key: cord-0900700-io7gfzc6
authors: Belloir, A.; Blanquart, F.
title: Estimating the global reduction in transmission and rise in detection capacity of the novel coronavirus SARS-CoV-2 in early 2020
date: 2020-09-11
journal: nan
DOI: 10.1101/2020.09.10.20192120
sha: 45cda1f18b989f49f7448716f7fa94c7a280cba5
doc_id: 900700
cord_uid: io7gfzc6

To better control the SARS-CoV-2 pandemic, it is essential to quantify the impact of control measures and the fraction of infected individuals that are detected. To this end we developed a deterministic transmission model based on the renewal equation and fitted the model to daily case and death data in the first few months of 2020 in 79 countries and states, representing more than 4 billions individuals. Based on a region-specific infected fatality ratio, we inferred the time-varying probability of case detection and the time-varying decline in transmissiblity. The model was validated by the good correlation between the predicted total number of infected and that found in serosurveys; and most importantly by the strong correlation between the inferred probability of detection and the number of daily tests per inhabitant, with 50% detection achieved with 0.003 daily tests per inhabitants. Most of the decline in transmission was explained by the reductions in transmissibility (social distancing), which avoided 107 deaths in the regions studied over the first four months of 2020. In contrast, symptom-based testing and isolation was not an efficient way to control the spread of the disease, as a large part of transmission happens before symptoms and only a small fraction of infected individuals was typically detected. We developed a phenomenological model to link the number of daily tests with the probability of detection and verified the prediction that increasing test capacity increases the probability of detection less than proportionally. Together these results suggest that little control can be achieved by symptom-based testing and isolation alone.

The coronavirus SARS-CoV-2 originated in November-December 2019 (1), appeared as a 31 cluster of cases of pneumonia of unknown etiology in the Wuhan province in China in 32

December 2019-January 2020, and subsequently spread in Asia, Europe, North America, and 33 the rest of the world in 2020. The rapid doubling time associated with the basic reproductive 34 number R0 at 2-3 (2-4), together with the fact that an estimated ~50% of transmission is 35 presymptomatic (5,6) make it difficult to control. A substantial proportion of infected 36 individuals need to be hospitalised: 1 to 18% with increasing age in China, 4% overall in France 37 (7-9). The infected fatality ratio (IFR) is around 1%, and much higher in the elderly (7-10). 38

By early March 2020, many regions of the world had imposed strong social distancing 39 measures to reduce transmission and contain the spread of SARS-CoV-2. These social 40 distancing measures were varied and included school closure, business closure, partial or full 41 lockdowns, stay-at-home order, the prohibition of gatherings, curfews, etc. These measures 42 resulted in the stabilisation or the inversion of the epidemic curve in many countries (11). This 43 was accompanied by an increase in the capacity to PCR-test potentially infected individuals. 44

To improve the control of the epidemic, it is necessary to understand the transmission dynamics 45 during the period of unrestricted growth in the first few months of 2020, and the impact of the 46 subsequent reduction in transmission owing to (i) the depletion of susceptible individuals , (ii) 47 the social distancing measures implemented, (iii) tests and isolation of cases. We develop a 48 dynamical epidemiological model that describes the transmission dynamics with a discrete-49 time renewal equation. Thanks to published estimates of the IFR, our model predicts the daily 50 number of all cases and the fraction of detected cases, and the daily number of deaths over the 51 course of the epidemic and can thus be readily fit to data from 79 countries, states and 52 provinces. Within each of these regions, we infer the time-varying probability of detection; the 53 time-varying transmissibility; and we deduce the impact of detection and case isolation on 54 transmission dynamics. The model is validated by the strong correlation between the predicted 55 attack rate and that found in serological surveys. Finally, we show that the capacity to detect 56 SARS-CoV-2 infections is strongly related to the number of tests performed per inhabitant, 57 develop a novel model that relate the number of tests to the probability of detection and verify 58 the model predictions. These results will serve to better understand and control transmission 59 dynamics. 60 lockdown (9 regions: British Columbia, Canada, Chile, Dominican Republic, Egypt, Iran, 126

Ontario, Sweden, Turkey); (ii) a smooth sigmoid reduction in transmissibility. When 127 comparing the fit of the two models with the Akaike Information Criterion (AIC), the smooth 128 reduction in transmissibility fitted that data better (an AIC difference greater than 4) in 50 129 regions out of 79. In these cases the reduction in transmissibility predated the date of the 130 strongest social distancing measure by 5 to 20 days ( Supplementary Fig. 3 ). In the 29 other 131 regions, both functional forms were similar ( Supplementary Fig. 2) . 132

In most regions, we find a strong reduction in transmissibility accompanied by an increase in 133 detection capacity. The basic reproduction number 0, decreased from 3.7 on average across 134 countries at the first date when 5 daily cases were reached, to 0.98 as of 8th of May (Fig. 2B) . 135

There is substantial variation in the inferred initial transmissibility across regions. The mean 136 probability of detection increased from 4% to 29% over the same period ( testing and case isolation. We found that the factor contributing most to reduced transmission 153 is the reduced transmissibility (Fig. 4B) . 154

The reduction in transmission owing to population immunity depends on the total number of 155 individuals ever infected (the attack rate) over the initial number of susceptible 156 individuals 0 , assumed to be the total population size of the region. The attack rate was smaller 157 than 2% in 47 regions out of 79. The reduction in the number of susceptible individuals that 158 could lead to herd immunity is thus very small in most regions, assuming that all individuals 159 are initially susceptible. The second factor is estimated from the inferred sigmoid curve for 160 0, . The third factor is estimated assuming that case detection is followed by strict isolation, 161 such that a detected case stops transmitting and the generation time is effectively truncated 162 (Fig. 4A) 

Relationship between probability of detection and intensity of testing: 203

We last relate the time-varying probability of detection to the intensity of testing. First, we 204 correlate the probability of detection (as of May 8th) with the number of tests performed by 205 inhabitants across regions. We did so for 62 regions where test data were available. There was 206 a strong correlation between probability of detection and number of tests per inhabitants 207 (regression coefficient β = 161 per daily test per inhabitant, p = 4.0e-5) (Fig. 5B) . 208

Second, to examine further how the changing number of tests affects the probability of 209 detection within a region and across time, we formulated a simple model of symptom-based 210 testing. The goal of this model is to relate within a region the number of tests conducted on a 211

given day (called ) with the inferred probability of detection on that day ( ). We assume that 212 in the period when the incidence of infections is much higher than the number of tests, the 213 decision to test individuals for SARS-CoV-2 is made on the basis of a set of symptoms. We do 214 not consider contact tracing, as during that period and in the countries examined the number of 215 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. 

The probability of detection should thus generally increase sublinearly with the number of tests 237 since > 1, and at best, should be proportional to the number of tests (when = 1). This is 238 because tests are prioritised on individuals that are more likely to be infected; as the number of 239 tests increases, the probability of positivity decreases. We also predict that in general, when 240 the number of infected is large, the probability of detection decreases with the number of 241 infected individuals (Material and Methods). 242

Both predictions were verified in data (Fig. 5) . We inferred for each region the best-fitting pair 243 of parameters ( , ) to relate the inferred probability of detection to the number of tests , 244 using both the approximated and the general model. We found that > 1 for most regions, 245 implying a sublinear relationship as predicted (Fig. 5C ). The general model where the 246 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint

Our model and inference rely on several assumptions. First of all, we describe transmission 279 dynamics within a simplified model that does not take into account age structure or household 280 structure. These forms of structure may be weak enough that they can be neglected when 281 describing the overall epidemic trajectory (20). Second, to infer jointly the time-varying 282 transmissibility and probability of detection within a dynamical model, we assumed the 283 temporal change took specific sigmoid functional forms. This differs from other approaches 284 which estimate daily transmissibility as the incidence at a given day divided by past incidence 285 weighted by the distribution of the generation time (21,22). These alternative approaches are 286 more flexible in that they can infer any pattern of time-varying transmissibility. However, they 287 cannot account exactly for the delay in case reporting, and can be very sensitive to noise in the 288 data (21). Fitting a dynamical model with imposed functional forms for transmissibility and 289 probability of detection reduces the sensitivity of inference to noise in the data. Third, and most 290 importantly, inference relies on daily deaths and cases. Deaths are assumed to be perfectly 291 reported. Cases are assumed to be partially reported with a time-varying detection probability. 292

The inferred absolute value of the probability of detection of course strongly relies on the 293 assumed IFR at around 1% on average (and tuned to the specific age structure of each region 294 considered). The approach was validated in a number of regions where systematic test or 295 seroprevalence surveys were conducted (Fig. 1) . It is possible that in some of the other regions 296 examined the number of deaths was greatly under-reported, in which case the true number of 297 infected would be much higher than predicted, and the probability of case detection much 298 smaller. However this should not affect the temporal trends in transmissibility or probability 299 of detection, provided that under-reporting is constant in time. Other emerging seroprevalence 300 surveys will give more information on the IFR (or death under-reporting) across regions, but it 301 is notable that the early estimate of IFR in mainland China (8) already allow good predictions 302 ( Fig. 1) . Lastly, our framework does not take into account the possibility that the IFR changes 303 in time. Such temporal variation in IFR could be caused by overwhelmed health systems 304 (increasing IFR) of better social distancing in at-risk groups (decreasing IFR). 305

Our method has several advantages. The discrete-time renewal equation makes the minimal 306 assumptions that the transmissibility of an infected individual depends on the age of infection. 307

It allows arbitrary distributions of the generation time, and arbitrary delays between infection 308 and case detection, and infection and death. The distributions of these delays determines the 309 dynamics of the changes in number of cases and deaths following a change in transmissibility. 310

Parameters can be inferred using multiple time series, improving the precision of inference. 311 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint

The daily cases, although dependent on the number of tests available, give an earlier signal of 312 changes in transmissibility than the daily deaths, and suffer less from stochastic effects. The 313 method allows different transmissibility for detected cases (here assumed to be zero, i.e. perfect 314 isolation after detection). This is particularly relevant for accurate inference of transmissibility, 315 as non-pharmaceutical interventions shorten the serial interval ( fig. 4A) (17) . Lastly, the 316 framework quantifies the immunity acquired by infected individuals. make it more linear. Furthermore, these contacts are isolated earlier than those identified 340 through symptom-based testing (5,26). For these two reasons, contact-tracing and testing is a 341 more efficient way to control the epidemic than symptom-based testing. Thus, if the capacity 342 to trace contacts is limited, the epidemic may be out control as soon as the daily incidence is 343 too large to trace a good fraction of contacts. This pleads for the use of digitical contact tracing 344 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint apps and/or rapid implementation of additionnal social distancing measures when incidence 345 increases. 346

Lastly, the inferred time-varying transmissibility correlated with mobility indicators (19, 27) . 347

More precisely, within a multivariate framework we found that the mobility in transit stations 348 was the most highly correlated with transmissibility, a pattern consistent in European countries 349 and the USA (Table 1) , and with a regression coefficient close to 1 (a given reduction in 350 mobility corresponds to an equivalent reduction in transmission). The mobility in transit 351 stations could be a general indicator of economic / social activity resulting in more 352 transmission. Public transports could also be a common context of transmission. In support of 353 our finding, individual use of public transport in Maryland was strongly associated with SARS-354

CoV-2 positivity (28). 355

In conclusion, we developed a framework to estimate time-varying transmissibility and 356 probability of detection from daily cases and deaths in a large number of countries and regions. 357

In the first few months of 2020, control of the epidemic was achieved mostly by reductions in 358 transmissibility, which avoided 10 millions deaths in these 79 regions (representing more than 359 half of the world's population), while case detection and isolation comparatively had a much 360 smaller effect. 361 362 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. 

And the number of detected individuals who were infected days ago changes as: 391

( + 1,0) = 0 (when = 0) (3a) 392 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. .

The total number of infected individuals, be they undetected or detected, that we may call 394 ( , ) = ( , ) + ( , ), follows the equations: 395

The fact that incidence (in the first equation) only depends on undetected cases ( , ) emerges 398 from the assumption that detected individuals ( , ) do not transmit. 399

While in the absence of testing and isolation, the infectiousness profile is given by ( ) = 400 perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. Generation time 432

We assume the generation time is lognormally distributed with mean 7 days and standard 433 deviation 4.5 days (9) (Supplementary Fig. 4) . This is the generation time when the infected 434 individual is not tested. A positive test is assumed to be followed by perfect isolation of the 435 infected individual and interruption of transmission. This effectively truncates the distribution 436 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. 

The time from symptom onset to case detection was inferred from published data on 150 cases 453 from various countries (13). We used the time between the midpoint date of symptom onset 454 and the midpoint date of case detection. We excluded 31 cases for which the date of case 455 detection was not available or there was very large uncertainty on the date of symptom onset. 456

We inferred that the time from symptom onset to detection was gamma-distributed with mean 457 

The distribution of the time from infection to death was estimated using data from 41 patients 467 in Wuhan analysed elsewhere (12) . The time from symptom onset to death was gamma-468 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in (Supplementary Fig. 1) . 477

The IFR climbs from close to 0% in 0 to 39 years old, up to 5 to 10% in individuals aged 80 478 years old or more. Simulating the deterministic model gives the expected number of detected cases ( ) and 489 deaths ( ) at time t as a function of model parameters. We assume that the probability to 490 observe a certain number of cases (resp. deaths) in the data at day t is the density of a negative 491 binomial distribution with mean given by the theoretical predictions for cases (resp. deaths), 492 and dispersion parameters that we infer. The overall likelihood is the product of these 493 probabilities over all days. For the number of deaths, we include the period from the first day 494 to the last day when at least 1 death and 5 cases were recorded. For the number of cases, we 495 include the period from the first day to the last day when at least 5 cases were recorded. 496

We mainly estimate the time-changing transmissibility 0, and the time-changing probability 497 of detection . 498 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. .

For the time-changing transmissibility, we fit two functional forms. First we assume that 0, 499 is a step function with a sharp transition from a high pre-control value to a low post-control 500 value, at a fixed date corresponding to the date of implementation of the control 501 measure: 502

For the sharp change in transmissibility, we infer the two values 0, and 0, . 505

Furthermore, to investigate the possibility that transmissibility changed in a more gradual way, 506 we assume 0, is a smooth declining sigmoid function: 507

Where 0, is the basic reproductive number before social distancing measures, 0, is the 509 basic reproductive number after social distancing, is the steepness of the logistic curve, and 510 is the time when the basic reproductive number is intermediate between 0, and 0, . 511

The step function is a special case of the logistic when is large and = . For the 512 smooth change in transmissibility, we infer the two values 0, and 0, , the steepness 513 and the time . 514

For the time-changing detection probability, we assume an increasing logistic function: 515

We infer the four parameters , , and . Note that we constrain the parameter , 517 the initial probability of detection, to be small, in [0.0001, 0.001]. We fit three models: (i) a 518 model based on death data only with the step function of transmissibility, (ii) a model based 519 on death and case data with the step transmissibility function; and (iii) a model based on death 520 and case data with the smooth transmissibility function. These three models are fitted by 521 maximum likelihood. We first find an optimal likelihood value by 50 iterations of the Nelder-522

Mead algorithm starting from different initial parameters. We then run a Markov chain Monte 523 Carlo (MCMC) sampling of the likelihood function with bounded parameters (equivalent to 524 uniform priors for all parameters in a Bayesian framework). We let the chain run for 106 steps 525 and record the parameter values from 2 × 105 to 106 steps. This sample is used both for 526 maximum likelihood parameters (if a better parameter set is found than with the Nelder-Mead 527 algorithm) and for confidence intervals. 528 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. ( , ) where ( ) is the probability that an individual is detected 535 at age of infection (given that it is detected) (Fig. 5A) . 536 -Non-SARS-CoV-2 infected individuals. The number of such individuals is assumed to be 537 constant and is denoted by . We acknowledge that a more complete model would allow for 538 this number to vary in time, for example to account for seasonal infections by respiratory 539 diseases like influenza or seasonal coronavirus that may contribute to the pool of testable 540 individuals. 541

We assume that contexts in which we apply our model are characterized by a number of tests 542 smaller than the number of testable individuals, < + where is the number of tests 543 available at time t. Thus the tests are prioritised on the subset of individuals most likely to 544 be infected by SARS-CoV-2. Individuals presenting to health centers with symptoms 545 suggestive of SARS-CoV-2 are characterised by a score such that the probability of SARS-546 COV-2 infection increases with the score. Given the limited number of tests available each 547 day, a threshold score is defined and tests are performed only for patients above this score. In the absence of detailed information on the choice of individuals to test in different regions 552 at different stages of the pandemic, we further assume for simplicity that the scores are 553 distributed exponentially. We set the rate of the exponential distribution to 1 without loss 554 of generality, and we denote > 1 the rate of : 555

All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint

The fact that > 1 guarantees that the probability that an individual is positive increases with 558 the score. Plugging the distributions (13) in the implicit formula to define the threshold score 559 (12) yields: 560

The probability of detection , defined as the ratio between positive tests results and the 562 number of testable infected individuals , is the area of the distribution above the threshold 563 : 564

Replacing with equation (15) in equation (14), we find that is the solution of: 566

This generally defines an implicit function ( , ) of the number of testable infected at day 568 t, and the number of available tests . We can simplify this general solution in two ways. 569

First, in the limit when the number of infected is much smaller than the number of uninfected 570 , and γ is not too large, the probability of detection is: 571

That is, the probability of detection increases as a root function of the normalised number of 573 tests. In general, when the number of testable infected individuals is not negligible, the 574 solution of equation (16) decreases with . When the number of testable infected individuals 575 is small, the solution (17a) can be better approximated by: 576

In this approximation the probability of detection decreases linearly with the number of 578 infected . 579

We verify the model predictions using the inferred probability of detection together with 581 data on the daily number of tests , and the number of testable infected individuals inferred 582 from the dynamical model in different regions. We used the nls method from the stats package 583 in the software R (33). 584 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint First, we use the general solution of equation (16). This solution is a non-linear function 585 ( , ) with parameters and . We infer the parameters and by minimizing the mean 586 square error between the inferred and the prediction. In most cases (except, notably New 587

York and New Jersey states) the coefficient of determination was as good with the 588 simplification of the model where is approximated as a root function of only 589 (equation(17a)) ( Supplementary Fig. 8) . The general solution improved the fit all the more than 590 the the attack rate was larger, as predicted by the model (Supplementary Fig. 8 reported. Since we ignore whether negative tests are not reported or reported at a later date (as 613 sometimes suggeted by a peak in the number of reported tests a few days after), we exclude 614 these datapoints and exclude regions where this artefact is often observed. 615 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint Bibliography 632 Figure 1 : Comparison of the total number of infected (attack rate) found in systematic serological test surveys with that predicted by our model. The segments are 95% confidence intervals (for the data, binomial confidence intervals; for the model, estimated from the MCMC sample). We used the model with the smooth sigmoid reduction in transmission; the model with the sharp transition gave very similar results. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in

The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint Figure 4 : Impact of control measures and immunity on transmission dynamics. Panel A illustrates how social distancing and case isolation reduce transmission of the disease. The basic reproduction number is given by the area under the curve. A reduction in transmissibility uniformly reduces the Rt (blue curve and area), while detection and case isolation truncates the serial interval (red curve). Panel B represents the distribution of the reduction in transmission caused by social distancing (blue), detection and isolation (red) and immunity of already infected individuals (green) across the 79 regions. Panel C represents the log10 number of deaths averted by social distancing between the beginning of the epidemic and the 8th May 2020. perpetuity.

preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in

The copyright holder for this this version posted September 11, 2020. . https://doi.org/10.1101/2020.09.10.20192120 doi: medRxiv preprint Figure 5 : Relationship between probability of detection and number of tests. Panel A shows stacked distributions of the disease score for positive (red) and negative (blue) individuals. The fraction of positive individuals increases with the score. The number of tests performed is the area to the right of the threshold (vertical line). Panel B represents the final probability of detection as a function of number of daily tests per capita (over the 7 days preceding 8th May) for the 62 regions with available test data. Panel C shows the predicted root-function relationship between proportion of detected and daily tests for the 33 regions with sufficient available test data. Panel D shows the proportion of detected a function of daily tests and the number of testable infected presenting for a test, for the New York state (one of the high-prevalence states where the proportion detected declines with the number of infected as predicted at high prevalence). 

Virol Httpvirological 633 Orgtphylodynamic-Anal-176-Genomes-6

of Novel Coronavirus-Infected Pneumonia

Early 638 dynamics of transmission and control of COVID-19: a mathematical modelling study. 639 Lancet Infect Dis

Pattern of early human-to-human transmission of Wuhan

Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact 646 tracing

Pre-649 symptomatic transmission of SARS-CoV-2 infection: a secondary analysis using 650 published data. medRxiv

Estimating the 652 burden of SARS-CoV-2 in France

Estimates of the 656 severity of coronavirus disease 2019: a model-based analysis

Estimating 660 clinical severity of COVID-19 from the transmission dynamics in Wuhan, China. Nat 661 Med

663 Estimation of SARS-CoV-2 mortality during the early stages of an epidemic: a 664 modeling study in Hubei, China, and six regions in Europe. medRxiv

Estimating 667 the effects of non-pharmaceutical interventions on COVID-19 in Europe

Estimating 670 clinical severity of COVID-19 from the transmission dynamics in Wuhan, China. Nat 671 Med

The Incubation 673 Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed 674 Cases: Estimation and Application

Antibody responses 676 to SARS-CoV-2 in patients with COVID-19

Negative Rate of Reverse Transcriptase Polymerase Chain Reaction-Based SARS-679

CoV-2 Tests by Time Since Exposure

Epidemiology and transmission of 682 COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a 683 retrospective cohort study

Serial interval of SARS-CoV-2 687 was shortened over time by nonpharmaceutical interventions

State-level 691 tracking of COVID-19 in the United States

Mobility trends 694 provide a leading indicator of changes in SARS-CoV-2 transmission. medRxiv

Systematic selection between age and 697 household structure for models aimed at emerging epidemic predictions

Practical 700 considerations for measuring the effective reproductive number, Rt. medRxiv

A New Framework and Software to 703

Estimate Time-Varying Reproduction Numbers During Epidemics

706 Reconstructing the global dynamics of unreported COVID-19 cases and infections | 707 CMMID Repository

Household 710 Secondary Attack Rate of COVID-19 and Associated Determinants. medRxiv

Characteristics of Household 713 Transmission of COVID-19

Feasibility of 716 controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob 717 Health

Rapid real-time tracking of non-pharmaceutical interventions and their association with 722 SARS-CoV-2 positivity: The COVID-19 Pandemic Pulse Study

726 Comparison of molecular testing strategies for COVID-19 control: a mathematical 727 modelling study

Epidemiological parameters of 730 coronavirus disease 2019: a pooled analysis of publicly reported individual data of 1155 731 cases from seven countries. medRxiv

Estimation in emerging epidemics: biases and remedies

736 Incubation Period and Other Epidemiological Characteristics of

Coronavirus Infections with Right Truncation: A Statistical Analysis of Publicly 738 Available Case Data

Core Team. R: A Language and Environment for Statistical Computing. Vienna, 740 Austria: R Foundation for Statistical Computing

We collected data on the number of individuals in age categories 0-9, 10- 19