The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak
Outbreak to pandemic
In response to global dispersion of severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2), quarantine measures have been implemented around the world. To understand how travel and quarantine influence the dynamics of the spread of this novel human virus, Chinazzi et al. applied a global metapopulation disease transmission model to epidemiological data from China. They concluded that the travel quarantine introduced in Wuhan on 23 January 2020 only delayed epidemic progression by 3 to 5 days within China, but international travel restrictions did help to slow spread elsewhere in the world until mid-February. Their results suggest that early detection, hand washing, self-isolation, and household quarantine will likely be more effective than travel restrictions at mitigating this pandemic.
Science, this issue p. 395
Abstract
Motivated by the rapid spread of coronavirus disease 2019 (COVID-19) in mainland China, we use a global metapopulation disease transmission model to project the impact of travel limitations on the national and international spread of the epidemic. The model is calibrated on the basis of internationally reported cases and shows that, at the start of the travel ban from Wuhan on 23 January 2020, most Chinese cities had already received many infected travelers. The travel quarantine of Wuhan delayed the overall epidemic progression by only 3 to 5 days in mainland China but had a more marked effect on the international scale, where case importations were reduced by nearly 80% until mid-February. Modeling results also indicate that sustained 90% travel restrictions to and from mainland China only modestly affect the epidemic trajectory unless combined with a 50% or higher reduction of transmission in the community.
Beginning in December 2019, Chinese health authorities have been closely monitoring a cluster of pneumonia cases in the city of Wuhan in Hubei province, China. The pathogen that causes the viral pneumonia in affected individuals is the newly recognized coronavirus known as severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2) (1). As of 3 March 2020, 80,151 cases (2) have been detected and confirmed in mainland China. Internationally, more than 10,566 additional cases have been detected and confirmed in 72 countries (3). In this work, we model both the domestic and international spread of the novel coronavirus disease 2019 (COVID-19) epidemic. We estimate the effects of the travel ban implemented in Wuhan and the international travel restrictions adopted by several countries in early February 2020.
To model the international spread of the COVID-19 outbreak, we used the global epidemic and mobility model (GLEAM), an individual-based, stochastic, and spatial epidemic model (4–7). GLEAM uses a metapopulation network approach integrated with real-world data where the world is divided into subpopulations centered around major transportation hubs (usually airports). The subpopulations are connected by the flux of individuals traveling daily among them. The model includes more than 3200 subpopulations in roughly 200 different countries and territories. The airline transportation data encompass daily origin-destination traffic flows from the Official Aviation Guide (OAG) and International Air Transport Association (IATA) databases (updated in 2019), whereas ground mobility flows are derived from the analysis and modeling of data collected from the statistics offices of 30 countries on five continents (5). Mobility variations in mainland China were derived from Baidu location-based services (LBS). Within each subpopulation, the human-to-human transmission of COVID-19 is modeled by using a compartmental representation of the disease in which individuals can occupy one of the following states: susceptible, latent, infectious, and removed. Susceptible individuals can acquire the virus through contacts with individuals in the infectious category and can subsequently become latent (i.e., infected but not yet able to transmit the infection). Latent individuals progress to the infectious stage at a rate inversely proportional to the latent period (which we assume to have the same duration as the incubation period), and infectious individuals progress to the removed stage at a rate inversely proportional to the infectious period. The sum of the mean latent and infectious periods defines the generation time. Removed individuals are those who can no longer infect others (i.e., they are isolated, hospitalized, have recovered, or have died).
The model generates an ensemble of possible epidemic scenarios described by the number of newly generated infections, time of disease arrival in each subpopulation, and number of traveling infection carriers. We assume a starting date of the epidemic that falls between 15 November 2019 and 1 December 2019, with 40 infections caused by zoonotic exposure (8–11). The transmission dynamic is calibrated by using an approximate Bayesian computation approach (12) to estimate the posterior distribution of the basic reproductive number R0 by exploring the likelihood of importation of COVID-19 infections to international locations (13). We assume that the overall global detection of imported infections can be as low as 40% (14, 15). Data on importation of cases were obtained from available published line lists (16, 17).
We performed a sensitivity analysis by considering different combinations of average latent and infectious periods, detection rates, initial conditions, and a generation time (Tg) ranging from 6 to 11 days on the basis of plausible ranges from the SARS epidemic and recent analysis of COVID-19 data (16, 18–23). Details and sensitivity analysis on all parameters are reported in the supplementary materials (12). Here we report the results for Tg = 7.5 days (20). The obtained posterior distribution provides an average R0 = 2.57 [90% confidence interval (CI): 2.37 to 2.78] and a doubling time of Td = 4.2 days (90% CI: 3.8 to 4.7 days). The obtained values are in the same range as previous analyses based on early COVID-19 data (9, 20, 24–26). Although the calibration obtained for different generation times provides different posterior distributions for R0, in the early stages of the epidemic the prevalence of infections and case importations is determined by the epidemic growth rate, and the obtained results (12) are consistent with those reported here.
Wuhan travel ban
On 22 January 2020, the projected median number of infections with no travel restrictions for mainland China, excluding Wuhan, was 7474 (90% CI: 3529 to 16,142). The overwhelming majority of infections were in Wuhan with a median number of 117,584 (90% CI: 62,468 to 199,581). To analyze the effect of the travel ban from Wuhan, we implemented long-range travel restrictions beginning on 23 January (airport shutdown). Furthermore, we modeled mobility limitations within mainland China by using de-identified and aggregated domestic population movement data between Chinese provinces for February 2020, as derived from Baidu LBS (12).
Initially, we assumed no changes in transmissibility and disease dynamics (the status quo scenario). The model output shows no noticeable differences in the epidemic trajectory of Wuhan but a delay of ~3 days for other locations in mainland China (Fig. 1A). The overall reduction of infections in mainland China, excluding Wuhan, was close to 10% by 31 January 2020, with a relative reduction of infections across specific locations ranging from 1 to 58% (Fig. 2). With a doubling time of 4 to 5 days, this level of reduction corresponds to only a modest delay (1 to 6 days) of the epidemic trajectory in mainland China. These results are in agreement with estimates from the combination of epidemiological and human mobility data (27). The model clearly indicates that, as of 23 January 2020, the epidemic was seeded in several locations across mainland China. As an independent validation test, we assessed the cumulative number of cases in mainland China provinces through 1 February 2020 (Fig. 1B), as reported from the official World Health Organization (WHO) situation report (28), and compared these results with model projections. The model projections are highly correlated with the observed data (Pearson’s correlation coefficient = 0.74, P < 0.00001), although, as expected, we found that there are significantly fewer reported cases than projected (Fig. 1B). If we assume that the number of reported cases in the WHO situation report and in the simulation are related through a simple binomial stochastic sampling process, we find that the median ascertainment rate of detecting an infected individual in mainland China is 24.4% (interquartile range: 12.7 to 35.8%). In other words, the modeling results suggest that, in mainland China, only one in four infections is detected and confirmed.

Fig. 1 Effect of the Wuhan travel ban on the COVID-19 epidemic.
(A) Trajectory of the COVID-19 epidemic in Chinese locations (excluding Wuhan) under the ban on travel to and from Wuhan as of 23 January 2020. Trajectories are also plotted for scenarios with relative transmissibility reduction r and international travel restrictions. Lines represent median cumulative number of infections; shaded areas represent 90% reference ranges. (B) Correlation between the number of cases reported in each province by the WHO situation report and model projections on 1 February 2020 (no provinces were reporting zero cases by this date). Circle size is proportional to the population size in each province. (C) Projections of the average detected number of daily international case importations for different modeling scenarios. Shaded areas represent 99% reference ranges. We report the observed data of international case importations with a travel history from China, classified by arrival date. We also report scenarios with relative transmissibility reduction r. Data points after 23 January 2020 were used for out-of-sample validation and were not used in the model calibration.

Fig. 2 Effects of Wuhan travel ban on COVID-19 incidence across mainland China.
(A) Relative incidence reduction as of 1 February 2020. Circle color represents the relative reduction in the number of infections, whereas circle size corresponds to population. (B) Projected cumulative number of infections by the same date, after implementation of travel restrictions in Wuhan. A resolution of 0.25° by 0.25° geographical cells was used in the model.
Relative risk of case importation
The model also allows us to estimate the number of case importations in international locations from mainland China. In Fig. 1C, we report the mean number of total international importation events in a fully status quo scenario as opposed to a travel ban. We find a 77% reduction in cases imported from mainland China to other countries as a result of the Wuhan travel ban in early February. Although the number of cases imported internationally decreases markedly at first, it picks up again in the following weeks with importation from locations in mainland China. The model indicates that, after the travel restrictions in Wuhan are implemented on 23 January, the five origin cities with the highest rates of international case importations are Shanghai, Beijing, Shenzhen, Guangzhou, and Kunming. Similarly, the model can rank countries across the world according to the relative risk of importing cases from mainland China. More precisely, the relative risk is defined for each country Y as the relative probability P(Y) that a single infected individual travels from an area affected by the epidemic to that specific destination Y. In other words, given the occurrence of one exported case, P(Y) is the relative probability that the disease carrier will appear in location Y, with respect to any other possible location. This risk depends on the travel flow from cities in mainland China to other countries and the disease prevalence in those cities. Notably, the traffic flows used in the model are origin-destination data that do not depend on traveling routes (i.e., a proxy for the actual mobility demand across cities). Figure 3 illustrates how the cities with the most COVID-19 cases in mainland China contribute to the relative risk of the 20 countries that are most susceptible to case importation, both before and after implementation of the Wuhan travel ban . In particular, before the travel ban, ≈86% of the internationally imported cases originated from Wuhan. After the travel ban, the top 10 contributors to the relative risk—of which the top three are Shanghai (28.1%), Beijing (14%), and Shenzhen (12.8%)—accounted for at least ≈80% of the internationally imported cases. The countries most at risk of importation after the implementation of the Wuhan travel ban are Japan (11% pre-ban, 13.9% post-ban), Thailand (22.8% pre-ban, 13% post-ban), the Republic of Korea (7.4% pre-ban, 11.3% post-ban), Taiwan (9.5% pre-ban, 10% post-ban), and the United States (4.7% pre-ban, 5.7% post-ban).

Fig. 3 Relative risk of case importation.
Contribution to the relative risk of importation from the 10 Chinese cities with the highest rates of disease (plus the rest of mainland China) until 22 January 2020 (left) and after the Wuhan travel ban from 23 January to 1 March 2020 (right). The listed countries are the 20 countries at greatest risk of case importation. Flows are proportional to the relative probability that a single imported case will travel from a given origin to a specific destination.
International travel restrictions and transmissibility reduction
Starting in early February 2020, 59 airline companies suspended or limited flights to mainland China, and several countries—including the United States, Russia, Australia, and Italy—have imposed government-issued travel restrictions (29–34). It is difficult to calculate exactly the level of traffic reduction imposed by these measures. For this reason, we analyzed two major scenarios in which international travel restrictions produce a 40 and 90% overall traffic reduction to and from mainland China. A relative reduction of transmissibility could be achieved through early detection and isolation of cases, as well as behavioral changes and awareness of the disease in the population. Along with travel reductions, we considered three scenarios pertaining to disease transmissibility: (i) a status quo situation with the same transmissibility as that from the model calibration through 23 January 2020; (ii) a moderate relative reduction of the original transmissibility (25%), corresponding to a transmissibility dampening factor of r = 0.75; and (iii) a strong reduction (50%) of the original transmissibility (r = 0.50). In Fig. 4, we show the combined effects of the travel and transmissibility reductions on the epidemic incidence in mainland China and the number of exported cases to other countries.

Fig. 4 Combined effects of travel and transmissibility reductions on the epidemic.
(A) Median total number of imported infections from mainland China with no transmissibility reduction and travel reductions of 40 and 90%. (B) Same as (A) for the moderate transmissibility reduction scenario (r = 0.75). (C) Same as (A) for the strong transmissibility reduction scenario (r = 0.5). Shaded areas represent 90% CIs. (D) Disease incidence in mainland China, excluding Wuhan, for the scenarios plotted in (A) to (C).
The simulated scenarios reveal that even in the case of 90% travel reductions (Fig. 4D), if transmissibility is not reduced (r = 1), the epidemic in mainland China would be delayed for no more than 2 weeks. The model projects that, in the status quo scenario, the peak of the epidemic in mainland China will be reached in late April to early May 2020. Notably, in the absence of transmissibility reductions, the epidemic would peak in Wuhan during the first week of March. The number of infections imported in other countries (Fig. 4, A to C) was initially affected by a 10-fold reduction, but by 1 March, when there is no transmissibility reduction (r = 1), we would again see 170 and 35 detected cases per day for the 40 and 90% travel restrictions scenarios, respectively. However, the concurrent presence of both travel and transmissibility reductions produces a much larger synergistic effect that becomes visible by delaying both the epidemic activity in mainland China and the number of internationally imported infections. In the moderate transmissibility reduction scenarios (r = 0.75), the epidemic peak is delayed to late June 2020, and the total number of international infection importations by 1 March is 26 cases per day for the 40% scenario and 5 per day for the 90% scenario. Even more restrictive travel limitations (>90%) would extend the period during which the importation of infections is greatly reduced. Strong transmissibility reduction (r = 0.5) along with travel restrictions would delay the epidemic growth in mainland China such that the daily incidence rate would never surpass 1 infection per 1000 people and the number of imported infections at international destinations would always be in the single-digit range. The effect of transmissibility reduction on the short-term epidemic curve in mainland China is also visible (Fig. 1A): There is a pronounced reduction in the number of infections by 22 February 2020, with respect to the status quo epidemic curve. We also report the estimated number of detected international importations, as determined by the model in the strong transmissibility reduction scenario (Fig. 1C). The results are consistent with the data collected from the travel history of international imported cases after 23 January 2020 (16, 17). Similar results are obtained by assuming that the transmissibility reduction interventions successfully reduce the reproductive number below the epidemic threshold in the second half of February, as data from mainland China seem to suggest (28).
Notably, many infected individuals from mainland China have not been detected and have potentially dispersed to international locations. By 1 February 2020, in the strong transmissibility reduction scenario, the model estimates 101 (90% CI: 50 to 173) importation events, with one or more potential infections that could seed multiple epidemic outbreaks across the world, potentially leading to the international expansion of the COVID-19 epidemic. This finding is consistent with the emergence of COVID-19 outbreaks in countries such as Italy, the Republic of Korea, and Iran in the second half of February 2020.
Our analysis, as with all modeling exercises, has several limitations and requires certain assumptions. The model parameters, such as generation time and incubation period, are chosen on the basis of early data associated with the COVID-19 outbreak and prior knowledge of SARS and Middle East respiratory syndrome (MERS) coronavirus epidemiology. Although the model is stable to variations in these parameters, more information on the key characteristic of the disease would considerably reduce uncertainties. At this stage, the transmission and mobility model does not account for heterogeneities due to age differences in susceptibility and contact patterns. The model calibration does not consider correlations among importations (family travel) and assumes that travel probabilities are homogeneous across all individuals in the catchment area of each transportation hub. We were not able to find reliable data on the effectiveness of containment measures (e.g., body temperature screening for passengers on flights departing from Wuhan International Airport) in mainland China before 23 January, so this information is not included in the model. In the travel restriction scenario, we assume long-term enforcement of individual mobility restrictions (travel was restricted until the end of June 2020), but this policy may not be feasible or sustainable for such a long period.
Discussion
The analysis of the COVID-19 outbreak and the modeling assessment of the effects of travel limitations could be beneficial to national and international agencies for public health response planning. We show that, by 23 January 2020, the epidemic had already spread to other cities within mainland China. The travel quarantine around Wuhan has only modestly delayed the spread of disease to other areas of mainland China. This finding is consistent with the results of separate studies on the diffusion of SARS-CoV-2 in mainland China (27, 35, 36). The model indicates that although the Wuhan travel ban was initially effective at reducing international case importations, the number of imported cases outside mainland China will continue to grow after 2 to 3 weeks. Furthermore, the modeling study shows that additional travel limitations (up to 90% of traffic) have only a modest effect unless paired with public health interventions and behavioral changes that can facilitate a considerable reduction in disease transmissibility (37). The model also indicates that, despite the strong restrictions on travel to and from mainland China since 23 January 2020, many individuals exposed to SARS-CoV-2 have been traveling internationally without being detected. Moving forward, we expect that travel restrictions to COVID-19–affected areas will have modest effects and that transmission reduction interventions will provide the greatest benefit for mitigating the epidemic. Our results provide data with potential uses for the definition of optimized containment schemes and mitigation policies, including the local and international dimensions of the COVID-19 epidemic.
Acknowledgments
Funding: M.E.H. acknowledges the support of the MIDAS-U54GM111274. S.M. and M.A. acknowledge support from the EU H2020 MOOD project. C.G. and L.R. acknowledge support from the EU H2020 Icarus project. M.C. and A.V. acknowledge support from Google Cloud Healthcare and Life Sciences Solutions via the GCP research credits program. The findings and conclusions in this study are those of the authors and do not necessarily represent the official position of the funding agencies, the National Institutes of Health, or the U.S. Department of Health and Human Services. Author contributions: M.C. and A.V. designed the research; M.C., J.T.D., M.A., C.G., M.L., S.M., A.P.yP., K.M., L.R., K.S., C.V., X.X., H.Y., M.E.H., I.M.L., and A.V. performed the research; M.C., J.T.D., A.P.yP., K.M., and A.V. analyzed the data; and M.C., J.T.D., M.A., C.G., M.L., S.M., A.P.yP., K.M., L.R., K.S., C.V., X.X., H.Y., M.E.H., I.M.L., and A.V. wrote and edited the paper. Competing interests: M.E.H. reports grants from the National Institute of General Medical Sciences during the conduct of the study; A.V. reports grants and personal fees from Metabiota, Inc., outside of the submitted work; M.C. and A.P.yP. report grants from Metabiota, Inc., outside of the submitted work; H.Y. reports grants from Glaxosmithkline (China) Investment Co., Ltd., Yichang HEC Changjiang Pharmaceutical Co., Ltd, Sanofi Pasteur, and Shanghai Roche Pharmaceuticals Company, outside of the submitted work. The authors declare no other relationships or activities that could appear to have influenced the submitted work. Data and materials availability: Proprietary airline data are commercially available from OAG and IATA databases. All other data that support the plots within this paper and other findings of this study are available at https://github.com/mobs-lab/COVID-19/blob/master/README.md (38). The GLEAM model is publicly available at www.gleamviz.org/. This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/. This license does not apply to figures/photos/artwork or other content included in the article that is credited to a third party; obtain authorization from the rights holder before using such material.
Supplementary Material
Summary
Material and Methods
Figs. S1 and S2
Table S1
MDAR Reproducibility Checklist
Resources
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Volume 368 | Issue 6489
24 April 2020
24 April 2020
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Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).
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Received: 20 January 2020
Accepted: 5 March 2020
Published in print: 24 April 2020
Acknowledgments
Funding: M.E.H. acknowledges the support of the MIDAS-U54GM111274. S.M. and M.A. acknowledge support from the EU H2020 MOOD project. C.G. and L.R. acknowledge support from the EU H2020 Icarus project. M.C. and A.V. acknowledge support from Google Cloud Healthcare and Life Sciences Solutions via the GCP research credits program. The findings and conclusions in this study are those of the authors and do not necessarily represent the official position of the funding agencies, the National Institutes of Health, or the U.S. Department of Health and Human Services. Author contributions: M.C. and A.V. designed the research; M.C., J.T.D., M.A., C.G., M.L., S.M., A.P.yP., K.M., L.R., K.S., C.V., X.X., H.Y., M.E.H., I.M.L., and A.V. performed the research; M.C., J.T.D., A.P.yP., K.M., and A.V. analyzed the data; and M.C., J.T.D., M.A., C.G., M.L., S.M., A.P.yP., K.M., L.R., K.S., C.V., X.X., H.Y., M.E.H., I.M.L., and A.V. wrote and edited the paper. Competing interests: M.E.H. reports grants from the National Institute of General Medical Sciences during the conduct of the study; A.V. reports grants and personal fees from Metabiota, Inc., outside of the submitted work; M.C. and A.P.yP. report grants from Metabiota, Inc., outside of the submitted work; H.Y. reports grants from Glaxosmithkline (China) Investment Co., Ltd., Yichang HEC Changjiang Pharmaceutical Co., Ltd, Sanofi Pasteur, and Shanghai Roche Pharmaceuticals Company, outside of the submitted work. The authors declare no other relationships or activities that could appear to have influenced the submitted work. Data and materials availability: Proprietary airline data are commercially available from OAG and IATA databases. All other data that support the plots within this paper and other findings of this study are available at https://github.com/mobs-lab/COVID-19/blob/master/README.md (38). The GLEAM model is publicly available at www.gleamviz.org/. This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/. This license does not apply to figures/photos/artwork or other content included in the article that is credited to a third party; obtain authorization from the rights holder before using such material.
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RE: Evidences of reduction in SARS-C0V-2 transmission due to local measures and policies in early stages of the pandemic
We read with great interest the article by Chinazzi et al. who used a global meta-population disease transmission model to demonstrate that travel limitations could be extremely beneficial on the national and international spread of the COVID-19 pandemic (1). Intensive control measures, including travel restrictions to and from major outbreak areas that act as disease source, were useful to limit the spread of the COVID-19 in China. Also, social isolation and hygiene, rather than long-distance travel restrictions, played the largest part in controlling SARS-CoV-2 spread (2). But Xiao and Torok says there is no value for the prevention and control of COVID-19 in lookdown areas and blocking the traffic (3).
First, the quick action of some Brazilian mayors and governors contributed positively to the delay in the death rate growth, resulting in even better results for the attack rate (the proportion of individuals that has been infected) when compared to most countries in Europe and North America. Most of the Brazilian states presented an attack rate below 2.3%, while it was much higher in São Paulo (3.3%), Rio de Janeiro (3.35%), Ceará (4.46%), Pernambuco (3%), Pará (5.05%) and Amazonas (10.6%) (4). On the other hand, the attack rates in Bahia (0.4%) was as low as in Germany (0.72%) (5). We note that the average attack rate in the US was 4.1%, including New York with 16.6% and New Jersey with 16.1% attack rates (6), comparable to those of Spain (15%) and Italy (9.8%) (5). Bahia's main immediate action was to reduce mobility by imposing travel limitations between municipalities and, in some of them, with strict travel and sanitary barriers. Bahia state government is also paying 3 months of electricity and water bills for low-income consumers. Bahia is in the northeast of Brazil, one of the poorest regions, but this region is more open to scientific advice. The region created a scientific committee, in close contact with the governors, to the development of the science and find ways to re-establish 'new normal' (7).
Second, Federal government officials in Brazil frequently minimized the effects of the pandemic, and hindered actions of local governments to reinforce social distancing, alternatively proposing the use of drugs without proper scientific evidence on their effectiveness (7,8). Despite all efforts by Brazilian mayors and governors to slow down the spread of COVID-19, an upward trend of the mobility rates in Transit Stations from March 23 to Jun 7 was reported in Community Mobility Reports (9), likely due to a lack of a federal policy to ensure minimum income to most vulnerable individuals for the duration of the pandemic. People are loosen social distancing and the COVID-19 contagion is growing at an accelerated rate in some regions of the country.
This incorrect reading of the current pandemic emerges as an institutional incorporation of the infamous Dunning-Kruger effect (10). In summary, mayors and governors showed their grasp on the control of the pandemic, but the national government was found wanting. There is an urgent need to plan actions among all mayors, governors and the federal government, assisted by a scientific committee, to limit human-to-human transmission and accelerate the development of therapeutics and vaccines.
This research was supported by the Brazilian National Council for Scientific and Technological Development - CNPq (Grants # 305291/2018-1, 308092/2015-5, 305842/2017-0, 302449/2019-1 and 302583/2017-3).
Contributors
All authors contributed equally to the final manuscript.
Declaration of interests
We declare no competing interests.
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4. Mellan T, et al. Report 21: Estimating COVID-19 cases and reproduction number in Brazil. (Imperial College, London, 2020).
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RE: A Fatal Error of COVID-19 Epidemiological Model Data Presentation and Interpretation: Social Distancing is Effective and Must Strictly be Enforced
No one can escape the fact that worldwide data presentation and epidemiological modeling on COVID-19's pandemic are expressed in terms of the absolute total new confirmed cases on that specific date such as the work of Matteo et al. (1). This presentation of data and its corresponding interpretations are erroneous and actually not indicative regarding the epidemiology of COVID-19, mitigation measures and flattening the curve (1). This is because the data need to be normalized over the total number of cases tested on that specific date; viz., the larger the pool number of subjects tested the more new confirmed cases will be reported. Hence, all infectious data have to be normalized over the total cases tested on that specific date.
This can be substantiated by examining the data collected, for example, on New York State (NYS). The raw data were obtained from the New York State Statewide COVID-19 Testing Data Collection (2). Figure1A depicts a plot of the daily new confirmed cases of COVID-19 "Y" in NYS while Figure1B represents its daily corresponding calculated percentage normalized data "%Z" with respect to the total cases tested starting from 12 March until 22 May (3). These numbers were calculated as the ratio of total number of confirmed cases Y to the total number of cases tested at that specific date multiplied by 100%.
The significance of the shape of the two profiles of Figure1 is that from 12-30 March, the two profiles mimic each other and both are increasing. After 30 March, these profiles are different in that in Figure 1B there is an apex or a peak on 31 March (arrow in Figure 1B) thereafter the curve smoothly declines or flattens, except at 14 April where there is an outlier (* in Figure1B), which might be attributed to errors in data collection or data entry from the source! This behavior is not seen for Y of Figure1A and the profile is erratic with several apexes or peaks with no clear pattern where this behavior continues throughout the range of data studied, which can be attributed to the faulty presentation of the data, resulting in its erroneous interpretations. Another important conclusion which can be drawn from Figure1B is that the profile represents a bell-shaped distribution function, which is absent in Figure1A.
What is extremely important about the peak on 31 March is that going back 14 days (the total number of days for incubation of SARS-CoV-2 virus) to 17 March, it is almost the same date of 15 March where social distancing has been implemented in NYS (4). The normalized data are almost matching the incubation period of SARS-CoV-2 virus, which is remarkable. This significant observation is not seen for the confirmed cases depicted in Figure1A, which is an additional caveat where Figure1A falsely predicts that social distancing is effective at much larger times with multiple peaks.
To quantitatively and statistically describe the profile of Figure1B, regression models were fitted to the data. Since we are only interested in the right-hand segment of Figure1B, only the data in this region were analyzed. The first date was 1 April following the apex where the profile started to decline. In the regression analyses, it was assumed that 1 April was day number 1.
Linear and nonlinear regression models were employed to assess the correlation between %Z and time of Figure1B using nonlinear NLREG® software. The relative fit for each model was determined on the basis of the values of the corresponding correlation coefficient, r.
The best-fitted model was found to be
ln (%Z) = – 0.0005 t2 – 0.0259 t + 3.98, r = 0.996 (1)
Here, ln is the natural log, and t is time in days.
The clinical significance of Equation 1 is that it can be used to give a priori and future values regarding %Z. Figure2 shows a comparison of the actual data (green curve) of Figure1B and values calculated (blue curve) from Equation 1 (3). As can be seen from Figure2, there is an excellent agreement between predictions and actual data, except for the outlier data point on 14 April (* in Figure2), which was discussed earlier. This agreement extends throughout the range of the data examined.
It is also of great significance to calculate the time when %Z drops to zero in Figure2. This value was calculated from Equation 1 and was found to be 67 days (only the positive root is of interest here). Therefore, there should be an additional 16 days (67-51 days) of social distancing in NY State, extending it to approximately the second week of June 2020 (from 22 May adding 16 extra days).
The work presented here unequivocally demonstrates that in the presentation and modeling of the epidemiology of COVID-19 or any epidemiological model of any disease, the data collected need to be normalized with respect to the total number of subjects tested on that specific date. This will give accurate interpretations regarding the progress and the spread of the disease as shown here. Most importantly the data examined here show that social distancing is very effective in preventing the spread of COVID-19, and therefore social distancing must strictly be enforced and should not be lifted under any circumstances. This is especially true with the current worldwide social and political turmoil, which is detrimental to controlling the spread of COVID-19, inevitably initiating a second wave of infection that can even be worse than the first.
References
1. M Chinazzi, J Davis, M Ajelli, et al. The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science 2, 395-400 (2020). DOI: 10.1126/science.aba9757.
2. https://health.data.ny.gov/Health/New-York-State-Statewide-COVID-19-Test....
3. All figures can be found at https://d6d676ef-adb8-4219-a8db-af0d6f9602bf.filesusr.com/ugd/dc408a_61b....
4. https://www.nytimes.com/2020/03/16/smarter-living/coronavirus-social-dis....
Legends
Figure1. Daily number of COVID-19 cases for New York State versus date expressed as (A) total number of confirmed cases Y at that specific date and (B) percentage daily normalized total confirmed cases %Z calculated as the ratio of total number of confirmed cases Y to the total number of cases tested at that specific date multiplied by 100%. The arrow on 31 March and the asterisk on 14 April of Figure 1B represent the peak of COVID-19 pandemic where the profile started to decline or flatten and the outlier, respectively. The raw data were obtained from the New York State Statewide COVID-19 Testing Data Collection (2).
Figure 2. A comparison of daily actual data (green curve) with calculated values (blue curve) obtained from Equation 1. The asterisk on 14 April represents the outlier of Figure1B.
RE: Travel Restriction Confines COVID-19 Outbreak
Travel Restriction Confines COVID-19 Outbreak
Madiha Zahra Syeda1#, Liujian Ouyang#1,2, Zhihua Chen3, Songmin Ying1*, Huahao Shen3,4*
1. Department of Pharmacology & Department of Respiratory and Critical Care Medicine of the Second Affiliated Hospital, Zhejiang University School of Medicine, Key Laboratory of Respiratory Disease of Zhejiang Province, Hangzhou 310009,
2. Chu Kochen Honors College of Zhejiang University
3. Key Laboratory of Respiratory Disease of Zhejiang Province, Department of Respiratory and Critical Care Medicine, Second Affiliated Hospital of Zhejiang University School of Medicine, Hangzhou, Zhejiang, 310009, China
4. State Key Laboratory of Respiratory Diseases, Guangzhou, Guangdong 510120, China
edited
#These authors have contributed equally
*Correspondence should be addressed to:
[email protected] (S.Y.), [email protected] (H.S.)
In their publication, Matteo et al. evaluated "The effect of travel restrictions on spread of COVID-19 outbreak" and concluded that travel ban was only modestly-effective in slowing down the spread of virus. Although reasonably designed, their analysis and model is probably overestimated and the conclusion is misleading. Available data on the spread of COVID-19 across China and other countries clearly indicates the effectiveness of travel restrictions by China. For instance, Zhejiang, a province of China, is close to Wuhan by distance, has 1215 confirmed cases of COVID-19 and 1 fatality, however, Italy, a nation with similar population size, showed much severe and rapid spread of disease with 15,113 confirmed cases and 1016 fatalities reported as of 13-Mar., 2020. Similarly, Iran confirmed 10,075 cases and 75 fatalities, as of 13-mar.,-2020. Furthermore, after first-100 confirmed cases, it took Zhejiang, 12-days to cross first 1000 infected cases (1006 cases as of 6th-Feb., 2020), Where it took only 7-days for Italy (1128 as of 1st-Mar.) and 5-days for Iran (1501 as of 2nd-Mar.) to report first-1000 cases. Soon after, the number of daily new-cases declined considerably in Zhejiang, while it is still increasing in other countries. It clearly indicates the lack of strict management policies in these regions, against COVID-19 outbreak.
Further, authors suggest that Wuhan lockdown decision was probably late, with infected cases already been imported to other provinces of China. Although imported cases were reported in other provinces, importance of travel ban on national and international level cannot be ignored, especially considering the high transmissibility of virus, and Chinese-New-Year event during which mass travel occurs. Authors also indicated that a large number of asymptomatic-individuals exposed to SARS-CoV-2 have been traveling internationally. Again, this fact emphasizes the need of stricter surveillance and timely travel restrictions to confine the virus. Quick and timely action to prevent the spread of virus is therefore the need of time. China has set an example, and international-community should learn a lesson from it.
Acknowledgement
This work is supported by Zhejiang University special scientific research fund for COVID-19 prevention and control.
RE: Questions about methodology
Having lived in China for many years, I'm curious about how you arrived at your conclusion that this only delayed the spread of the virus to the rest of China by a few days (or, as you put it, "the model output shows no noticeable differences in the epidemic trajectory of Wuhan, while it shows a delay of about 3 days in the rest of mainland China"). Maybe in general terms, yes, it was already spreading. China waited too long to ban travel to and from Wuhan if it wanted to completely control the spread of the disease. It was too late. It was already going to spread because infected people were already moving throughout the country.
So far (March 12), Wuhan has had just short of 50,000 confirmed infections and more than 2,436 deaths (https://ncov.dxy.cn/ncovh5/view/pneumonia). But other cities are nowhere near that. Eight of the 436 infected people in Beijing died. Three of 346 in Shanghai, two of 120 Xi'an. Kunming had 0 out of 53. Changchun had 0 of 45. And in the city where I live, Yinchuan, zero of 36. Another nearby city, Guyuan had zero of five. Actually, there were no reported deaths in the entire province. But if these and hundreds more similar cities are all considered "no noticible differences in the epidemic trajectory," I question the model. Is it only used to identify that each city is likely to have cases of the disease? Granted, maybe there are 4 times as many unreported cases, as your report mentions, but if these are the" seeds," of the epidemic most have been treated and sent home now.
You seem to downplay that there was real tangible benefit gained from keeping hundreds of millions of Chinese people from traveling during Chinese New Year. This meant that hundreds or thousands of infected people didn't leave Wuhan and hundreds of thousands of other healthy people didn't go to the city and expose themselves, then go back home after the holiday, thus vastly accelerating the rate at which hospitals in every city could easily have become overwhelmed by COVID-19 patients. There's a reason Yinchuan and other cities copied Wuhan and built pop-up hospitals. They didn't have enough beds to keep treating existing patients and have an epidemic.
The mainland portion of the study seems to only focus on Wuhan travel, not the fact that Chinese people criss-cross all across the country during Spring Festival and millions of passengers pass through Wuhan. China didn't just shut down transportation from Wuhan, but basically transportation ground to a halt and people were either told not to travel or were too afraid to travel. Immediately airports were mostly empty. Within days dozens of train routes were canceled. For the whole country. Soon intercity busses were shut down. It became difficult to travel.
That's why comparing what happened with Wuhan with other cities isn't really an apples to apples comparison.
Not only that, but travel wasn't the only factor at play. Within days, throughout the country, nobody was allowed outside. People weren't allowed to go leave their apartments for more than an hour every other day to buy groceries. Most of the transmission seemed to be among family members. Certainly all of these measures combined contributed to the rapid reduction of COVID-19 cases in China we are seeing now, right? Had a billion people continued going about their daily business, we'd be looking at hospitals that were overwhelmed in hundreds of Chinese cities, not just in Wuhan. But that didn't happen. It was like a zombie apocalypse. Wuhan was overwhelmed, but most of China stayed home. And is still there.
Two American friends of mine who tried to fly from Yinchuan (far from Wuhan) to Xi'an (also far from Wuhan on their way to Bangkok on Jan. 27th. When officials asked if anyone on that first flight (which only had 30 or 40 passengers on it to begin with) had been to Wuhan recently, one person said yes. They quarantined the entire plane for three days while he was tested. They finally were released when that one person proved to not be sick. This was early on. Later it likely would have been a 14 day quarantine. But my point is this wasn't travel from Wuhan. But they were already on the lookout for people who had been in Wuhan and might be spreading the virus. Isn't it possible that these efforts also played a role in slowing the transmission? Surely once people return to work and school in China it will spread again.
I'm not a scientist, just a teacher. I feel terrible for all of the people who have been quarantined for more than a month (many of my friends and students included). But I am grateful as well for the sacrifices they've made to slow down its transition if it means my elderly parents might be spared in the US.