a simplified representation of the natural history of the disease. For example, it assumes uniform mixing of the population being tested and a uniform distribution of likelihood of a positive test. The model is formulated at a population level; it does not permit the tracking of individuals. For example, we cannot incorporate the change in test sensitivity with time from infection [30]. In a low population prevalence, we expect a high number of false positives given assumed specificities of 99.5% and 90%. Individuals who recover from the disease are granted permanent immunity in our model, although the risk of reinfection now appears possible [31–36]. Our pooling model assumed nasal or naso-pharyngeal swab samples. Because of the nature of saliva, the small sensitivity deduction assumption in our model may not be valid due to greater sample dilution [37]. Finally, the model does not naturally incorporate phased, pulsed, or partial testing (1^st graders on Monday, 2^nd graders on Tuesday, etc.). To account for this we suggest users model the smaller groups and multiply results rather than attempt to run scenarios on the full population.

Despite these limitations, sensitivity, pooling, and frequency modeling can guide institutions on best-fit testing strategies that align to their practical constraints. Organizations can apply this model to determine their best testing strategy given current community prevalence and operational and financial resources that enable sustained testing to stay safely open during the pandemic.

Supporting information

S1 File Technical details about the model.

(PDF)

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32909003

10.1371/journal.pone.0248783.r001

Decision Letter 0

Simuunza

Martin Chtolongo

Academic Editor

2021

Martin Chtolongo Simuunza

Submission Version

Transfer Alert

This paper was transferred from another journal. As a result, its full editorial history (including decision letters, peer reviews and author responses) may not be present.

22 Feb 2021

PONE-D-20-36267

Identifying Optimal COVID-19 Testing Strategies for Schools and Businesses: Balancing Testing Frequency, Individual Test Technology, and Cost

PLOS ONE

Dear Dr. Berke,

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5. Include the word "sensitivity" after the percentages in lines 62 and 63.

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Academic Editor

PLOS ONE

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Reviewers' comments:

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Comments to the Author

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The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

**********

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Reviewer #1: Yes

**********

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Reviewer #1: Yes

**********

5. Review Comments to the Author

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Reviewer #1: This is very good, original, and profound research work done and a well written manuscript paper. My review is therefore limited to the following minor comments only.

In the supplementary material detailing the model used, under testing strategies; for effect of Symptom tracking alone, you mention that you assume 78% of cases entering a symptomatic phase are caught and a fraction b of these cases self isolate. However, in the manuscript in line 144 – 145 you mention that for the results obtained you had assumed that symptom tracking will catch 66% of symptomatic infections. Kindly clarify this disparity in percentages considered. Wouldn’t it give a substantial disparity in the simulation results obtained as well?

For a population as small as the one modelled in this study (1500 subjects), a stochastic model may be more appropriate. Was this considered?

As alluded to in the manuscript, asymptomatic individuals may also reach just as high detectable viral load levels for the various testing technologies. However, when it comes to infectiousness, some corner of available literature on COVI-19 and earlier communications from the United Nations suggest that the asymptomatic individuals may not be as infectious as symptomatic individuals hence their per capita rate of effective contacts I.e (β) may not be the same as for individuals with symptomatic infection. This has not been considered in the model shown in the supplementary material in 3.2 (Equations). It may not be necessary to consider this at this point but chances are that incorporating this may produce different results and this scenario may be a more accurate representation of the natural history of the infection.

The “in text” referencing should be written in square brackets e.g as [14] and not as superscripts e.g as 14, 23.

The sentence between lines 42 and 44 reads’ “As schools and businesses re-open and attempt to stay open, promptly detecting people with infectious COVID-19 is essential, especially as the risk of transmission is expected to increase with colder weather, more time indoors, and closer contact with others….”.

My impression was that as economies open, people interact more outdoors as they are more frequently away from the indoor safety of their homes such as during lock downs. Perhaps just check that statement again on the part that says “more time indoors”.

The sentence between lines 77 and 79 should read as “To compare the effects of test sensitivity and specificity, test frequency, the impact of pooling, and other key factors influencing testing strategy, we considered a classical epidemiological susceptible, infectious-asymptomatic, infectious-symptomatic, removed (SIR) compartmental model for the tested population.

The sentence describing beta (β) is incomplete in the supplementary material detailing the model. It only partly says that beta is the contact rate. I believe beta can be more accurately described as the per capita rate of effective contacts.

**********

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Reviewer #1: No

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10.1371/journal.pone.0248783.r002

Author response to Decision Letter 0

Submission Version

25 Feb 2021

February 24, 2021

Martin Chtolongo Simuunza, PhD

Academic Editor

PLOS ONE

Dear Dr. Simuunza:

We appreciate the comments and suggestions of the reviewer and have incorporated their recommendations or provided alternative considerations. Below is our response to their comments in a point-by-point format, with the original reviewer comment in italics.

EDITOR COMMENTS:

Ensure that your referencing style conforms to that prescribed in the PLOS One guidelines.

References have been updated to match PLOS One formatting guidelines.

Provide references for the tests you mention in lines 53 to 56.

Reference added:

A. La Marca, M. Capuzzo, T. Paglia, L. Roli, T. Trenti, and S. M. Nelson, “Testing for SARS-CoV-2 (COVID-19): a systematic review and clinical guide to molecular and serological in-vitro diagnostic assays,” Reproductive BioMedicine Online, vol. 41, no. 3, pp. 483–499, Sep. 2020, doi: 10.1016/j.rbmo.2020.06.001.

Figure 1 title should read " Schematic representation of the model"

Updated.

Tables 2, 3 and 4 are presenting results. Should it be not appropriate that they are presented in the results section instead of results?

There is only one table in the manuscript. We assume this refers to the figures. We have adjusted the placement of the figures so that they are in the Results section.

Include the word "sensitivity" after the percentages in lines 62 and 63.

We added sensitivity in lines 234 and 235, which is what we believe you were referring to.

Thank you for stating the following in the Competing Interests section:

"The authors have declared that no competing interests exist."

We note that one or more of the authors are employed by a commercial company: UnitedHealth Group Inc, ProHealth Care.

Please also include the following statement within your amended Funding Statement.

If your commercial affiliation did play a role in your study, please state and explain this role within your updated Funding Statement.

We have updated the funding statement to read:

Authors [GL, NS, CK, DG, EB] are employees of Optum Labs at UnitedHealth Group. Author [DG] also serves as the Chief of Infectious Disease for ProHealth NY, part of Optum. These funders provided support in the form of salaries for authors [GL, NS, CK, DG, EB], but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Please also provide an updated Competing Interests Statement declaring this commercial affiliation along with any other relevant declarations relating to employment, consultancy, patents, products in development, or marketed products, etc.

GL is an employee of UnitedHealth Group and owns stock in the company. DG is employed as the Senior Infectious Disease Fellow at the commercial company, UnitedHealth Group, Inc and serves as the Chief of Infectious Diseases for ProHealth NY an Optum Company.

Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information.

We have added a caption for the supplementary file.

REVIEWER COMMENTS

Reviewer #1: This is very good, original, and profound research work done and a well written manuscript paper. My review is therefore limited to the following minor comments only.

The supplemental information has been updated to reflect the assumption that symptom tracking will catch 66% of symptomatic infections. The source of this choice is the Nature Medicine article below:

C. Menni et al., “Real-time tracking of self-reported symptoms to predict potential COVID-19,” Nature Medicine, vol. 26, no. 7, Art. no. 7, Jul. 2020, doi: 10.1038/s41591-020-0916-2.

However, as the reviewer notes, this value certainly has an impact on the simulation results, and there is continuing discussion in the literature about the efficacy of symptom tracking. For this reason, this is an adjustable parameter in the online calculator.

For a population as small as the one modelled in this study (1500 subjects), a stochastic model may be more appropriate. Was this considered?

Our aim in this project was to build the simplest model we could think of that could incorporate pooling and deal with the realities of a dynamic underlying (and unknown!) community prevalence of disease. For this reason, we built the model on basic SIR-type deterministic dynamics. One of the reasons for this was to ensure that the model (and its limitations) could easily be explained to policy makers and others (school superintendents, long-term care facility administrators, parents,…). For this reason, we did not consider variations or other modeling approaches, e.g., stochastic models or agent-based approaches, that might better capture some elements of the situation.

It is true that the model does not incorporate a distinction in infectiousness between symptomatic and asymptomatic individuals. In the name of simplicity, we assume, however, asymptomatic infectious individuals are as contagious as symptomatic ones. Notably, this “stacks the deck” against any testing program one might design. Thus, this is a conservative simplifying assumption. While we certainly don’t advocate being wasteful with testing capacity, our objective was to err on the side of overbuilding testing programs.

The “in text” referencing should be written in square brackets e.g as [14] and not as superscripts e.g as 14, 23.

References have been updated to match PLOS One formatting guidelines.

When this draft was originally written, during fall in the northern hemisphere, there was great concern about colder temperatures in winter leading to more indoor activities (and potentially more infections). For example, in some localities in the US, some restaurants stayed open in the fall by utilizing outdoor dining. The reviewer is correct, of course, that re-opening schools and businesses will also lead to the more contacts between individuals from distinct households.

The sentence has been rewritten to read: “As schools and businesses re-open and attempt to stay open, promptly detecting people with infectious COVID-19 is essential, especially as the risk of transmission may be expected to increase as contact networks increase in size and complexity.”

The description of β in the supplementary material has been updated.

Attachment

Submitted filename: Response To Reviewers.docx

10.1371/journal.pone.0248783.r003

Decision Letter 1

Simuunza

Martin Chtolongo

Academic Editor

2021

Martin Chtolongo Simuunza

Submission Version

5 Mar 2021

Identifying Optimal COVID-19 Testing Strategies for Schools and Businesses: Balancing Testing Frequency, Individual Test Technology, and Cost

PONE-D-20-36267R1

Dear Dr. Berke,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Martin Chtolongo Simuunza, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

Reviewer #1: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

Reviewer #1: Yes

**********

6. Review Comments to the Author

Reviewer #1: Major comment:

All my corrections have been sufficiently attended to. The paper is now well written and the methodology scientifically sound.

Minor corrections:

- Line 283 – 287 recheck for correct grammar.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

10.1371/journal.pone.0248783.r004

Acceptance letter

Simuunza

Martin Chtolongo

Academic Editor

2021

Martin Chtolongo Simuunza

9 Mar 2021

PONE-D-20-36267R1

Identifying optimal COVID-19 testing strategies for schools and businesses: Balancing testing frequency, individual test technology, and cost

Dear Dr. Berke:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

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Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Dr. Martin Chtolongo Simuunza

Academic Editor

PLOS ONE