Quantifying asymptomatic infection and transmission of COVID-19 in New York City using observed cases, serology, and testing capacity Rahul Subramaniana , Qixin Hea , and Mercedes Pascuala,b,1 aDepartment of Ecology and Evolution, Biological Sciences Division, University of Chicago, Chicago, IL 60637; and bSanta Fe Institute, Santa Fe, NM 87501 Edited by Nils Chr. Stenseth, University of Oslo, Oslo, Norway, and approved January 20, 2021 (received for review September 18, 2020) The contributions of asymptomatic infections to herd immunity secondary cases arising from a primary case in the absence of and community transmission are key to the resurgence and con- immunity, and is estimated on the basis of a particular epi- trol of COVID-19, but are difficult to estimate using current models demiological model. Mathematical models for the population that ignore changes in testing capacity. Using a model that incor- dynamics of COVID-19 incorporate different features such as porates daily testing information fit to the case and serology asymptomatic and presymptomatic transmission, superspread- data from New York City, we show that the proportion of symp- ing, or heterogeneity in susceptibility. A considerable range of tomatic cases is low, ranging from 13 to 18%, and that the R0 estimates has been reported, ranging from at least 1.5 (4) reproductive number may be larger than often assumed. Asymp- to 5.7 (5) in Wuhan. A much narrower range, between two and tomatic infections contribute substantially to herd immunity, and three, is frequently cited in the popular press, or assumed when to community transmission together with presymptomatic ones. simulating models (6) or fitting these to data (7, 8). This assump- If asymptomatic infections transmit at similar rates as symp- tion may be based on the dynamics of COVID-19 in regions tomatic ones, the overall reproductive number across all classes that implemented interventions early (9–13). A more precise is larger than often assumed, with estimates ranging from 3.2 estimate of R0 from a city where substantial transmission was to 4.4. If they transmit poorly, then symptomatic cases have a occurring prior to intervention, such as New York City, would larger reproductive number ranging from 3.9 to 8.1. Even in this provide a relevant baseline. Furthermore, if “superspreading” regime, presymptomatic and asymptomatic cases together com- by a small fraction of symptomatic infections fuels COVID-19 POPULATION BIOLOGY prise at least 50% of the force of infection at the outbreak transmission, a precise estimate of the mean number of sec- peak. We find no regimes in which all infection subpopulations ondary cases arising from such an individual may be just as have reproductive numbers lower than three. These findings valuable. A model that precisely estimates the fraction of symp- elucidate the uncertainty that current case and serology data tomatic cases may help epidemiologists discern whether either cannot resolve, despite consideration of different model struc- the overall or symptomatic reproductive numbers are higher than tures. They also emphasize how temporal data on testing can assumed. reduce and better define this uncertainty, as we move forward The probability that a COVID-19 infection is symptomatic is through longer surveillance and second epidemic waves. Comple- difficult to estimate (14), and a wide range of values have been mentary information is required to determine the transmissibility of asymptomatic cases, which we discuss. Regardless, current Significance assumptions about the basic reproductive number of severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) should be reconsidered. As health officials face another wave of COVID-19, they require estimates of the proportion of infected cases that COVID-19 j testing submodel j asymptomatic transmission j develop symptoms, and the extent to which symptomatic epidemiological model j epidemiological parameter estimates and asymptomatic cases contribute to community transmis- sion. Recent asymptomatic testing guidelines are ambiguous. Using an epidemiological model that includes testing capac- ince the emergence of the novel coronavirus in December ity, we show that many infections are nonsymptomatic but S2019 (1), the COVID-19 pandemic has resulted in over 16 contribute substantially to community transmission in the million cases and 600,000 deaths worldwide (2). Schools and aggregate. Their individual transmissibility remains uncer- universities in the United States are gradually reopening amid tain. If they transmit as well as symptomatic infections, the concerns that a second wave of the epidemic may reemerge in epidemic may spread at faster rates than current models the fall and winter of 2020. often assume. If they do not, then each symptomatic case As they craft testing policies and intervention strategies to generates, on average, a higher number of secondary infec- mitigate a second wave, public health officials need to better tions than typically assumed. Regardless, controlling trans- understand the role that symptomatic and asymptomatic individ- mission requires community-wide interventions informed by uals play in the community transmission of COVID-19 and in extensive, well-documented asymptomatic testing. the development of herd immunity to the disease. However, fun- damental epidemiological questions remain poorly understood, Author contributions: R.S. and M.P. developed the methodology; R.S., Q.H., and M.P. including what fraction of cases are symptomatic and how well conceptualized the research; R.S. performed the research; and R.S. wrote the paper with asymptomatic cases can transmit relative to symptomatic ones. contributions from Q.H. and M.P.y These questions are especially urgent given ambiguity in recent The authors declare no competing interest.y Centers for Disease Control and Prevention (CDC) guidelines This article is a PNAS Direct Submission.y regarding the testing of asymptomatic individuals (3). This open access article is distributed under Creative Commons Attribution License 4.0 Answering these questions can also provide further insight (CC BY).y on the basic reproductive number of severe acute respiratory 1 To whom correspondence may be addressed. Email: [email protected] syndrome coronavirus 2 (SARS-CoV-2), and how the virus This article contains supporting information online at https://www.pnas.org/lookup/suppl/ would spread in a population in the absence of interventions. doi:10.1073/pnas.2019716118/-/DCSupplemental.y This number, known as R0, is defined as the mean number of Published February 10, 2021. PNAS 2021 Vol. 118 No. 9 e2019716118 https://doi.org/10.1073/pnas.2019716118 j 1 of 10 Downloaded by guest on September 25, 2021 suggested (14–16). Estimates from cruise ship outbreaks (17), one with no presymptomatic transmission (the SEIAR model; Wuhan evacuees (18), long-term care facilities (19), and contact Fig. 1B) and one with no asymptomatic transmission (the SEPIR tracing of index cases (15) may not be representative of the gen- model; Fig. 1C). By varying specific parameters weighting the eral population. Increases in the testing capacity for COVID-19 transmission rate of P and A relative to that of symptomatic over time (9, 20, 21) make population-level estimation of this individuals, we can continuously move across these two extreme probability difficult due to confounding with other parameters structures. Daily reports of the number of tests conducted in such as the reporting, hospitalization, and fatality rates. When New York City are fed in as a covariate in the testing submodel the testing capacity is limited in the early stages of an outbreak, (SI Appendix). The model takes into account CDC priorities in severe cases are more likely to be tested, which can bias estimates sampling and testing: All hospitalized cases are sampled and of the probability that an infection is symptomatic and of the eventually tested, while nonsevere symptomatic individuals are fatality rate. Changes in testing capacity over time also confound sampled and tested only if excess capacity is available at the the definition itself of asymptomatic individuals in transmission time of sampling. We also incorporate the retesting of hospital- models, when these are not differentiated from unreported cases. ized individuals as they leave the hospital. This model is fit to These changes can also bias the reported deaths attributed to observed cases in New York City from March 1, 2020 to June 1, COVID-19. 2020 and to serological estimates of herd immunity in New York These challenges can be improved upon by explicitly incorpo- City from March 8, 2020 to April 19, 2020 (Materials and Meth- rating changes in testing capacity into an epidemiological process ods and SI Appendix). We compare the full model with the two model. While some early models of the COVID-19 outbreak in nested simplified versions. Although all three model structures Wuhan attempted to take into account changes in testing capac- are supported by the case data, the model with no asymp- ity (21) or differences in reporting rate during periods of the tomatic transmission is not supported when these data are con- epidemic (9), the limited information on these trends in Wuhan sidered in conjunction with serology information (SI Appendix, meant that they had to be estimated on a coarse temporal scale Table S2). (2- to 3-wk intervals) and had to be inferred along with other To evaluate the strength of transmission in asymptomatic cases parameters