Quantifying Asymptomatic Infection and Transmission of COVID-19 in New York City Using Observed Cases, Serology, and Testing

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POPULATION BIOLOGY 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 in the model. In the United States, many states and relative to symptomatic cases, we construct a Monte Carlo profile municipalities such as New York City (22, 23) have published using the full SEPIAR model (SI Appendix, Fig. S5). We iso- daily estimates of the number of total COVID-19 tests con- late parameter combinations from the profile that are supported ducted, together with the number of positive COVID-19 tests. by the case and serology data, and examine the values of those While these data are often used by public health officials to combinations. Particular parameters of interest that we focus on gauge the spread of the COVID-19 outbreak, they have yet to include the proportion of cases that are symptomatic, pS , the be incorporated explicitly into epidemiological models. ratio of the transmission rate of asymptomatic individuals to that We present an epidemiological model that incorporates RT- of symptomatic individuals, ba, and the reproductive numbers. PCR testing as an integral process informed by empirical levels. We use R0 to denote the symptomatic reproductive number (i.e., The explicit consideration of testing allows us to clearly define the mean number of secondary cases arising from each primary asymptomatic individuals as those that will never transition to symptomatic case), and use R0NGM to denote the overall repro- displaying symptoms, and to differentiate them from those who ductive number for the model (i.e., the mean number of cases have been unreported because they were not tested. We fit the arising from a primary infection, where the average considers all model to PCR-confirmed COVID-19 cases in New York City, types of infections). using publicly available data provided by the New York State The proportion of COVID-19 cases that are symptomatic is Department of Public Health (23). The resulting model can well identified, with a CI ranging from 12.9 to 17.4% (Fig. 2). clearly delineate symptomatic and asymptomatic infections inde- Although a wide range of parameter combinations for the pro- pendently from the reporting rate. We subsequently fit the model portion of symptomatic infection are supported by the case data to estimates of prior exposure obtained from a recent serologi- on its own, a much narrower estimate is obtained when the case cal study in New York City (24) to further constrain inference and serology data are considered together (Fig. 2 A and B). results. Within this range, estimates of herd immunity are consistent with Our model obtains a precise estimate for the symptomatic the dynamics of observed serology (Fig. 2C), in particular, the proportion of COVID-19 cases. We show that most COVID- rapid rise in seroprevalence over March and April 2020. We vali- 19 infections are asymptomatic, and that these asymptomatic dated the inference pipeline by fitting the model to two simulated infections together with presymptomatic ones substantially drive trajectories from two parameter combinations that are both sup- community transmission, contributing 50% or more of the total ported by the case, serology, and testing data but correspond force of infection. Furthermore, depending on the transmissi- to regimes with strong or weak asymptomatic transmission. As bility of individual asymptomatic cases relative to symptomatic shown in SI Appendix, Fig. S11B, models fit to both of these ones, either the overall reproductive number or the symptomatic trajectories instead of observed cases are able to accurately esti- reproductive number may be higher than typically assumed. Our mate and recover the proportion of symptomatic cases used in results highlight the importance of testing and contact tracing the simulations. of asymptomatic individuals, and of making these data publicly The overall reproductive number or symptomatic reproductive available as health officials prepare for and manage a second number may be larger than is often assumed. From our profile wave. of the relative asymptomatic transmission rate ba, we identify two main regimes of transmission that are supported by both the Results case and serology data (Fig. 3), in which either R0 orR0NGM is We present a stochastic epidemiological model (Fig. 1) that higher than the two to three range often assumed for COVID- explicitly incorporates daily changes in testing capacity and 19. Notably, we find no parameter combinations in which both the lag between sampling and testing (see Materials and Meth- reproductive numbers are below three and fall within this range. ods). The underlying model, referred to hereafter as the In the first regime, asymptomatic individuals transmit at SEPIAR model (Fig. 1A), has a susceptible–exposed–infectious– almost the same rate as symptomatic individuals. That is, ba is recovered (SEIR) structure with compartments for both severe large, even close to one in some parameter combinations. The (hospitalized) and nonsevere symptomatic infections as well overall reproductive number takes on values between 3.2 and 4.4, as presymptomatic (P) and asymptomatic (A) infections (thus and asymptomatic cases substantially contribute to the overall SEPIAR). We also consider two nested simplified versions: force of infection (Fig. 4).

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POPULATION BIOLOGY Fig. 2. The probability of symptomatic infection. (A) Simulated vs. observed cases from the profile of the asymptomatic transmission strength (ba) using the SEPIAR model. The red line is the median from 100 simulations using the MLE, while the red shaded region denotes the 2.5 to 97.5% quantiles across 100 simulations from all parameter combinations within two log-likelihood units of the profile MLE. Likelihoods here are with respect to case data. The observed daily case counts are denoted by the blue line. (B) Model likelihood as a function of the proportion of cases that are symptomatic (pS) for each parameter combination from A. The y axis shows the likelihood for that parameter combination with respect to serology data. All parameter combinations above the blue line have likelihoods within two log-likelihood units of the MLE (defined with respect to serology). This corresponds to a range of values for pS of approximately 13 to 18%. (C) Comparison of observed vs. simulated estimates of herd immunity in the population from parameter combinations supported by both case and antibody data (all points above the blue line in B). The red line denotes the median value of herd immunity (the proportion of the population that has recovered [R/N]) at that point in time in 100 simulations from the MLE parameter combination. The red shaded region denotes the 2.5 to 97.5% quantiles for these simulations from all parameter combinations within two log-likelihood units of the MLE with respect to serology (all parameter combinations above the blue line in B). The blue line denotes estimates of herd immunity from a recent serological survey in New York City (24). The blue shading denotes 95% CIs for those serology estimates using the methods of ref. 24.

parameters from the fitted SEPIAR model that are supported Fig. S12). Testing only symptomatic cases can result in at least by case and serology data, we generate a range of IFRs that a fourfold increase in the IFR that is calculated. Limitations in would be expected under two different testing strategies. Since testing capacity may also impact the estimated IFR. If the test- we do not model deaths from COVID-19 hospitalized patients ing capacity is limited at the start of the outbreak, the observed in our model, we estimate the proportion of hospitalizations IFR measured during the epidemic (the orange vertical line in that result in death using confirmed COVID-19 hospitalizations SI Appendix, Fig. S12) will be higher than the IFR expected if and deaths in New York City during the study period. In the all symptomatic cases were tested. Variation in individual model first testing strategy, all cases are observed; in the second one, parameters within the range supported by the case and serology all symptomatic cases but no asymptomatic ones are observed data does not result in substantial variation in the IFR calculated (red and blue shaded histograms, respectively, in SI Appendix, for each testing scenario.

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Plots of ( ) the reproductive number of symptomatic individuals ( ) and ( ) the overall reproductive number ( ), as a function of the relative Fig. 3. A R0 B R0NGM strength of presymptomatic transmission (bp) and the relative strength of asymptomatic transmission (ba). Each point represents one parameter combination within two log-likelihood units of the MLE (with respect to serology) from the ba proﬁle. (C) Plot of the overall reproductive number vs. the reproductive number in symptomatic individuals for the same points colored by ba. The black arrows show the direction of increasing strength of asymptomatic transmission (ba) and presymptomatic transmission (bp). For this same plot, except colored by the strength of presymptomatic transmission (bp), see SI Appendix, Fig. S6. For ease of plotting, we exclude two parameter combinations which had very low relative rates of presymptomatic transmission (i.e., bp was lower than 0.020). The two outlier combinations had high reproductive numbers ( = 17.77, = 3.95 and = 4.97, = 4.37). These outliers are included in R0 R0NGM R0 R0NGM SI Appendix, Fig. S7.

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POPULATION BIOLOGY If asymptomatic individuals are unlikely to transmit and tested. The statistical model assumes that, in every year, only a do so with low probability, then the small fraction of cases fraction of influenza cases are confirmed and that noninfluenza that are symptomatic are transmitting at a high rate, in line respiratory cases exhibit seasonality. We use flu and syndrome with recently reported “superspreading” events (47, 48). Super- surveillance estimates from previous years to estimate the frac- spreading events are instances in which a single infected indi- tion of influenza cases that are not confirmed and the shape vidual infects a large number of people. These events can be of the seasonality on non–influenza-related respiratory illness. hard to measure on a population level in the absence of detailed During the 2020 epidemic, COVID-19 mitigation measures that transmission data. In classic superspreading dynamics, most pri- reduced urban mobility may have also reduced transmission of mary cases do not result in many secondary cases, while a subset other respiratory diseases such as influenza. The model captures of primary cases result in a large number of secondary cases some of this decrease, since the number of severe non-COVID (8, 49, 50). This heterogeneity in the reproductive number is, respiratory cases is a function of the number of confirmed flu indeed, what we observe when asymptomatic individuals trans- cases in the same season. The model thus captures the impact mit poorly. Our model is admittedly a coarse description of this of decreased flu cases in 2020 due to changes in mobility pat- heterogeneity, since it incorporates only two different classes terns. This framework could be used in conjunction with other of infections, symptomatic or asymptomatic. Future models can epidemiological models, and extended to other municipalities build upon this framework with additional classes for age, socioe- or countries with location-specific testing priorities, retesting conomic status, location, or susceptibility (51), using fine-scale procedures, or diagnostic tests. case data. These models could elucidate how infections in hospi- In cities where mobility information is available, the statisti- tals or home care settings may be contributing to the high R0 of cal model may include overall population mobility as a covariate. symptomatic cases. However, our results also indicate that, even In other cities that report the daily number of hospitalized indi- when the symptomatic reproductive number is large, presymp- viduals with COVID-19 symptoms who were tested each day, tomatic and asymptomatic infections contribute together to at one could subtract from this number the total COVID-19 hos- least 50% of the overall force of infection. pitalizations estimated by the epidemiological model, to obtain It follows that community-wide interventions that account the number of non–COVID-19–positive hospitalized cases that for nonsymptomatic cases should be crucial for mitigating out- were tested. Depending on the information available for each breaks. If asymptomatic cases transmit poorly, then concurrent location, future iterations of this framework could explicitly additional interventions targeting superspreading symptomatic incorporate different diagnostic tests and their respective sen- infections may help reduce community transmission. sitivities and specificities. It could also be used to examine how Resolving the nonidentifiability of the relative strength of altering testing strategies such as switching from symptom-based asymptomatic transmission (ba) would require extensive com- testing to community testing may improve transmission param- munity testing and contact tracing of asymptomatic cases. Com- eter inference and efficacy of control efforts. This may be an munity testing on its own can provide an estimate of the total important consideration for countries that have limited testing proportion of cases that are asymptomatic, but it may not provide capacity but are still in the midst of the first pandemic wave, insight on whether those asymptomatic individuals can transmit such as India. and how well they can transmit. Symptomatic and asymptomatic Given the potential role of population density and socioeco- individuals have similar viral loads (52), but a high viral load nomic status on contact rates and access to care, there may be does not necessarily imply high transmissibility. One limitation considerable heterogeneity in infection rates and seropositivity of early contact tracing studies is that estimates of transmissibility in different neighborhoods of New York City. While overdis- may oversample symptomatic index cases and contacts, particu- persion in measurement error can implicitly account for this larly during the early phase of an epidemic (15, 53). In certain variation in our implementation, future formulations could do studies, only symptomatic contacts are further investigated. Ide- so explicitly with a spatial model of transmission between neigh- ally, one would use frequent systematic community testing for borhoods and within specific settings such as hospitals and home studies identifying both symptomatic and asymptomatic poten- care networks. This level of resolution would require, how- tial index cases for further contact tracing and testing of all ever, observed cases, testing capacity, and hospitalizations within contacts regardless of symptoms. Furthermore, fixing the proba- each unit. Incorporating human movement estimates into the bility that an infection becomes symptomatic based on the results model could enable analysis of how the infectious period of of serology-informed models such as ours could increase the the virus may impact the clustering of cases within particular precision with which contact tracing studies can estimate the neighborhoods. strength of asymptomatic transmission. Colleges that are cur- Future studies can investigate the impact of including a test- rently reopening may be ideal test locations for this kind of ing submodel on parameter estimation and the level of detail combined approach, which may also help detect superspreading required in such a submodel. For example, one could compare events. the results of parameter estimation from fitting a given epidemi- While it cannot capture all testing intricacies, our frame- ological model with a queue-based testing model to those that work illustrates how transmission models can incorporate daily assume a fixed reporting rate and a delay in the reporting of changes in testing capacity and identify parameters that were cases. We expect the former to exhibit more uncertainty when previously difficult to estimate, such as the probability that an informed by surveillance data from the beginning of the pan- infection will become symptomatic. While we do not explicitly demic, when little testing capacity is available, but to reduce denote differences between laboratories, hospitals, or diagnos- this uncertainty as the time series is extended and this capacity tic tests, we account for this variation by including additional changes. Models that assume a fixed reporting rate may under- measurement noise after simulating the RT-PCR testing process. estimate the range in uncertainty of epidemiological parameters We also consider how sampling individuals without COVID-19 that are heavily informed by the early part of the time series, may deplete the daily testing capacity. In particular, hospital- and may even underestimate the values of the parameters them- ized individuals with non–COVID-19–related severe respiratory selves. Models with a queue-based testing submodel may obtain disease may have a higher priority for testing than nonsevere more-precise estimates of parameters that impact the end of COVID-19 cases. Our model uses syndrome surveillance reports the outbreak, such as those related to the depletion of suscep- (54–57) of respiratory illness from New York City hospitals in tible individuals, acquisition of immunity, or, in our model, the previous years, along with weekly influenza cases, to estimate the impact of social distancing and stay-at-home orders on overall number of non–COVID-19 severe respiratory cases that were transmission. Even if including some form of testing model that

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POPULATION BIOLOGY Assumptions about which infected classes are infectious and how they New York City. In the Mount Sinai study, random, deidentified, and cross- contribute to the transmission rate allow us to reduce the SEPIAR model to sectional samples were obtained over the course of the outbreak from the SEPIR or SEIAR models. Presymptomatic individuals transmit for an aver- patients at obstetrics and gynecology visits and deliveries and oncology- age of about a day [0.92 d (25)] at a transmission rate equal to the baseline related visits, as well as hospitalizations due elected or planned surgeries, transmission rate β(t) multiplied by a scaling factor b = bp. Asymptomatic transplant surgeries, preoperative medical assessments, and related outpa- infections transmit for an average of 5 d, equal to the average duration tient visits, cardiology office visits, or other regular office or treatment visits between the onset of symptoms and hospitalization in severe cases, at whose purpose was unrelated to COVID-19 (24). The assay used to mea- a transmission rate equal to the baseline rate β(t) multiplied by scaling sure seroprevalence (24) elicits neutralizing antibodies (58) and can detect factor ba. seroconversion in severe, mild, and asymptomatic cases (58). We treat the The models are implemented numerically via an Euler approximation of seroprevalence measurement at each time point as a measure of short-term the deterministic equations to which demographic stochasticity is added. herd immunity in the population, specifically, of the proportion of the popu- Specifically, the number of individuals making state transitions from com- lation that has already recovered from COVID-19 infection. We assume that partments with more than one exit is drawn from an Euler-multinomial this herd immunity does not decay over the course of the study, since anti- distribution (74). The number of individuals making state transitions from bodies have been shown to persist for at least 5 mo (59). We compare the compartments with only one exit is drawn from a binomial distribution. seroprevalence at each time point from the serology data to the recovered fraction of the population R/N from simulated trajectories of the epidemi- Description of Testing Model. The model takes into account daily changes in ological model. When calculating the likelihood of each trajectory at each the testing capacity, using estimates of daily tests conducted in New York observation time with respect to the seroprevalence data, we assume that City from the New York State Department of Health (23), as well as the the number of people who seroconverted in the Mount Sinai study is drawn retesting of severe and nonsevere symptomatic cases prior to leaving the from a binomial distribution with p equal to the value of R/N in the sim- hospital or quarantine. We assume that there are two categories of cases— ulated trajectory at that time, and N equal to the total number of people severe (hospitalized) cases and nonsevere cases subject to different testing sampled. We sum the log-likelihoods across all observation time points and priorities (75): the initial testing of new hospitalized COVID-19 cases (high- then average over all trajectories using the logmeanexp function in the est priority), the retesting of those individuals when they leave the hospital, R package POMP (82) to obtain a log-likelihood for each parameter com- the testing of new nonsevere symptomatic COVID-19 cases, and, finally, the bination with respect to the serology data. We isolate all combinations retesting of those symptomatic cases (lowest priority). All severe COVID-19 supported by the serology data that have log-likelihoods within two units cases after March 1 are sampled when they enter the hospital and eventu- of the MLE. ally tested once enough capacity is available. We assume that symptomatic For each combination, we examine the proportion of cases that are nonsevere cases are sampled at the same time, in the course of their infec- symptomatic, pS, the reproductive number in symptomatic individuals, R0, and the overall reproductive number for the model, . We derive the tion, as severe cases. However, we assume that they are not tested if they R0NGM following expression for using the next-generation matrix (84): recover before enough testing capacity is available. During the early stages R0NGM of the epidemic, the CDC recommended test-based strategies to determine when to conclude home isolation or hospitalization (76). Accordingly, we β ∗ b β ∗ b (1 − p ) βp β(1 − p )p = p + a S + S + H S . R0NGM [1] assume that hospitalized cases are retested twice (over a 24-h period) after φU φS φS γ the average length of time in the hospital (13 d), while nonsevere cases are likewise retested twice after the end of a 14-d quarantine period. Calculation of the IFR. The IFR is frequently defined as the ratio of deaths to We also take into account the potential for non–COVID-19 severe respi- cases. Let IFR represent the IFR with respect to all cases, ratory cases to be sampled in hospitals and tested (with the same priority all as hospitalized COVID-19 cases). We use confirmed influenza cases (77) Confirmed deaths and syndrome surveillance reports of respiratory disease from emergency IFR = . [2] all All cases departments in New York City hospitals in previous years (78) to estimate the number of non–COVID-19 severe respiratory cases that may have been This is equivalent to the proportion of all cases that result in death. We can sampled (SI Appendix). We assume that the RT-PCR testing has a sensitivity estimate this quantity using the parameters from the fitted SEPIAR model. of 90% (79), that testing takes 48 h (80), and that there is an additional Recall that pS is the probability that a case is symptomatic, and pH is the negative-binomial distributed dispersion after the RT-PCR testing with stan- probability that a symptomatic case becomes hospitalized. These quantities dard deviation σM. This dispersion takes into account variation in sampling are equivalent to the proportion of all cases that are symptomatic, and the and testing protocols across laboratories and hospitals, as well as variation proportion of symptomatic cases that are hospitalized. Let pF represent the in the sensitivity and time required for different PCR assays. proportion of all hospitalizations that are fatal. Since this parameter is not fitted in the SEPIAR model, we estimate it from observed data by divid- Overview of the Model Fitting and Inference Strategy. Unless otherwise ing the total number of confirmed COVID-19 deaths by the total number mentioned, we fit the following parameters: the recovery rate for non- of confirmed COVID-19 hospitalizations in New York City during the study severe symptomatic infections (γ); the scaling factors for asymptomatic, period. We use data updated on June 15, 2020 from the New York City presymptomatic, and postintervention transmission (ba, bp, and bq); the Health Department COVID-19 Data Portal (22), and obtain an estimate of symptomatic probability (pS) and the hospitalization probability (pH); the pF = 0.33. We can then write an expression for IFRall using the parameters reproductive number for symptomatic cases (R0); the dispersion parameter estimated with the fitted SEPIAR model, for RT-PCR testing (σM); and the initial number of infected (I0) and exposed (E0) individuals at the start of the simulation on March 1, 2020. We use IFRall = pSpHpF, [3] the iterated filtering algorithm MIF (81) within the R-package POMP (for partially observed Markov process models) to fit parameter combinations and obtain this quantity for each parameter combination supported by case by likelihood maximization. The iterated filtering algorithm is specifically and serology data (red histogram in SI Appendix, Fig. S12). designed for fitting stochastic and nonlinear models with hidden variables Let IFRsymp represent the IFR that would be estimated if all symptomatic in the presence of both process and measurement error. We apply the cases were observed but no asymptomatic ones were observed. This is sequential Monte Carlo algorithm pfilter (82) to evaluate the likelihood of equivalent to the proportion of all symptomatic cases that result in death, the final parameter combinations obtained with the computational search. Likelihoods are estimated by simulating state variables at each observa- Confirmed deaths IFRsymp = = pHpF [4] tion time from an underlying Markov process model, and then calculating All symptomatic cases the likelihood of each observation given the simulated value of the state variable and a measurement model. For the analysis of the full SEPIAR (shown in the blue histogram of SI Appendix, Fig. S12). model, we generate a Monte Carlo profile (83) for the relative strength of We compare these two quantities with the observed IFR, calculated by asymptomatic transmission (ba). dividing the total deaths by the total number of PCR-confirmed COVID cases For all resulting parameter combinations within two log-likelihood units in New York City during the study period (the orange line in SI Appendix, of the maximum-likelihood estimates (MLE), we then calculate the likeli- Fig. S12). hood with respect to serology, using seroprevalence data previously published by ref. 24 from a screening group representative of the general Additional Details. Further details of the SEPIAR equations, testing model, population, using plasma samples from patients at Mount Sinai Hospital in Monte Carlo profile of the SEPIAR model, initial grid searches, and model

8 of 10 | PNAS Subramanian et al. https://doi.org/10.1073/pnas.2019716118 Quantifying asymptomatic infection and transmission of COVID-19 in New York City using observed cases, serology, and testing capacity Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 7 .T Davis T. J. 27. coronavirus novel of interval Serial Akhmetzhanov, R. A. Linton, M. N. Nishiura, H. 25. Nishiura H. pro- 18. asymptomatic the Estimating Chowell, G. Zarebski, A. Kagaya, K. Mizumoto, K. 17. 6 .Gatto M. 26. Stadlbauer D. 24. testing. COVID-19 statewide State York New Health, https:// of Data. Department COVID-19: State Hygiene, NewYork Mental 23. and Health of Department City York New 22. on measures intervention of effects Estimating Pfeiffer, U. D. Wu, L. Yuan, Y. H. L, J. 21. Xie 9 Q. in infections 20. SARS-CoV-2 asymptomatic of proportion High Goh, Y. Y. Feaster, M. 19. Byambasuren O. 16. Poletti P. 15. scenarios. planning pandemic COVID-19 Prevention, and Control Disease for Centers 14. 3 .Ganyani T. 13. Cowling J. B. 12. Rockl J. Wilder-Smith, A. Gayle, A. A. Liu, Y. 11. 0 .Zhang J. 10. uniyn smtmtcifcinadtasiso fCVD1 nNwYr iyuigobserved using City York capacity New testing in and COVID-19 serology, of cases, transmission and infection asymptomatic Quantifying al. et Subramanian https://github.com/pascualgroup/COVID at Github in deposited been has Availability. Data NYC overall the of derivation and models, SEIAR and number reproductive SEPIR the of comparison .A oa,D .Ree,E .CrooOea .T cifr .T ae,Wrong Mayer, T. B. Li Schiffer, R. T. 9. J. Cardozo-Ojeda, F. E. Reeves, B. D. Goyal, A. 8. Lourenco J. 7. Moghadas M. S. 6. Sanche S. 5. in coronavirus novel a of assessment SARS-CoV- transmissibility Early Mandl, for D. K. testing Majumder, M. of 4. Overview Prevention, and Control Disease in for COVID-19 track Centers to the dashboard 3. just web-based interactive than An Gardner, infections—More L. Du, Coronavirus H. Fauci, Dong, E. S. A. 2. Marston, D. H. Paules, I. C. 1. rpi hs fteCVD1 admci h S.mdxv[rpit (2020). [Preprint] medRxiv USA. the in pandemic 2020). July COVID-19 6 (Accessed the https://doi.org/10.1101/2020.07.06.20140285 of phase cryptic (2020). measures. containment emergency infections. (COVID-19) City. York (COVID-19). infections Princess Diamond the 2020. board Japan, on Yokohama, cases ship, (COVID-19) cruise 2019 disease coronavirus of portion meta-analysis. Microbiol. and Med. review Assoc. Systematic J. transmission: community 802 for potential 5e cesd7Ags 2020. August 7 Accessed u53e. https://health.data.ny.gov/Health/New-York-State-Statewide-COVID-19-Testing/xdss- 2020. August 7 Accessed www1.nyc.gov/site/doh/covid/covid-19-data.page. capabilities 2020). March diagnostic https://doi.org/10.1101/2020. 31 (2020). improving (Accessed [Preprint] 03.31.20049387 of medRxiv approach. account modelling taking a using Wuhan in outbreak COVID-19 medRxiv model. March numerical 15 novel (Accessed a 2020). with https://doi.org/10.1101/2020.03.15.20036624 study (2020). empirical [Preprint] An pandemic: COVID-19 2020. (2020). April 2416–2419 USA, California, Pasadena, facilities, care long-term June 23 (Accessed https://arxiv.org/abs/2006.08471 2020). (2020). [Preprint] arXiv infection. 2020. August 5 Accessed https://www.cdc.gov/coronavirus/2019-ncov/hcp/planning-scenarios.html. 2020. March data, onset (2020). symptom on based (COVID-19) ooaiu ies 09adiflez nHn og nosrainlstudy. observational An Kong: Health Hong Pub. in influenza and 2019 disease coronavirus coronavirus. SARS to compared higher is study. modelling and descriptive A China: Dis. Province, Infect. Hubei outside predict 2019 ease structure network contact (SARS-CoV-2). coronavirus (2020). novel and [Preprint] load medRxiv 2020). events. August Viral 7 super-spreading (Accessed https://doi.org/10.1101/2020.08.07.20169920. time: and transmission and SARS-VoV-2 place person, SARS-CoV- the of stage https://doi.org/10.1101/2020.03.24.20042291 2020). the March (2020). 26 assess [Preprint] (Accessed to medRxiv surveys epidemic. serological 2 large-scale for need diate outbreaks. COVID-19 (2020). of trol 2. coronavirus syndrome 2020). (Accessed 26, https://doi.org/10.2139/ssrn.3524675 January (2020). [Preprint] SSRN China. Wuhan, 2020. August 7 Accessed https://www.cdc.gov/coronavirus/2019-ncov/hcp/testing-overview.html. (COVID-19). 2 time. real cold. common Epi usata nouetdifcinfclttsterpddseiainof dissemination rapid the facilitates infection undocumented Substantial al., et feto ag-cl etn ltomi rvninadcnrlo the of control and prevention in platform testing large-scale of Effect al., et (85). Model vligeieilg n rnmsindnmc fcrnvrsdis- coronavirus of dynamics transmission and epidemiology Evolving al., et pedaddnmc fteCVD1 pdmci tl:Efcsof Effects Italy: in epidemic COVID-19 the of dynamics and Spread al., et actIfc.Dis. Infect. 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Infect. J. Int. Dis. Infect. J. Int. 0 NGM mr.Ifc.Ds J. Dis. Infect. Emerg. 803 3–3 (2020). 533–534 20, r rvddin provided are , net i.Can. Dis. Infect. Science rc al cd c.U.S.A. Sci. Acad. Natl. Proc. uoSurveill. Euro rc al cd c.U.S.A. Sci. Acad. Natl. Proc. 8–8 (2020). 284–286 93, (2020). 154–155 94, 8–9 (2020). 489–493 368, .Ta.Med. Trav. J. v h erdcienme fCOVID-19 of number reproductive The ov, ¨ 2–3 (2020). 223–234 5, 40(2020). 1470 26, IAppendix SI 008 (2020). 2000180 25, aa2 (2020). taaa021 27, uoSurveill. Euro mr.Ifc.Dis. Infect. Emerg. . 17513–17515 117, 10484–10491 117, 2000257 25, Lancet Lancet Off. 26, 5 D OI ResponseTeam COVID CDC networks surveillance 55. influenza Using Washburne, D. A. Hupert, N. Silverman, D. J. 54. Park J. Y. 53. Lee S. 52. and Superspreading Getz, Gomes M. W. M. Kopp, G. M. E. P. 51. Schreiber, J. S. Lloyd-Smith, superspreading. of O. Dimensions J. May, M. 50. R. Galvani, P. A. 49. and Adam heterogeneity D. transmission 48. Evaluating Zhou, X. Li, M. Wang, L. Li, Y. Zhang, Y. 47. Flaxman S. 2019 46. Wuhan of transmission human-to-human early of Pattern Althaus, L. C. Riou, J. 45. Kucharski J. A. 44. to guide A Adam, D. 37. Fox J. S. 36. Gostic M. K. 35. mortality and Hospitalization Richardson S. Seoane, 34. L. Fort, D. Burton, J. Price-Haywood, COVID- with G. patients E. in death 33. to pathways Understanding Taccone, S. F. Vincent, L. J. 32. outbreak COVID-19 the for utilization care Critical Cecconi, M. Pesenti, A. Grasselli, G. 31. for Ferguson positive N. test 30. Wuhan from evacuees Japanese Three Agency, News Reuters 29. Nishiura H. 28. 6 .M ilr .Soeig .Mn .M hds ydoi uvilnefrinfluenza for surveillance Gehret Syndromic M. P. Rhodes, M. 57. S. Min, A. Stoneking, L. Hiller, M. K. 56. Pan A. 43. coronavirus Novel Wu Jewell, T. J. P. C. 42. Ho, A. Cummings, A. D. Bridgen, R. J. Read, M. J. 41. for Imai metric N. key a 40. it’s why and virus COVID-19 the for R-naught is What Schumaker, E. 39. fears. coronavirus sparking number simple deceptively The Yong, E. 38. upr rvddb h nvriyo hcg’ eerhComputing Research Chicago’s and of resources for University with King completed the Aaron advance was thank by Center. to work We provided This nexus). science support discussions. environment data insightful energy his the Computational at NRT-INFEWS: research (1735359: ship ACKNOWLEDGMENTS. nLmad,Iay al xeineadfrcs uiga mrec response. emergency an during forecast and experience Early JAMA Italy: Lombardy, in 2020). London, College Imperial 9, (Rep. demand” healthcare and mortality COVID19 August 2020. 23 Accessed 30/japanese-evacuees-from-wuhan-test-positive-for-virus.html. symptoms. no had two virus, flights. evacuation on data passengers Med. Japanese using Estimation infection: h ntdSae,JnayFbur 2020. January-February States, United the States. United the in SARS-CoV-2 of Med. prevalence state-specific estimate to 2020. in (2020). center treatment Korea. community of [Preprint] a Republic in the infection medRxiv SARS-CoV-2 with patients threshold, symptomatic immunity 2020). herd April 27 (Accessed the https://doi.org/10.1101/2020.04.27.20081893 lowers emergence. SARS-CoV-2 disease on variation individual (2005). of effect the Kong. Hong China. of metropolis Health a in COVID-19 of event super-spreading Europe. in COVID-19 2020. January to 2019 (2020). 2000058 December (2019-nCoV), coronavirus novel study. modelling mathematical 2020). June 23 https://doi.org/10.1101/2020.06.22.20137489 (Accessed (2020). [Preprint] medRxiv waves. demic Rt. number, area. City York (2020). New 2059 the in COVID-19 with hospitalized patients 5700 COVID-19. with patients white and (2020). 2534–2543 patients black among 19. e ok e ok USA. York, New York, New review. systematic department—A emergency the in (2020). China. Wuhan, in outbreak COVID-19 China. Wuhan, in 28 2020). (Accessed January https://doi.org/10.1101/2020.01.23.20018549 (2020). [Preprint] predictions. epidemic medRxiv and parameters epidemiological of estimation Early 2019-nCoV: 2020. August 23 Accessed 19-virus-key-metric-opening-plans/story?id=7086899. plans. re-opening 2020. August 23 Accessed will-new-coronavirus-spread/605632/. https://www.theatlantic.com/science/archive/2020/01/how-fast-and-far- 2020. January (2020). actRsi.Med. Respir. Lancet ac16(2020). eabc1126 12, (2020). 419 9, mr.Ifc.Ds J. Dis. Infect. Emerg. 5514 (2020). 1545–1546 323, tal. et soito fpbi elhitretoswt h pdmooyo the of epidemiology the with interventions health public of Association al., et 75(2020). 3705 17, Tasisblt f21-CV Rp ,Ipra olg odn 2020). London, College Imperial 3, (Rep. 2019-nCoV” of “Transmissibility al. , et siaigciia eeiyo OI-9fo h rnmsindynamics transmission the from COVID-19 of severity clinical Estimating al., et h mato smtmtcCVD1 netoso uuepan- future on infections COVID-19 asymptomatic of impact The al., et lseigadsprpedn oeta fSR-o- netosin infections SARS-CoV-2 of potential superspreading and Clustering al., et otc rcn uigcrnvrsdsaeotra,SuhKorea, South outbreak, disease coronavirus during tracing Contact al., et lnclcus n oeua ia hdigaogaypoai and asymptomatic among shedding viral molecular and course Clinical , h aeo neacraneto oe ooaiu (2019-nCoV) coronavirus novel of underascertainment of rate The al., et siaigteefcso o-hraetclitretoson interventions non-pharmaceutical of effects the Estimating al., et LSCmu.Biol. Comput. PLoS a.Med. Nat. rcia osdrtosfrmauigteefciereproductive effective the measuring for considerations Practical al., et ydoi uvilnedrn admc(11 09outbreak, 2009 (H1N1) pandemic during surveillance Syndromic al., et Ipc fnnpamcuia nevnin NI)t reduce to (NPIS) interventions non-pharmaceutical of “Impact al., et tal. et al yaiso rnmsinadcnrlo OI-9 A COVID-19: of control and transmission of dynamics Early al., et a.Med. Nat. 6My22.https://abcnews.go.com/Health/r0-covid- 2020. May 26 News, ABC niiulvraini ucpiiiyo xoueto exposure or susceptibility in variation Individual al., et rsnigcaatrsis oobdte,adotoe among outcomes and comorbidities, characteristics, Presenting , Nature Tepnei’ iudrto metric. misunderstood pandemic’s R—The AAItr.Med. Intern. JAMA 7411 (2020). 1714–1719 26, 3–3 (2020). 430–432 8, ..wsspotdb nNFRsac Trainee- Research NSF an by supported was R.S. 4526 (2020). 2465–2468 26, vdnefrlmtderysra fCVD1 within COVID-19 of spread early limited for Evidence al., et mr.Ifc.Ds J. Dis. Infect. Emerg. 0–1 (2020). 506–510 26, 5–6 (2020). 257–261 584, CNBC actIfc.Dis. Infect. Lancet 1049(2020). e1008409 16, 0Jnay22.https://www.cnbc.com/2020/01/ 2020. January 30 , JAMA https://doi.org/10.1073/pnas.2019716118 4715 (2020). 1447–1452 180, 9512 (2020). 1915–1923 323, ob otl kyRep. Wkly Mortal. Morb. 74(2011). 1724 17, 5–5 (2020). 553–558 20, lSOne PloS Nature n.J nio.Rs Publ. Res. Environ. J. Int. .Eg.J Med. J. Engl. N. 782(2013). e73832 8, Nature 9–9 (2005). 293–295 438, Nature PNAS uoSurveill. Euro JAMA h Atlantic The 355–359 438, 346–348 583, 680–684 69, c.Transl. Sci. 2052– 323, | f10 of 9 .Clin. J. 382, 28 , 25,

POPULATION BIOLOGY 58. F. Amanat et al., A serological assay to detect SARS-CoV-2 seroconversion in humans. 73. US Census Bureau, Quickfacts New York City, New York. https://www.census. Nat. Med. 26, 1033–1036 (2020). gov/quickfacts/fact/table/newyorkcitynewyork/POP010210#POP010210. Accessed 29 59. A. Wajnberg et al., Robust neutralizing antibodies to SARS-CoV-2 infection persist for August 2020. months. Science 370, 1227–1230 (2020). 74. D. He, E. L. Ionides, A. A. King, Plug-and-play inference for disease dynamics: Measles 60. F. Krammer, V. Simon, Serology assays to manage COVID-19. Science 368, 1060–1061 in large and small populations as a case study. J. R. Soc. Interface 7, 271–283 (2020). (2010). 61. A. Grifoni et al., Targets of T cell responses to SARS-CoV-2 coronavirus in humans with 75. US Public Health Service, Priorities for testing patients with suspected COVID-19 infec- COVID-19 disease and unexposed individuals. Cell 181, 1489–1501 (2020). tion. https://www.fsmb.org/siteassets/advocacy/pdf/hhs-covid-19-testing-guidance. 62. Q. Zhang et al., Inborn errors of type I IFN immunity in patients with life-threatening pdf. Accessed 29 August 2020. COVID-19. Science 370, eabd4570 (2020). 76. Centers for Disease Control and Prevention, Discontinuation of isolation for persons 63. P. Bastard et al., Autoantibodies against type I IFNs in patients with life-threatening with COVID-19 not in healthcare settings. https://www.cdc.gov/coronavirus/2019- COVID-19. Science 370, eabd4585 (2020). ncov/hcp/disposition-in-home-patients.html#previous-updates. Accessed 29 August 64. H. Ward et al., Declining prevalence of antibody positivity to SARS-CoV-2: A commu- 2020. nity study of 365,000 adults. medRxiv [Preprint] (2020). https://doi.org/10.1101/2020. 77. New York State Department of Health, Influenza laboratory-confirmed cases by 10.26.20219725 (Accessed 27 October 2020). county: Beginning 2009-10 season. https://health.data.ny.gov/Health/Influenza- 65. J. Zuo et al., Robust SARS-CoV-2-specific T-cell immunity is maintained at 6 months Laboratory-Confirmed-Cases-By-County-Beg/jr8b-6gh6. Accessed 29 August following primary infection. bioRxiv [Preprint] (2020). https://doi.org/10.1101/2020. 2020. 11.01.362319 (Accessed 2 November 2020). 78. City of New York, Department of Health, Syndromic surveillance data. https:// 66. J. R. Fauver et al., Coast-to-coast spread of SARS-CoV-2 during the early epidemic in a816-health.nyc.gov/hdi/epiquery/visualizations?PageType=ps&PopulationSource= the United States. Cell 181, 990–996.e5 (2020). Syndromic. Accessed 29 August 2020. 67. R. M. Anderson, B. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics 79. US Food and Drug Administration, In vitro diagnostics EUAs: Individual EUAs for and Control (Oxford University Press, 1992). molecular diagnostic tests for SARS-CoV-2. https://www.fda.gov/medical-devices/ 68. H. Y. Yuan et al., The importance of the timing of quarantine measures before coronavirus-disease-2019-covid-19-emergency-use-authorizations-medical-devices/ symptom onset to prevent COVID-19 outbreaks—Illustrated by Hong Kong’s interven- vitro-diagnostics-euas#individual-molecular. Accessed 1 September 2020. tion model. medRxiv [Preprint] (2020). https://doi.org/10.1101/2020.05.03.20089482 80. J. Appleby, Why it takes so long to get most COVID-19 test results. NPR, 28 (Accessed 6 May 2020). March 2020. https://www.npr.org/sections/health-shots/2020/03/28/822869504/why-it- 69. S. A. Lauer et al., The incubation period of coronavirus disease 2019 (COVID-19) from takes-so-long-to-get-most-covid-19-test-results. Accessed 1 September 2020. publicly reported confirmed cases: Estimation and application. Ann. Intern. Med. 172, 81. E. L. Ionides, D. Nguyen, Y. Atchade,´ S. Stoev, A. A. King, Inference for dynamic and 577–582 (2020). latent variable models via iterated, perturbed Bayes maps. Proc. Natl. Acad. Sci. U.S.A. 70. City of New York, Office of the Mayor, Statement from Mayor de Blasio on 112, 719–724 (2015). bars, restaurants, and entertainment venues. https://www1.nyc.gov/office-of-the- 82. A. A. King, D. Nguyen, E. L. Ionides, Statistical inference for partially observed Markov mayor/news/152-20/statement-mayor-de-blasio-bars-restaurants-entertainment- processes via the R package POMP. J. Stat. Software 69, 43 (2016). venues. Accessed 29 August 2020. 83. E. L. Ionides, C. Breto, J. Park, R. A. Smith, A. A. King, Monte Carlo profile confidence 71. City of New York, Office of the Mayor, Emergency Executive Order No. 100. intervals for dynamic systems. J. R. Soc. Interface 14, 20170126 (2017). https://www1.nyc.gov/assets/home/downloads/pdf/executive-orders/2020/eeo-100. 84. O. Diekmann, J. A. P. Heesterbeek, M. G. Roberts, The construction of next- pdf. Accessed 29 August 2020. generation matrices for compartmental epidemic models. J. R. Soc. Interface 7, 72. Press Office, Governor of New York, Governor Cuomo signs the ‘New York state 873–885 (2010). on pause’ executive order. https://www.governor.ny.gov/news/governor-cuomo-signs- 85. R. Subramanian et al., COVID NYC Epi Model. Github. https://github.com/ new-york-state-pause-executive-order. Accessed 29 August 2020. pascualgroup/COVID NYC Epi Model. Deposited 3 February 2021.

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