Test sensitivity is secondary to frequency and turnaround time for COVID-19 screening

To examine how repeated population screening would reduce the average infectiousness of individuals, we first modeled the viral loads and infectiousness curves of 10,000 simulated individuals using the predicted viral trajectories of SARS-CoV-2 infections based on key features of latency, growth, peak, and decline identified in the literature (Fig. 1A; see Materials and Methods). Accounting for these within-host viral kinetics, we calculated what percentage of their total infectiousness would be removed by screening and isolation (Fig. 1B) with tests at LOD of 10³ and 10⁵ and at different testing frequencies. Here, infectiousness was taken to be proportional to the logarithm of viral load in excess of 10⁶ cp/ml (with alternative assumptions addressed in sensitivity analyses; see the Supplementary Materials), consistent with the observation that presymptomatic patients are most infectious just before the onset of symptoms (21) and evidence that the efficiency of viral transmission coincides with peak viral loads, which was also identified during the related 2003 SARS outbreak (22, 23). We considered that 35% of patients would undergo symptomatic isolation within 3 days of their peak viral load if they had not been tested and isolated first, and 65% would have sufficiently mild or no symptoms such that they would not isolate unless they were detected by testing. On the basis of recent results, we modeled asymptomatic and symptomatic infections as having the same initial viral loads (1, 24–26) but with faster clearance among asymptomatics (see Materials and Methods) (24, 26–29).

This analysis demonstrated that there was little difference in averting infectiousness between the two classes of test. Marked reductions in total infectiousness of the individuals were observed by testing daily or every third day, 62 to 66% reduction when testing weekly, and 45 to 47% under biweekly testing (Fig. 1C). Because viral loads and infectiousness vary across individuals, we also analyzed the impact of different screening regimens on the distribution of individuals’ infectiousness, revealing that more sporadic testing leads to an increased likelihood that individuals will test positive after they are no longer infectious or be missed by testing entirely (Fig. 1D).

Above, we assumed that each infection was independent. To investigate the effects of population screening strategies at the population level, we used simulations to monitor whether epidemics were contained or became uncontrolled while varying the frequencies at which the test was administered, ranging from daily testing to testing every 14 days, and considering tests with LOD of 10³ and 10⁵, analogous to RT-qPCR and RT-LAMP/rapid antigen tests, respectively. We integrated individual viral load trajectories into two different epidemiological models to ensure that important observations were independent of the specific modeling approach. The first model is a simple fully mixed model representing a population of 20,000, similar to a large university setting, with a constant rate of external infection approximately equal to one new import per day. The second model is a previously described agent-based model with both within-household and age-stratified contact structure based on census microdata in a city representative of New York City (30), which we initialized with 100 cases without additional external infections. Individual viral loads were simulated for each infection, and individuals who received a positive test result were isolated, but contact tracing and monitoring were not included to more conservatively estimate the impacts of screening alone (31, 32). Model details and parameters are fully described in Materials and Methods.

We observed that a population screening regimen administering either test with high-frequency limited viral spread, measured by both a reduction in the reproductive number R (Fig. 2, A and B; see Materials and Methods for calculation procedure) and the total infections that persisted despite different screening programs, expressed relative to no screening (Fig. 2, C and D). Testing frequency was found to be the primary driver of population-level epidemic control, with only a small margin of improvement provided by using a more sensitive test. Direct examination of simulations showed that with no testing or biweekly testing, infections were uncontrolled, whereas screening weekly with either LOD = 10³ or 10⁵ effectively attenuated surges of infections (examples are shown in Fig. 3).

The relationship between test sensitivity and the frequency of testing required to control outbreaks in both the fully mixed model and the agent-based model generalize beyond the examples shown in Fig. 2 and are also seen at other testing frequencies, sensitivities, and asymptomatic fractions. We simulated both models at LODs of 10³, 10⁵, and 10⁶ and for testing ranging from daily to every 14 days. For those, we measured each population screening policy’s impact on total infections (fig. S1, A and B) and on R (fig. S1, C and D). In Fig. 2, we modeled infectiousness as proportional to log₁₀ of viral load. To address whether these findings are sensitive to this modeled relationship, we performed similar simulations with infectiousness proportional to viral load (fig. S2) or uniform above 10⁶/ml (fig. S3). We found that results were robust to these large variations in the modeled relationship between infectiousness and viral load. To further address whether our results depended on the exact 35% fraction of individuals assumed to be behaviorally symptomatic, we performed sensitivity analyses with fewer (20%) or more (50%) symptomatic individuals and found no meaningful difference in results (fig. S4).

An important variable in testing is the time between a test’s sample collection and the reporting of a diagnosis. To examine how time to reporting affected epidemic control, we reanalyzed both the reduction in individuals’ infectiousness and the epidemiological simulations, comparing the results of instantaneous reporting (reflecting a rapid point-of-care assay), 1-day delay, and 2-day delay (Fig. 4, A and B). Delays in reporting markedly decreased the reduction in infectiousness in individuals as seen by the total infectiousness removed (Fig. 4C), the distribution of infectiousness in individuals (Fig. 4D), or the dynamics of the epidemiological models (Fig. 5). This result was robust to the modeled relationship between infectiousness and viral load in both simulation models and for various test sensitivities and frequencies (fig. S5). These results highlight that delays in reporting lead to markedly less effective control of viral spread and emphasize that fast reporting of results is critical in any screening regimen. These results also reinforce the relatively smaller benefits of improved LODs.

Communities vary in their transmission dynamics because of difference in rates of imported infections and in the basic reproductive number R₀, both of which will influence the frequency and sensitivity with which screening tests must occur. We performed two analyses to illustrate this point. First, we varied the rate of external infection in our fully mixed model and confirmed that when the external rate of infection is higher, more frequent screening is required to prevent outbreaks (fig. S6A). Second, we varied the reproductive number R₀ between infected individuals in both models and confirmed that at higher R₀, more frequent screening is also required (fig. S6, B and C). This may be relevant to institutions like college campuses or military bases wherein frequent classroom setting or dormitory living is likely to increase contact rates. Thus, the specific strategy for successful population screening will depend on the current community infection prevalence and transmission rate.

The generality of our findings to different epidemiological parameters (fig. S6), relationships between viral load and infectiousness (figs. S2 and S3), and proportion of symptomatic individuals (fig. S4) led us to ask whether a more general mathematical formula could predict R without requiring epidemiological simulation. We derived such a formula (text S1) and found that its predicted values of R were nearly perfectly correlated with simulation-estimated values (Pearson’s r = 0.998, P < 10⁻⁶; fig. S7), providing a mathematical alternative to simulation-based sensitivity analyses.

The impact of repeated population screening on transmission dynamics led us to hypothesize that testing could be used as an active tool to mitigate an ongoing epidemic. To test this idea, we simulated an outbreak situation using both the fully mixed and agent-based models but with three additional conditions. First, we assumed that in an ongoing pandemic, other mitigating interventions would cause the reproductive number to be lower although nevertheless larger than one. Second, we considered that not all individuals would want to or be able to participate in a SARS-CoV-2 screening program. Third, we assumed that the collection of samples for testing, if performed on a large scale, could result in imperfect sample collection, causing an increase in the false-negative rate, independent of an assay’s analytical sensitivity. These modifications are fully described in Materials and Methods.

We simulated epidemics in which screening began only at the point when uncontrolled infections reached 4% prevalence. On the basis of results from our previous analyses, we considered a less sensitive but rapid test with LOD 10⁵ cp/ml and a 0-day delay in results and further assumed that 10% of would-be positive samples would be negative because of improper sample collection. We then examined scenarios of testing every 3 days and every 7 days, with either 50 or 75% of individuals participating, starting from a partially mitigated R₀ = 1.5. We found that testing 75% of individuals every 3 days was sufficient to drive the epidemic toward extinction within 6 weeks and reduce cumulative incidence by 88% and that other combinations also had successful but less rapid mitigating impacts, particularly when compared with no intervention (Fig. 6). Notably, even weekly testing with 50% participation was able to reduce the peak and length of the outbreak, illustrating how even partial screening using a test with 100× lower molecular sensitivity than PCR can have public health benefits when used frequently (Fig. 6). Repeating these simulations using a test with LOD 10⁶ led to similar results (fig. S8). To further generalize these results, we modified our mathematical formula to predict the impacts of per-individual test refusal and per-test sampling-related sensitivity on the reproductive number R (see text S1).

Viral loads were drawn from a simple viral kinetics model intended to capture (i) a variable latent period, (ii) a rapid growth phase from the lower limit of PCR detectability to a peak viral load, (iii) a slower decay phase, and (iv) prolonged clearance for symptomatic infections versus asymptomatic infections. These dynamics were based on the following observations.

Latent periods before symptoms have been estimated to be around 5 days (40). Latent periods before detection via virological tests at secondary sites of replication or shedding have been estimated to be up to 4 days (41), corresponding to a latent or eclipse phase observed with other viruses (42). Viral load appears to peak before symptom onset (21) and peaks within 2 days of challenge in a macaque model (43, 44), although it should be noted that macaque challenge doses were high. Viral load decreases monotonically from the time of symptom onset (21, 45–48) but may be high and detectable 3 or more days before symptom onset (1, 49). Peak viral loads are difficult to measure because of lack of prospective sampling studies of individuals before exposure and infection, but viral loads have been reported in the range of 𝒪(10⁴) to 𝒪(10⁹) cp/ml (12, 47, 48). Viral loads appear to become undetectable by PCR within 3 weeks of symptom onset (45, 48, 50), but detectability and timing may differ, depending on the degree or presence of symptoms (50, 51). The majority of studies reviewed by Cevik et al. (18) found initial viral loads to be similar between symptomatic and asymptomatic infections (1, 24–26), but viral clearance was significantly and substantially faster among asymptomatic infections (24, 26–29). Last, we note that the general understanding of viral kinetics may vary depending on the mode of sampling, as demonstrated via a comparison between sputum and swab samples (12). For a comprehensive review of viral load dynamics, duration of shedding, and infectiousness, see (18).

To mimic growth and decay, log₁₀ viral loads were specified by a continuous piecewise linear “hinge” function, specified uniquely with three control points: (t₀,3), (t_peak, V_peak),(t_f,6) (Fig. 7A, green squares). The first point represents the time at which an individual’s viral load first crosses 10³, with t₀ ∼ unif[2.5,3.5], measured in days since exposure. The second point represents the peak viral load. Peak height was drawn V_peak ∼ unif[7,11], and peak timing was drawn with respect to the start of the exponential growth phase, t_peak − t₀ ∼ 0.5 + gamma(1.5) with a maximum of 3. The third point represents the time at which an individual’s viral load crosses beneath the 10⁶ threshold, at which point viral loads no longer cause active cultures in laboratory experiments (11–13, 18). For asymptomatic infections, this point was drawn with respect to peak timing, t_f − t_peak ∼ unif[4,9]. For symptomatic infections, a symptom onset time was first drawn with respect to peak timing, t_symptoms − t_peak ∼ unif[0,3], and then, the third control point was drawn with respect to symptom onset, t_f − t_symptoms ∼ unif[4,9]. Thus, symptomatic trajectories are systematically longer, in both duration of infectiousness (see below) and duration of viral shedding, reflecting the documented prolonged clearance and relationship with viral culture experiments (Fig. 7B, red circles). In simulations, each viral load’s parameters were drawn independently of others, and the continuous function described here was evaluated at 28 integer time points (Fig. 7, black dots) representing a 4-week span of viral load values.

Infectiousness F was assumed to be directly related to viral load V in one of three ways. In the main text, each individual’s relative infectiousness was proportional log₁₀ of viral load’s excess beyond 10⁶, i.e., $F \infty {\text{log}}_{10}(V)-6$. In the supplementary sensitivity analyses, we investigated two opposing extremes. To capture a more extreme relationship between infectiousness and viral load, we considered F to be directly proportional to viral load’s excess above 10⁶, i.e., $F\propto {10}^{{\text{log}}_{10}(V)-6}=V\times {10}^{-6}$, and to capture a more extreme relationship, but in the opposing direction, we considered F to simply be a constant when viral load exceeded 10⁶, i.e., F ∝ 1_{V > 10}⁶. We call these three functions log-proportional, proportional, and threshold throughout the text and the Supplementary Materials.

We note that a comprehensive review of viral loads, shedding, and infectiousness (18) found that, across the surveyed literature, no virus could be cultured beyond 9 days after symptoms. Thus, the choice of the final control point in our symptomatic viral load model (Fig. 7B), which corresponds to the latest time at which an individual is infectious, is, at most, 9 days after symptom onset.

Recently, He et al. (21) published an analysis of infectiousness relative to symptom onset that was corrected by Bonhoeffer et al. [see (21) for details]. Among our infectiousness functions, this inferred relationship bears the greatest similarity, over time, to the log-proportional infectiousness function, as visualized in Figs. 1 and 4. The proportional and threshold models therefore represent one of many types of sensitivity analysis. Results for those models can be found in figs. S2, S3, and S5. In all simulations, the value of the proportionality constant implied by the infectiousness functions above was chosen to achieve the targeted value of R₀ for that simulation and confirmed via simulation as described below.