Acaba de sair um artigo na Science. Os autores concluem que o principal responsável pela transmissão do coronavírus é o indivíduo não documentado (assintomático). Esse grupo representa 80% do total.

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Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)

Ruiyun Li1*, Sen Pei2*†, Bin Chen3*, Yimeng Song4, Tao Zhang5, Wan Yang6, Jeffrey Shaman2†

1MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Faculty of Medicine, Imperial College London, London W2 1PG, UK. 2Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY 10032, USA. 3Department of Land, Air and Water Resources, University of California, Davis, Davis, CA 95616, USA. 4Department of Urban Planning and Design, The University of Hong Kong, Hong Kong. 5Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 10084, P. R. China. 6Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.

*These authors contributed equally to this work.

†Corresponding author. Email: (S.P.); (J.S.)

Estimation of the prevalence and contagiousness of undocumented novel coronavirus (SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV2, including the fraction of undocumented infections and their contagiousness. We estimate 86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January 2020 travel restrictions. Per person, the transmission rate of undocumented infections was 55% of documented infections ([46%–62%]), yet, due to their greater numbers, undocumented infections were the infection source for 79% of documented cases. These findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this virus will be particularly challenging.

The novel coronavirus that emerged in Wuhan, China (SARS- CoV2) at the end of 2019 quickly spread to all Chinese prov- inces and, as of 1 March 2020, to 58 other countries (1, 2). Efforts to contain the virus are ongoing; however, given the many uncertainties regarding pathogen transmissibility and virulence, the effectiveness of these efforts is unknown.

The fraction of undocumented but infectious cases is a critical epidemiological characteristic that modulates the pandemic potential of an emergent respiratory virus (3–6). These undocumented infections often experience mild, lim- ited or no symptoms and hence go unrecognized, and, de- pending on their contagiousness and numbers, can expose a far greater portion of the population to virus than would oth- erwise occur. Here, to assess the full epidemic potential of SARS-CoV2, we use a model-inference framework to estimate the contagiousness and proportion of undocumented infec- tions in China during the weeks before and after the shut- down of travel in and out of Wuhan.

We developed a mathematical model that simulates the spatiotemporal dynamics of infections among 375 Chinese cities (see supplementary materials). In the model, we di- vided infections into two classes: (i) documented infected in- dividuals with symptoms severe enough to be confirmed, i.e., observed infections; and (ii) undocumented infected individ- uals. These two classes of infection have separate rates of transmission: β, the transmission rate due to documented

infected individuals; and μβ, the transmission rate due to un- documented individuals, which is β reduced by a factor μ.

Spatial spread of SARS-CoV2 across cities is captured by the daily number of people traveling from city j to city i and a multiplicative factor. Specifically, daily numbers of travel- ers between 375 Chinese cities during the Spring Festival pe- riod (“Chunyun”) were derived from human mobility data collected by the Tencent Location-based Service during the 2018 Chunyun period (1 February–12 March 2018) (7). Chun- yun is a period of 40 days—15 days before and 25 days after the Lunar New Year—during which there are high rates of travel within China. To estimate human mobility during the 2020 Chunyun period, which began 10 January, we aligned the 2018 Tencent data based on relative timing to the Spring Festival. For example, we used mobility data from 1 February 2018 to represent human movement on 10 January 2020, as these days were similarly distant from the Lunar New Year. During the 2018 Chunyun, a total of 1.73 billion travel events were captured in the Tencent data; whereas 2.97 billion trips are reported (7). To compensate for underreporting and rec- oncile these two numbers, a travel multiplicative factor, θ, which is greater than 1, is included (see supplementary mate- rials).

To infer SARS-CoV2 transmission dynamics during the early stage of the outbreak, we simulated observations during 10–23 January 2020 (i.e., the period before the initiation of

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travel restrictions, fig. S1) using an iterated filter-ensemble adjustment Kalman filter (IF-EAKF) framework (8–10). With this combined model-inference system, we estimated the tra- jectories of four model state variables (Si, Ei, Iir , Iiu : the sus-

ceptible, exposed, documented infected, and undocumented infected sub-populations in city i) for each of the 375 cities, while simultaneously inferring six model parameters (Z, D, μ, β, α, θ: the average latent period, the average duration of in- fection, the transmission reduction factor for undocumented infections, the transmission rate for documented infections; the fraction of documented infections, and the travel multi- plicative factor).

Details of model initialization, including the initial seed- ing of exposed and undocumented infections, are provided in the supplementary materials. To account for delays in infec- tion confirmation, we also defined a time-to-event observa- tion model using a Gamma distribution (see supplementary materials). Specifically, for each new case in group Iir , a re-

porting delay td (in days) was generated from a Gamma dis- tribution with a mean value of Td. In fitting both synthetic and the observed outbreaks, we performed simulations with the model-inference system using different fixed values of Td (6 days ≤ Td ≤ 10 days) and different maximum seeding, Seedmax (1500 ≤ Seedmax ≤ 2500) (see supplementary materials, fig. S2). The best fitting model-inference posterior was iden- tified by log-likelihood.

We first tested the model-inference framework versus al- ternate model forms and using synthetic outbreaks generated by the model in free simulation. These tests verified the abil- ity of the model-inference framework to accurately estimate all six target model parameters simultaneously (see supple- mentary methods and figs. S3 to S14). Indeed, the system could identify a variety of parameter combinations and dis- tinguish outbreaks generated with high α and low μ from low α and high μ. This parameter identifiability is facilitated by the assimilation of observed case data from multiple (375) cit- ies into the model-inference system and the incorporation of human movement in the mathematical model structure (see supplementary methods and figs. S15 and S16).

We next applied the model-inference framework to the observed outbreak before the travel restrictions of 23 Janu- ary—a total of 801 documented cases throughout China, as reported by 8 February 2020 (1). Figure 1, A to C, shows sim- ulations of reported cases generated using the best-fitting model parameter estimates. The distribution of these sto- chastic simulations captures the range of observed cases well. In addition, the best-fitting model captures the spread of in- fections with the novel coronavirus (COVID-19) to other cities in China (fig. S17). Our median estimate of the effective re- productive number, Re—equivalent to the basic reproductive number (R0) at the beginning of the epidemic—is 2.38 (95%

CI: 2.04−2.77), indicating a high capacity for sustained trans- mission of COVID-19 (Table 1 and Fig. 1D). This finding aligns with other recent estimates of the reproductive number for this time period (6, 11–15). In addition, the median estimates for the latent and infectious periods are approximately 3.69 and 3.48 days, respectively. We also find that, during 10–23 January, only 14% (95% CI: 10–18%) of total infections in China were reported. This estimate reveals a very high rate of undocumented infections: 86%. This finding is inde- pendently corroborated by the infection rate among foreign nationals evacuated from Wuhan (see supplementary materi- als). These undocumented infections are estimated to have been half as contagious per individual as reported infections (μ = 0.55; 95% CI: 0.46–0.62). Other model fittings made us- ing alternate values of Td and Seedmax or different distribu- tional assumptions produced similar parameter estimates (figs. S18 to S22), as did estimations made using an alternate model structure with separate average infection periods for undocumented and documented infections (see supplemen- tary methods, table S1). Further sensitivity testing indicated that α and μ are uniquely identifiable given the model struc- ture and abundance of observations utilized (see supplemen- tary methods and Fig. 1, E and F). In particular, Fig. 1F shows that the highest log-likelihood fittings are centered in the 95% CI estimates for α and μ and drop off with distance from the best fitting solution (α= 0.14 and μ = 0.55).

Using the best-fitting model (Table 1 and Fig. 1), we esti- mated 13,118 (95% CI: 2,974–23,435) total new COVID-19 in- fections (documented and undocumented combined) during 10–23 January in Wuhan city. Further, 86.2% (95% CI: 81.5%– 89.8%) of all infections were infected from undocumented cases. Nationwide, the total number of infections during 10– 23 January was 16,829 (95% CI: 3,797–30,271) with 86.2% (95% CI: 81.6%–89.8%) infected by undocumented cases.

To further examine the impact of contagious, undocu- mented COVID-19 infections on overall transmission and re- ported case counts, we generated a set of hypothetical outbreaks using the best-fitting parameter estimates but with μ = 0, i.e., the undocumented infections are no longer conta- gious (Fig. 2). We find that without transmission from undoc- umented cases, reported infections during 10–23 January are reduced 78.8% across all of China and 66.1% in Wuhan. Fur- ther, there are fewer cities with more than 10 cumulative doc- umented cases: only 1 city with more than 10 documented cases versus the 10 observed by 23 January (Fig. 2). This find- ing indicates that contagious, undocumented infections facil- itated the geographic spread of SARS-CoV2 within China.

We also modeled the transmission of COVID-19 in China after 23 January, when greater control measures were ef- fected. These control measures included travel restrictions imposed between major cities and Wuhan; self-quarantine and contact precautions advocated by the government; and

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more available rapid testing for infection confirmation (11, 12). These measures along with changes in medical care-seek- ing behavior due to increased awareness of the virus and in- creased personal protective behavior (e.g., wearing of facemasks, social distancing, self-isolation when sick), likely altered the epidemiological characteristics of the outbreak af- ter 23 January. To quantify these differences, we re-estimated the system parameters using the model-inference framework and city-level daily cases reported between 24 January and 8 February. As inter-city mobility was restricted after 23 Janu- ary, we tested two altered travel scenarios: (i) scenario 1: a 98% reduction of travel in and out of Wuhan and an 80% reduction of travel between all other cities, as indicated by changes in the Baidu Mobility Index (16) (table S2); and (ii) scenario 2: a complete stoppage of inter-city travel (i.e., θ to 0) (see supplementary methods for more de- tails).

The results of inference for the 24 January–8 February pe- riod are presented in Table 2, figs. S23 to S26, and table S3. As control measures have continually shifted, we present es- timates for both 24 January–3 February (Period 1) and 24 January–8 February (Period 2). For both periods, the best- fitting model for Scenario 1 had a reduced reporting delay, Td, of 6 days (vs. 10 days before 23 January), consistent with more rapid confirmation of infections. Estimates of both the latency and infectious periods were similar to those made for 10–23 January; however, α, β, and Re all shifted considerably. The transmission rate of documented cases, β, dropped to 0.52 (95% CI: 0.39–0.71) during Period 1 and 0.35 (95% CI: 0.27–0.50) during Period 2, less than half the estimate prior to travel restrictions (Table 2). The fraction of all infections that were documented, α, was estimated to be 0.65 (95% CI: 0.60–0.69), i.e., 65% of infections were documented during Period 1, up from 14% prior to travel restrictions, and re- mained nearly the same for Period 2. The reproductive num- ber was 1.36 (95% CI: 1.14–1.63) during Period 1 and 0.99 (95% CI: 0.76–1.33) during Period 2, down from 2.38 prior to travel restrictions. While the estimate for the relative transmission rate, μ, is lower than before 23 January, the contagiousness of undocumented infections, represented by μβ, was substan- tially reduced, possibly reflecting that only very mild, less contagious infections remain undocumented or that individ- ual protective behavior and contact precautions have proven effective. Similar parameter estimates are derived under Sce- nario 2 (no travel at all) (table S3). These inference results for both Period 1 and 2 should be interpreted with caution as care-seeking behavior and control measures were continually in flux at these times.

Overall, our findings indicate that a large proportion of COVID-19 infections were undocumented prior to the imple- mentation of travel restrictions and other heightened control measures in China on 23 January, and that a large proportion

of the total force of infection was mediated through these un- documented infections (Table 1). This high proportion of un- documented infections, many of whom were likely not severely symptomatic, appears to have facilitated the rapid spread of the virus throughout China. Indeed, suppression of the infectiousness of these undocumented cases in model simulations reduces the total number of documented cases and the overall spread of SARS-CoV2 (Fig. 2). In addition, the best-fitting model has a reporting delay of 9 days from initial infectiousness to confirmation; in contrast line-list data for the same 10–23 January period indicates an average 6.6 day delay from initial manifestation of symptoms to confirmation (17). This discrepancy suggests pre-symptomatic shedding may be typical among documented infections. The relative timing of viremia and shedding onset and peak versus symp- tom onset and peak has been shown to potentially affect out- break control success (18).

Our findings also indicate that a radical increase in the identification and isolation of currently undocumented infec- tions would be needed to fully control SARS-CoV2. Increased news coverage and awareness of the virus in the general pop- ulation have already likely prompted increased rates of seek- ing medical care for respiratory symptoms. In addition, awareness among healthcare providers, public health offi- cials and the availability of viral identification assays suggest that capacity for identifying previously missed infections has increased. Further, general population and government re- sponse efforts have increased the use of face masks, restricted travel, delayed school reopening and isolated suspected per- sons, all of which could additionally slow the spread of SARS- CoV2.

Combined, these measures are expected to increase re- porting rates, reduce the proportion of undocumented infec- tions, and decrease the growth and spread of infection. Indeed, estimation of the epidemiological characteristics of the outbreak after 23 January in China, indicate that govern- ment control efforts and population awareness have reduced the rate of spread of the virus (i.e., lower β, μβ, Re), increased the reporting rate, and lessened the burden on already over- extended healthcare systems.

Importantly, the situation on the ground in China is changing day-to-day. New travel restrictions and control measures are being imposed on new populations in different cities, and these rapidly varying effects make certain estima- tion of the epidemiological characteristics for the outbreak difficult. Further, reporting inaccuracies and changing care- seeking behavior add another level of uncertainty to our esti- mations. While the data and findings presented here indicate that travel restrictions and control measures have reduced SARS-CoV2 transmission considerably, whether these con- trols are sufficient for reducing Re below 1 for the length of time needed to eliminate the disease locally and prevent a

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rebound outbreak once control measures are relaxed is un- clear. Further, similar control measures and travel re- strictions would have to be implemented outside China to prevent reintroduction of the virus.

The results for 10–23 January 2020 delineate the charac- teristics of the SARS-CoV2 moving through a developed soci- ety, China, without major restrictions or control. These findings provide a baseline assessment of the fraction of un- documented infections and their relative infectiousness for such an environment. However, differences in control activ- ity, viral surveillance and testing, and case definition and re- porting would likely impact rates of infection documentation. Thus, the key findings, that 86% of infections went undocu- mented and that, per person, these undocumented infections were 55% as contagious as documented infections, could shift in other countries with different control, surveillance and re- porting practices.

Our findings underscore the seriousness and pandemic potential of SARS-CoV2. The 2009 H1N1 pandemic influenza virus also caused many mild cases, quickly spread globally, and eventually became endemic. Presently, there are four, en- demic, coronavirus strains currently circulating in human populations (229E, HKU1, NL63, OC43). If the novel corona- virus follows the pattern of 2009 H1N1 pandemic influenza, it will also spread globally and become a fifth endemic coro- navirus within the human population.


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Funding: This work was supported by US NIH grants GM110748 and AI145883. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute of General Medical Sciences, the National Institute for Allergy and Infectious Diseases, or the National Institutes of Health. Author contributions: R.L., S.P., B.C., W.Y. and J.S. conceived the study. R.L., B.C., Y.S. and T.Z. curated data. S.P. performed the analysis. R.L., S.P., W.Y. and J.S. wrote the first draft of the manuscript. B.C, Y.S. and T.Z. reviewed and edited the manuscript. Competing interests: J.S. and Columbia University disclose partial ownership of SK Analytics. J.S. also reports receiving consulting fees from Merck and BNI. All other authors declare no competing interests. Data and materials availability: All code and data are available in the supplementary materials and posted online at and (19).


Materials and Methods
Figs. S1 to S26
Tables S1 to S3
References (20–37)
MDAR Reproducibility Checklist Data S1

15 February 2020; accepted 12 March 2020 Published online 16 March 2020 10.1126/science.abb3221

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Table 1. Best-fit model posterior estimates of key epidemiological parameters for simulation with the full metapopulation model during 10–23 January 2020 (Seedmax = 2000, Td = 9 days).


Transmission rate (β, days−1) Relative transmission rate (μ) Latency period (Z, days) Infectious period (D, days) Reporting rate (α)

Basic reproductive number (Re) Mobility factor (θ)

Median (95% CIs)

1.12 (1.04, 1.18) 0.55 (0.46, 0.62) 3.69 (3.28, 4.03) 3.48 (3.18, 3.74) 0.14 (0.10, 0.18) 2.38 (2.04, 2.77) 1.36 (1.28, 1.43)

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Table 2. Best-fit model posterior estimates of key epidemiological parameters for simulation of the model during 24 January–3 February and 24 January–8 February (Seedmax = 2000 on 10 January, Td = 9 days before 24 January, Td = 6 days between 24 January and 8 February). Travel to and from Wuhan is reduced by 98%, and other inter-city travel is reduced by 80%.


24 January–3 February [Median (95% CIs)]

24 January–8 February [Median (95% CIs)] 0.35 (0.27, 0.50) 0.44 (0.29, 0.66) 3.44 (3.26, 4.06) 3.30 (2.81, 4.36) 0.69 (0.62, 073) 0.99 (0.76, 1.33)

Transmission rate (β, days−1) page6image4088242320 page6image4088242800 page6image40882432160.52 (0.39, 0.71)

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Relative transmission rate (μ) Latency period (Z, days) Infectious period (D, days) Reporting rate (α)

Effective reproductive number (Re)

0.49 (0.37, 0.69) 3.60 (3.41, 3.91) 3.13 (2.74, 3.76) 0.65 (0.60, 0.69) 1.36 (1.14, 1.63)

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Fig. 1. Best-fit model and sensitivity analysis. Simulation of daily reported cases in all cities (A), Wuhan city (B) and Hubei province (C). The blue box and whiskers show the median, interquartile range, and 95% credible intervals derived from 300 simulations using the best-fit model (Table 1). The red x’s are daily reported cases. The distribution of estimated Re is shown in (D). The impact of varying α and μ on Re with all other parameters held constant at Table 1 mean values (E). The black solid line indicates parameter combinations of (α,μ) yielding Re = 2.38. The estimated parameter combination α = 0.14 and μ = 0.55 is shown by the red x; the dashed box indicates the 95% credible interval of that estimate. Log-likelihood for simulations with combinations of (α,μ) and all other parameters held constant at Table 1 mean values (F). For each parameter combination, 300 simulations were performed. The best-fit estimated parameter combination α = 0.14 and μ = 0.55 is shown by the red x (note that the x is plotted at the lower left corner of its respective heat map pixel, i.e., the pixel with the highest log likelihood); the dashed box indicates the 95% credible interval of that estimate.

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Fig. 2. Impact of undocumented infections on the transmission of SARS-CoV2. Simulations generated using the parameters reported in Table 1 with μ = 0.55 (red) and μ = 0 (blue) showing daily documented cases in all cities (A), daily documented cases in Wuhan city (B) and the number of cities with ≥ 10 cumulative documented cases (C). The box and whiskers show the median, interquartile range, and 95% credible intervals derived from 300 simulations.

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Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)

Ruiyun Li, Sen Pei, Bin Chen, Yimeng Song, Tao Zhang, Wan Yang and Jeffrey Shaman

published online March 16, 2020





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