A meta-analysis comparing the clinical study results of symptoms, results of nucleic acid tests with those of the BinaxNow antigen test is summarized in Table 1. Columns 1-5 of Table 1 show the typical daily rates of viral growth in the nasal passages of individuals infected with the SARS-CoV-2 virus (as measured by qPCR), the level of symptomology, and the probability of disease transmission during these time intervals.
In the qPCR tests, the virus is detectable in nasal swabs as soon as 1.5 to 2 days post infection remains detectable for many days, and usually wanes to undetectable levels by 2 weeks after infection. The nucleic acid assay is, therefore, not necessarily effective as a screening test for infectious virus because the assay can also detect the presence of viral RNA (not necessarily intact viruses), which implies that for certain infected individuals the nucleic acid test will be positive for weeks (if not months) after infection [34, 35]. Moreover, the results of the nucleic acid test are usually communicated back to the user 24 to 48 hours after the swab sample is taken. Thus, decisions based on nucleic acid tests are effectively displaced by 24 to 48 hours from the data shown in Column 5 of Table 1. The typical pattern of viral load in an infected individual as measured by the BinaxNOW antigen test is presented in column 6 of Table 1. These data were adapted from Perchetti et al.  and James et al. . This antigen test is not as sensitive as nucleic acid tests for detecting the extremely low viral loads present at the early onset of a SARS-CoV-2 infection. The likely limit of detection of this antigen test is about 100 times less than the qPCR tests (~10E5 cp/ml). Perchetti et al.  have shown that the BinaxNOW card has an analytical sensitivity approximately equivalent to a generic qPCR cycle threshold value of 29 to 30. This antigen test, however, does appear to detect the virus in what could be described as the “Goldilocks” zone, which is the period when an infected individual is most likely to be infectious (i.e., 4-7 days post infection; see Table 1, column 3). Also noteworthy is that antigen tests revert to identification of weak or negative results once the individual’s immune system is actively killing the virus and the risk of transmission is low. The analytic specificity of the BinaxNOW card exceeds 98% [36, 28].
Different laboratories have determined the level of sensitivity of the BinaxNOW test, and results vary from 52% for asymptomatic persons (83% for symptomatic persons)  to 96.5% (95% confidence interval 90.0% – 99.3%) . As shown by Paltiel et al.  and Larremore et al. , the level of false negatives can be limited by testing at frequent intervals — that is, daily, every 2 days, or every 3 days.
To conduct our analysis, we customized the publicly available computer code  in the R programming language that was originally written to implement the SEIR model of Paltiel et al.  Our customization of this code allowed us to expand the output parameters and to examine the costs and benefits of varying specific epidemic parameters or changing specific attributes with respect to testing. For the data presented in this paper, we used a given set of parameters that remained invariant, and then tested the impact of different test cadences, different R0 values, and different population sizes on the costs and benefits of these testing cadences. The parameters that we kept as invariant in the tool for our calculations were as follows.
- Number of times per day testing will be done: 1
- Number of days per week: 5
- Days of incubation:3 [40, 16]
- Time to recovery: 10 days 
- Percent asymptomatic advancing to symptoms: 30% [42, 43, 44]
- Test sensitivity: 80% [36, 29, 28]
- Test specificity: 98% [36, 28]
- Antigen test kit cost: $5.00 
- Testing horizon: 80 days
An important additional parameter is that the model allows for “exogenous shocks.” That is, it allows the introduction of infections to the population at prescribed intervals and of prescribed size. Unless otherwise noted, we allowed 10 new infections per week into the test populations. Detailed below are results of modeling using the tool we developed for four different scenarios that are easily obtained by simply adjusting the different parameters in the tool.
Assumptions for carrying out these tests are as follows. All individuals who test positive will be retested, and if they retest positive, they will be sent home for quarantine for 10 days. We define these individuals as true positives. Individuals who retest negative will be allowed to resume normal activities. They are assumed to be false positives. True positives after quarantine return to normal activities and are not tested again. False positives will remain in the “susceptible” pool and tested according to the scheduled cadence.
Scenario 1: The results of testing a population of 30,000 individuals using three different test cadences is shown in Table 2. This population size is typical of the total student and staff population of the public school system in a mid-sized county in the United States. The three test cadences examined using the antigen test kit were as follows: 1) daily testing for a given time (i.e., 1 to 15 weeks) followed by a second test regimen of testing every 4 weeks for the remainder of a 16-week test horizon, 2) testing every 2 days for a given period of weeks followed by every 4 weeks, and 3) testing every 3 days for a given period of weeks followed by every 4 weeks. The model is flexible and allows the user to compare test cadences of daily, every 2 days, every 3 days, weekly, every 2 weeks, every 3 weeks, and every 4 weeks.
The results in Table 2 shown in bold font highlight the test conditions that resulted in the best outcomes from combinations of the above cadences in terms of low cost, low numbers of people in quarantine, large numbers of infections prevented, and the lowest costs per case averted. The best outcome occurs around weeks 4 to 6 of daily testing followed by every 4-week testing, or around weeks 6 to 8 of every 2 day testing (followed by 4-week testing), or around weeks 9 to 11 of every 3 day testing (followed by every 4-week testing). Comparing the three test cadences shows that primary testing daily would be the most expensive approach both in terms of total cost (~$4.0M) and cost per case averted (~$170). The lowest cost alternative is the cadence that uses every 3-day initial testing followed by every 4-week testing. This approach saves about $300K relative to the every-2-day cadence, and about $1.5M relative to the daily cadence. These results demonstrate the value of this modeling approach in providing policymakers with an analytical means of comparing different potential testing scenarios to determine the most efficacious outcomes for the circumstances or available resources.
Scenario 2: A comparison of output using three different R0 values in the model is summarized in Table 3. The table shows only those ranges of testing cadences that resulted in the best outcomes in terms of low cost, low numbers of people in quarantine, large numbers of infections prevented, and the lowest costs per case averted. An R0 of 2.3 was chosen because it represents the wild-type strain of SARS-CoV-2 that has been prevalent in the U.S. . The R0 of 3.0 was chosen for comparison because some variants (e.g., the Alpha variant) have an R0 that is bigger by a factor of 0.3 to 0.7 . The R0 value of 1.5 was chosen because this is the rate of spread observed when the population in consideration actively wears masks, practices social distancing, and maintains hand hygiene 
According to the data in Table 3, good hygiene would save approximately $400K in testing costs (i.e., compare R0 2.3 to R0 1.5). If a new variant has an R0 of 3.0, however, the cadence of testing every 3 days followed by testing every 4 weeks is never able to decrease infections below 45% of the tested population. Remember that in this model, we are allowing new infections to enter this population at rate of 10 new cases per week. In this scenario, one would have to increase the rate of primary testing to every 2 days to see a decrease in new cases to below 20% of the tested population (see Table 3). The every-2-day regimen for a period of 10-12 weeks reduces the infection rate to below 20% at a cost of roughly $4M. Unfortunately, variants with R0 in the range of 4-7 already have been identified [17, 19, 45, 46]. We also tested an R0 of 6 in our model using the same conditions stated for Table 3, and the only testing cadence that impacted the degree of infection significantly (i.e., 79% of cases averted) was daily testing. The cost of this daily testing schedule was $9,835,355. Clearly, variants with an R0 greater than 3.0 will be very expensive to manage.
Scenario 3: To determine if our model is capable of being scaled-up to handle testing of larger populations, we evaluated the same testing strategy employed above (i.e., primary screen of daily, every 2 day, or every 3 days, followed by a secondary screening of every 4 weeks) for population sizes of ten thousand, one hundred thousand, and 1 million people, respectively (Table 4). For ease of comparison, only those ranges of test cadences that produced the best outcomes are presented. The best test outcomes occurred at different times based on the size of the population being tested. For example, in comparing the cost per case averted across the three different population sets, the best test cadence consisted of primary testing every 3 days for a given period followed by secondary testing every 4 weeks (see Table 4). Also note that the times for primary testing that resulted in the best outcomes seemed to be 10 to 12 weeks for the 10,000 population, 8 to 10 weeks for the 100,000 population, and 7 to 9 weeks for the 1,000,000 population. Thus, the model helps provide flexible, actionable intelligence regardless of the size of the population being tested.
Scenario 4: In another set of experiments, we considered testing strategies for a typical long-term-care facility. Output of the model for these cases is detailed in Table 5. The size of the population tested in this facility was assumed to be 100 considering both the patients and staff. Criteria for a successful testing strategy are unique to these types of facilities. For example, a large percentage of the patients in long-term-care facilities likely have significant underlying health conditions, and therefore keeping the number of infections to a minimum is a high priority. Moreover, since visitor access to these facilities is restricted, this reduces the possibility of asymptomatic but infected individuals carrying the virus into the facilities. Our computations for long-term care facilities employed the following test parameters: two new outside infections into the facility every four weeks, R0 of 1.5 (as increased safety protocols are more likely), and a mortality level of infections of 8% . Results in Table 5 show that daily testing for 15 weeks still resulted in approximately 10% of the individuals at a typical long-term care center becoming infected; and testing resulted in a cost of approximately $30,000. Testing regimens of every 2 days or every 3 days resulted in 11%-15% of the individuals becoming infected while the costs for these testing regimens were approximately $16,000 and $11,000, respectively. Even though the mortality rate for these nursing home settings was parameterized at 8%, this higher mortality rate did change the percent infection rate, or the cost of testing. We conclude that this model helps provide information for fact-based decisions on testing in long-term-care facilities.