On Friday, July 10th, the US reported 66,281 new COVID-19 cases, reaching a new high since the outbreak.
Is the infection resurging? Or is this just an indication that we’ve become better at testing? How many undocumented cases are still out there? According to a study ¹ by Stanford researchers, antibody test results suggest that there are significantly more unreported cases than reported ones. Critics of this study have questioned the accuracy regarding this method on the account of specificity. Recently, researchers have found that antibody testing has close to 40% false negatives ², underscoring the difficulties of measuring the infected population.
The fraction of undocumented cases, also known as the ascertainment rate, is crucial for understanding the COVID-19 situation. Reported in May, a group of researchers developed mathematical models and a model-inference framework³ ⁴ ⁵ to estimate the ascertainment rate (𝜶) along with other critical parameters such as average latency period (𝜡), duration of infection(𝑫), and the transmission rate (𝛽) for both documented and undocumented cases. The model takes input from daily reported infections, deaths, and human mobility data and applies data analysis techniques known as Bayesian inference and Ensemble Kalman Filter, producing the estimation of those parameters.
We use their model ⁵ and published code with the latest data to calculate the total daily infections, unreported cases, and basic reproductive numbers in the Washington DC Metro Area. We also analyzed the effect of quarantine and correlated the reduction of human mobility with the reduction of virus transmission potential. Here is what we found:
The ascertainment rate describes the fraction of infections that are reported. We calculated the ascertainment rate from February to July and Figure 1 shows the result. It indicates that the ascertainment rate has been steadily increasing since May, which can be attributed to the acceleration of testing nationwide.
Applying the ascertainment rate to the reported case numbers, we obtained the unreported case numbers and plotted them in a stacked histogram. Figure 2 shows an increase in total cases in the DC Metro area since the end of June.
Figure 3 shows that total nationwide new cases resurged since the beginning of June.
Basic Reproduction Rate (Rₒ) and Effective Reproduction Rate (Rₑ)
The basic reproduction number (Rₒ) measures the transmission potential of a disease. It is defined as the average number of secondary infections produced by an infection case in a population where everyone is susceptible ⁶ ⁷. It depends on several factors: the rate of contacts in the host population, the probability of infection being transmitted during contact, and the duration of infectiousness. When Rₒ>1, the number of infection cases increases.
We found 11 counties in the DC Metro area that have reported case numbers over 1,000. Figure 4 shows that Rₒ of all those counties dropped to below 1 during quarantine. However, Rₒ started climbing above 1 at the end of May for all but 3 counties. By early July, there are 6 counties with Rₒ still above 1.
The effective reproduction number (Rₑ) takes into account the fraction of the susceptible population, defined as Rₑ=Rₒ×S/N, where S is the susceptible population and N is the total population. It measures the average number of secondary cases per infectious cases in a population made up of both susceptible and non-susceptible hosts. As a result, Rₑ will be lower than Rₒ because some individuals are immune. In the real world, if Rₑ>1, the number of cases increases ⁶ ⁷ .
Figure 5 shows the top 11 counties in the DC Metro Area from February to July. Similar to Rₒ, there are currently 6 counties with Rₑ above 1.
Herd Immunity and Susceptible Population
Herd Immunity requires the fraction of the susceptible population (susceptibility) to drop below 1/Rₒ ⁷. When Rₒ is 2, as shown at the current time in Figure 4, that threshold is 50%. We calculated the susceptible population for all counties from February to July.
For those 6 counties with an Rₒ above 1, Figure 6 indicates that their susceptibility is much higher than the threshold. Figure 7 shows that the susceptibility of the US nationwide is even higher than the DC Metro Area.
In the study by Pei ⁵, human mobility is modeled using US Census intercounty commuting data. During quarantine, the mobility data is scaled down using mobile phone data from SafeGraph⁸. We compared the scaling factor of mobile phone data with Metro transit ridership data.
Figures 8 shows the percentage change measured by Metro ridership and cell phone data in Washington DC, Arlington County, Montgomery County, and Fairfax County. The Metro ridership decreases more than the mobile phone calls, which suggests that people avoided public transit during quarantine. The increase in mobile phone calls in DC between March 20th and March 30th could be attributed to the Cherry Blossom Festival, despite the event being officially canceled.
We selected the top 70 counties nationwide ordered by total cases and attempted to correlate the decrease of intercounty traffic with the decrease in Rₒ during early quarantine. Figure 9 shows scattered data forming a wedge pattern with its upper bound trending upwards.
We thank Dr. Jeffrey Shaman for his helpful email correspondence and the sharing of code and datasets from his team.
- Mallapaty, Smriti. “Antibody Tests Suggest That Coronavirus Infections Vastly Exceed Official Counts.” Nature, 17 Apr. 2020, www.nature.com/articles/d41586-020-01095-0, 10.1038/d41586–020–01095–0.
- Imai, Kazuo, et al. “Clinical Evaluation of an Immunochromatographic IgM/IgG Antibody Assay and Chest Computed Tomography for the Diagnosis of COVID-19.” Journal of Clinical Virology, vol. 128, July 2020, p. 104393, www.ncbi.nlm.nih.gov/pmc/articles/PMC7191278/, 10.1016/j.jcv.2020.104393.
- Pei, Sen, et al. Reconciling Diverse Estimates of COVID-19 Infection Rates. http://www.columbia.edu/~jls106/pei_etal_reporting_rates.pdf
- Li, R. et al. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2). Science 368, 489–493 (2020). https://science.sciencemag.org/content/368/6490/489.full
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- “SafeGraph | POI Data, Business Listings, & Foot-Traffic Data.” Safegraph.Com, 2020, www.safegraph.com/.
- CDC. “Cases in the U.S.” Centers for Disease Control and Prevention, 12 July 2020, www.cdc.gov/coronavirus/2019-ncov/cases-updates/cases-in-us.html.