Coronaviruses are enveloped, single-stranded, positive-sense RNA viruses belonging to the family of Coronaviridae
]. They cause generally mild respiratory infections, even though they are occasionally lethal. Since their discovery and first characterization in 1965 [2
], three major, large-scale outbreaks have occurred, caused by emerging, highly pathogenic coronaviruses, namely, the “Severe Acute Respiratory Syndrome” (SARS) outbreak in 2003 in mainland China [3
], the “Middle East Respiratory Syndrome” (MERS) outbreak in 2012 in Saudi Arabia [4
] and the MERS outbreak in 2015 in South Korea [6
]. These outbreaks have resulted in more than 8000 and 2200 confirmed SARS and MERS cases, respectively [8
Recently, a fourth coronavirus outbreak has occurred in Wuhan, the capital city of the Hubei province and the seventh largest city of People’s Republic of China [9
Since 31 December 2019, when the Wuhan Municipal Health Commission reported 27 cases of viral pneumonia, including 7 critically ill cases, the pneumonia outbreak has received considerable global attention. A novel coronavirus was identified as the causative agent by the Chinese authorities on 7 January 2020, and on 10 January 2020, the World Health Organization (WHO) designated the novel coronavirus as 2019-nCoV. On the same day, the WHO released a wide range of interim guidance for all countries on how they can get prepared for coping with this emergency, including how to monitor for potentially infected people, collect and test samples, manage patients, control and mitigate the burden generated by the infection in health centers, maintain the right drug supplies and effectively communicate with the lay public regarding the new virus [12
By the morning of 23 January 2020, more than 571 confirmed cases with 17 deaths had been reported in other parts of mainland China, and in various countries including South Korea, Japan, Thailand, Singapore, the Philippines, Mexico and the United States of America. As of 6 February 2020 (02:45 GMT), 28,276 cases, of which 3863 are in critical condition, and 565 deaths had been reported.
The transmission potential, often measured in terms of the basic reproduction number, the outbreak peak time and value and duration under current and evolving intervention measures, remain unclear, and warrant further investigation.
On 20 January 2020, the Chinese government revised the law provisions concerning infectious diseases to add the 2019-nCoV as a class B agent (a pathogen that can cause an epidemic outbreak). On the same day, public health officials announced a further revision to classify the novel virus as a class A agent (a pathogen that can cause an epidemic in a short time). Some non-pharmaceutical interventions (NPIs), including intensive contact tracing followed by quarantine of individuals potentially exposed to the disease, and isolation of infected, symptomatic individuals, were implemented, but their effectiveness during the early stage is questionable.
Quantifying the effectiveness of these interventions is of crucial importance for Wuhan as well as for other cities in their preparedness and rapid response to the importation of infected cases. With the arrival of the Spring Festival, massive traveling is expected to mobilize a large segment of the population, by which the novel coronavirus may be broadly reseeded.
Extreme, unprecedented measures have been taken. For example, on 23 January 2020, the Chinese authorities introduced travel restrictions affecting five cities (Wuhan, Huanggang, Ezhou, Chibi and Zhijiang), effectively shutting down the movement of more than 40 million people.
However, how these expensive and resource-intensive measures can contribute to the prevention and control of the infection in these cities and other parts of the country, and how long these travel restrictions should be maintained, remain to be determined. In the context of a novel coronavirus affecting a naïve population, estimation of the basic reproduction number is important for determining the potential and severity of an outbreak, and providing critical information for designing and implementing disease outbreak responses in terms of the identification of the most appropriate, evidence-based interventions, mitigation measures and the determination of the intensity of such programs in order to achieve the maximal protection of the population with the minimal interruption of social-economic activities [8
As recognized by the WHO [13
], mathematical models, especially those which are timely, play a key role in informing evidence-based decisions by health decision- and policy-makers. To the best of our knowledge, only a few mathematical models have so far been publicly released, including a Bats-Hosts-Reservoir-People transmission network model and a returning traveler study aimed to compute underestimated coronavirus cases [14
No study has focused on the practical implications of public health interventions and measures. Therefore, the present study was undertaken to fill in this gap of knowledge.
Based on the 2019-nCoV cases’ data until 22 January 2020, we have estimated the basic reproduction numbers using different methods (likelihood-based and model-based approaches). The mean control reproduction number was estimated to be as high as 6.47 (95% CI 5.71–7.23), in comparison with the values of the SARS epidemics (R0
= 4.91) in Beijing, China, in 2003 [26
], and MERS in Jeddah (R0
= 3.5–6.7) and Riyadh (R0
= 2.0–2.8), Kingdom of Saudi Arabia, in 2014 [27
Our value is higher than other published estimates (for instance, Reference [28
]). Such a high reproduction number is consistent with the opinion that the virus has gone through at least three–four generations of transmission in the period covered by this study [24
]. Note that our estimation is based on a dataset collected during a period of intensive social contacts. Before the Chinese New Year (25 January 2020), there were lots of annual summing-up meetings and/or parties, with higher than usual close contacts, leading to a higher likelihood of infection transmission than that of the earlier periods covered by other studies. Furthermore, we noted that more recently published studies based on datasets during periods comparable with ours reported similar findings in terms of a high basic reproduction number (for instance, Reference [29
], where authors, using an exponential growth method, computed a basic reproduction number of 6.11 (95% CI 4.51–8.16), assuming no changes in reporting rate and with a serial interval of 8.4 ± 3.8 days). Variability in the estimation of the basic reproduction number is also a well-known methodological issue, and standardized methods both for calculating and reporting it are still lacking [30
]. During the initial phases of an epidemics outbreak, only small datasets/time-points can be used. Some crucial information may be missing, and the quality, accuracy and reliability of data improves over time. In these situations, estimations are highly dependent on the specific datasets utilized and revising/updating such datasets could influence the results. We note that several key clinical parameters could be inferred from relevant clinical data based on sero-epidemiological surveys, and the possibility of spreading the infection from asymptomatic cases was only reported recently [31
Our finding of a high reproduction number implies the potential of a very serious epidemic unless rather swift public health interventions are implemented [32
], during the season when the social contacts is the highest.
Note that the serial interval is an essential factor affecting the accuracy of the likelihood function estimation. According to the current report, the incubation period of Wuhan patients with coronavirus pneumonia is about 2 to 15 days. We then assume that the serial interval follows the gamma distribution with varying mean and variance, which allows us to examine the influence on the reproduction number. With the distribution of serial interval with mean 6 days and variance 2 days, the likelihood-based estimation of the reproduction number is consistent with the model-based estimation. It shows that longer serial intervals induce greater reproduction numbers, and hence, more new infections, which further confirms that the epidemic may be more serious than what has been reported until now [15
Based on the reported data, we have estimated that the number of people who were identified through contact tracing and quarantined was 5897, as of 22 January 2020. In comparison with the total population size of Wuhan, the effort of close contact tracing and quarantine was insufficient and appears to have a limited impact in terms of reducing the number of infected cases and/or slowing down the epidemic. The contour plot of R_c = 1 gives the threshold values of contact rate and quarantine rate for a city to avoid an outbreak. This high threshold rate of quarantine puts an extremely high requirement for the city’s public health infrastructure and its citizens’ adherence to personal protective and public health interventions, including a reduction of transmission-effective contacts, separation and restriction during the quarantine.
Such a high level of quarantine rate and reduction of contact is possible only when the number of imported cases from the epicenter is minimal, speaking in terms of the value of the travel restriction. A strict travel restriction to the city of Wuhan is expensive and resource-consuming, imposing a substantial challenge to the decision- and policy-makers and the city’s resilience. Moreover, such a measure could only delay the transmission of the infectious disorder.
In conclusion, our simulations show that the appropriate duration of this travel restriction depends on a combination of effective quarantine and reduction of contact within the city.
Considering the latest events (the lock-down of Wuhan on 23 January 2020, the adoption of the travel restriction strategy by other regions and provinces, the introduction of new detection technologies, etc.), the present model needs to be revised in that the basic reproduction number estimated here is no longer suitable for predicting future epidemic trends (Table 4
). This will be the aim of a forthcoming article.