Temporal dynamics of viral load and false negative rate influence the levels of testing necessary to combat COVID-19 spread

Abstract

Colleges and other organizations are considering testing plans to return to operation as the COVID-19 pandemic continues. Pre-symptomatic spread and high false negative rates for testing may make it difficult to stop viral spread. Here, we develop a stochastic agent-based model of COVID-19 in a university sized population, considering the dynamics of both viral load and false negative rate of tests on the ability of testing to combat viral spread. Reported dynamics of SARS-CoV-2 can lead to an apparent false negative rate from ~ 17 to ~ 48%. Nonuniform distributions of viral load and false negative rate lead to higher requirements for frequency and fraction of population tested in order to bring the apparent Reproduction number (Rt) below 1. Thus, it is important to consider non-uniform dynamics of viral spread and false negative rate in order to model effective testing plans.

Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1

Viral transmission data and test false negative rate data both suggest that SARS-CoV-2 is undetectable until ~ 2 days prior to symptom onset. Shown in cyan is the viral load data by day from onset of symptoms from He et al.. Shown in magenta is the false negative rate of tests by day from Kucirka et al.. Transmission probability begins increasing ~ 2 days before symptom onset, at the same time that the false negative rate of tests begins dropping.

Figure 2

A stochastic agent-based model of COVID-19 transmission. This is a stochastic SEIR model implemented in MATLAB. Each transition in state is based on if–then statements with specific probabilities described in Fig. 3. (A) Individuals start as susceptible, and the initial population is seeded with 10 random infected individuals, each starting at a random point of progression through the disease, and with random symptoms. Upon being infected, an individual become exposed (presymptomatic), and is assigned a day for symptom onset. Detectability for testing and infectiousness both begin at 2 days prior to onset of symptoms. Infectious individuals can be either asymptomatic, or symptomatic with mild or severe symptoms. Those with severe symptoms will self-isolate and initiate contact tracing through seeking medical attention. Asymptomatic individuals and those with mild symptoms can be isolated through contact tracing or through detection by a test. Infectious individuals will recover randomly with a median time of 14 days. (B) An example of 100 independent simulations with the model. Shown are susceptible, infected (encompassing exposed, infectious, and isolated individuals), and recovered individuals in simulations where no interventions were implemented. Each individual simulation is represented as semi-transparent points, while the median value of all simulations is plotted as a line.

Figure 3

Model Parameters. (A) Probability distribution of onset of symptoms from He et al. (B) Breakdown of symptom groups in the model. (C) Probability distribution of recovery based on a median time to recovery of 14 days. (D) R0 of 2.5 scaled to a uniform transmission probability distribution. The gray box indicates where the cumulative probability reaches 1. Individuals must be detected prior to this, on average, in order to reduce the apparent R0 below 1. (E) The R0 of 2.5 scaled to the viral load based on He et al. The gray box is the same as above. (D) The R0 of 2.5 scaled to the positive test rate from Kucirka et al.. This was done because the changes in positive test rate are likely related to viral load, and so may be an alternative representation of transmission likelihood. The gray box is the same as above.

Figure 4

Effects of False Negative rates on detection. (A) Non-uniform false negative dynamics can delay detection of infected individuals. Shown is the chance of first being detected at each day of disease progression based on three scenarios with the same average false negative rate across the 14 days shown, but different temporal dynamics. For this graph, we assume that symptom onset begins at day 5. In yellow is the undetectable period prior to 2 days before symptom onset. The two days before symptom onset is shown in gray. Viral load data suggests that as much as 44% of transmissibility may occur in these two days. The line represents histograms of the first day that an individual would be detected by a daily test with the given false negative rate dynamics. (B) The undetectable period and temporal dynamics of the false negative rate lead to high apparent false negative rates. The first day of the model was run 100 times with 10,000 sick individuals. In cyan we show the model run with the simple assumption that infected individuals were undetectable before viral load begins, (2 days prior to symptom onset, based on the He et al. data), and that after that point the tests will always detect infected individuals. In magenta, the model uses the dynamic false negative rates from Kucirka et al., in which both test error and inability to detect due to low viral load are mixed together. Also included as a comparison is the effect of perfect tests shown in gray.

Figure 5

High asymptomatic transmission and dynamic false negative rate lead to a requirement for more testing to bring the viral spread under control. Heatmaps show the effective Reproduction number (Rt) from 100 simulations run with the given proportion of the population tested at the indicated frequency. The top row of matrices shows the median Rt, while the bottom row of matrices shows the value of the upper 95th percentile (i.e. conditions that will work in 19 out of 20 situations). While the scenario 1 perfect tests suggest testing the entire population every two weeks may work to stop spread of the virus, using scenario 4 parameters predicts that testing the entire population daily was necessary.

Figure 6

In the presence of masking, fewer tests and lower frequencies of testing can be successful in driving Rt below 1. (A) Here we implemented 70% of the population using a mask that is 67% effective with the parameters of Scenario 4, early transmission of virus based on the He et al. viral load data, and dynamic false negative rates for tests based on Kucirka et al. The top row of matrices shows the median effective Reproduction number (Rt), while the bottom row of matrices shows the value of the upper 95th percentile. Masking drove the median Rt from 2.5 to ~ 1.3. Tests were then able to drive the 95th percentile Rt below 1 with less aggressive testing schemes than in Fig. 5. (B) The same conditions as (A), with an included 1 day turn around delay in testing results. The magenta line shows the border between an Rt above 1 and an Rt below 1 without a delay. (C) As in (B) with a 2 day turn around delay in testing results.

Figure 7

Assumptions about the behavior of people with mild symptoms influence the amount of testing required. Scenario 4 from Fig. 6 was repeated with the addition that people experiencing mild symptoms self-isolate on the day of symptom onset. Under these conditions, testing everyone every 4 days is sufficient to bring 95% of situations to an Rt of 1.00 or below.

Figure 8

Superspreading leads to more variability between discrete simulations, but requires the same amount of testing as normally distributed transmission probabilities. (A) On the left is the normal distribution of R0s assigned to individuals, while the right distribution is a superspreader distribution where 20% of the population is responsible for 80% of the infections. (B) 500 runs of the model with either the normal distribution or the superspreader distrubtion of R0s and the Scenario 4 transmission and false negative rate dynamics. Medians of each population are shown as solid lines. Note that the medians of infected and recovered in the superspreader conditions fall on the x-axis line. (C) Effective reproduction number (Rt) for the indicated testing frequency and proportion of population for the superspreader R0 distribution. As in Fig. 5, only daily testing of 100% of individuals is sufficient to drive Rt below 1 under these assumptions.