The aim of this study was to conduct a rapid systematic review and meta-analysis of estimates of the incubation period of COVID-19.

Rapid systematic review and meta-analysis of observational research.

International studies on incubation period of COVID-19.

Searches were carried out in PubMed, Google Scholar, Embase, Cochrane Library as well as the preprint servers MedRxiv and BioRxiv. Studies were selected for meta-analysis if they reported either the parameters and CIs of the distributions fit to the data, or sufficient information to facilitate calculation of those values. After initial eligibility screening, 24 studies were selected for initial review, nine of these were shortlisted for meta-analysis. Final estimates are from meta-analysis of eight studies.

Parameters of a lognormal distribution of incubation periods.

The incubation period distribution may be modelled with a lognormal distribution with pooled mu and sigma parameters (95% CIs) of 1.63 (95% CI 1.51 to 1.75) and 0.50 (95% CI 0.46 to 0.55), respectively. The corresponding mean (95% CIs) was 5.8 (95% CI 5.0 to 6.7) days. It should be noted that uncertainty increases towards the tail of the distribution: the pooled parameter estimates (95% CIs) resulted in a median incubation period of 5.1 (95% CI 4.5 to 5.8) days, whereas the 95th percentile was 11.7 (95% CI 9.7 to 14.2) days.

The choice of which parameter values are adopted will depend on how the information is used, the associated risks and the perceived consequences of decisions to be taken. These recommendations will need to be revisited once further relevant information becomes available. Accordingly, we present an R Shiny app that facilitates updating these estimates as new data become available.

This study provides a pooled estimate of the distribution of incubation periods which may be used in subsequent modelling studies or to inform decision-making.

Several studies used data that were publicly available, therefore there is potential that some of the data may be used for more than one study.

This estimate will need to be revisited as subsequent data become available. Accordingly, we present an R Shiny app to allow the meta-analysis to be updated with new estimates.

Reliable estimates of the incubation period are important for decision-making around the control of infectious diseases in human populations. Knowledge of the incubation period can be used directly to inform decision-making around infectious disease control. For example, the maximum incubation period can be used to inform the duration of quarantine, or active monitoring periods of people who have been at high risk of exposure. Estimates of the duration of the incubation period, coupled with estimates of the latent period, serial interval or generation times, may help infer the duration of the presymptomatic infectious period, which is important in understanding both the transmission of infection and opportunities for control.

Earlier work has shown that for models of respiratory infections, statements regarding incubation periods are often poorly referenced, inconsistent or based on limited data.

We hypothesised that a pooled estimate of the distribution of incubation periods could be obtained through a meta-analysis of data published to date. Therefore, the aim of this study was to conduct a rapid systematic review and meta-analysis of estimates of the incubation periods of COVID-19, defined as the period of time (in days) from virus exposure to the onset of symptoms. Specifically, we aimed to find a pooled estimate for the parameters of an appropriate distribution that could be subsequently used as an input in modelling studies and that might help quantify uncertainty around the key percentiles of the distribution as an aid to decision-making.

For the purpose of this study we followed the Meta-analysis of Observational Studies in Epidemiology guidelines.

It was not appropriate or possible to involve patients or the public in the design, or conduct, or reporting, or dissemination plans of our research.

A survey of the literature between 1 December 2019 and 8 April 2020 for all countries was implemented using the following search strategy. Publications on the electronic databases PubMed, Google Scholar, Embase, Cochrane Library as well as the preprint servers MedRxiv and BioRxiv were searched with the following keywords: ‘Novel coronavirus’ OR ‘SARS-CoV-2’ OR ‘2019-nCoV’ OR ‘COVID-19’ AND ‘incubation period’ OR ‘incubation’ (

Results of searches were screened in two stages. First, titles and abstracts were screened, and only relevant articles retained. Studies were removed if they dealt with specific cohorts of cases that did not reflect the overall population. Next, articles were read in detail, studies were selected for meta-analysis if they reported either the parameters and CIs of the distributions fit to the data, or sufficient information to facilitate calculation of those values. Specifically, this included studies that reported: the point estimate and CIs or SEs of each parameter; the mean and SD on the original (non-transformed) scale with CIs; the mean and one or more percentiles of the distribution (with CIs); or two or more percentiles of the distribution (with CIs). Studies were excluded if they described the distribution (eg, with mean, median, percentile) but did not report any uncertainty around that figure. The selection of studies to include in the meta-analysis was conducted by the primary author (CM).

Once studies were shortlisted, two authors (CM, SJM) independently conducted appraisals of study quality. To the authors’ knowledge, no quality assessment tools are available to appraise studies reporting the incubation period of infectious disease. We used the Newcastle-Ottawa Scale for assessing the quality of non-randomised studies in meta-analyses

On initial appraisal, it was apparent that the majority of studies fitted a lognormal distribution to the data. Earlier work has shown that this distribution is appropriate for many acute infectious diseases.

A variable (X) has a lognormal distribution when the log-transformed values follow a normal distribution with mean, mu, and variance, sigma^{2}, that is:

Methods exist for the meta-analysis of studies that combine a mix of log-transformed and non-transformed data.

Where the values for each parameter (mu and sigma) were available from the studies, along with corresponding CIs/SEs, these were extracted as reported. In the remaining studies, the values were calculated where possible from the information presented.

The mu and sigma parameters of the original lognormal distribution were calculated as:

where ^{2}), and

Similarly, upper and lower CIs of mu and sigma were found by substituting the upper and lower bounds of the mean or SD (from the original scale) into the equation above, one at a time, while holding the value for the other parameter constant (as the point estimate for that parameter).

Where studies reported the results as the mean and 95th percentile on the original scale, the ‘lognorm’ package in R was used to calculate the original values of mu and sigma and corresponding SEs or CIs.

For studies reporting CIs, the SE was calculated as (upper bound – lower bound)/(2×1.96). Finally, for studies reporting the parameters relative to a referent value, the SE was calculated as:

where SE^{1} and SE^{2} are the SEs of the estimate of the referent category and coefficient, respectively.

A random effects meta-analysis was conducted in RStudio V.1.2.5033,^{2} statistic and investigated by conducting subgroup analyses of the data set.

The mean and SD of the pooled estimate were converted to the original (ie, non-log transformed) scale as:

The upper and lower CIs were found by substituting, one at a time, the upper and lower bounds for mu and sigma and recalculating the subsequent figures for mean and SD.

The resulting distribution was plotted using the ‘ggplot2’ package in R.

Finally, an R Shiny app was created which allows the meta-analysis estimates to be updated as new data become available.

After initial search and selection of relevant papers and removing duplicates, 24 studies were available for appraisal.

Two papers were removed as they dealt with specific cohorts of cases—young adults

One study was removed since only the abstract was in English and there was not enough detail to extract the relevant results.

Several papers were removed since they contained insufficient data or method description to facilitate their inclusion:

One study was removed since there was not enough detail in the paper to determine whether new parameters were being estimated or whether the parameters quoted were input values for their model.

Seven papers were removed since the data were largely descriptive, with no CIs reported.

One study was removed because the error terms associated with the mean, median and percentiles were not reported and there was not enough information presented to recover the parameters of the lognormal distribution.

One study was removed

Of the shortlisted studies (n=11), six reported lognormal distributions as best fitting the data.

The final two studies reporting a Weibull

Study size and extracted data for the lognormal mu and sigma parameters from the nine studies that were used for meta-analysis

Author | n | Publication status | Location | Observation period | Mean | 97.5th | Lognormal parameters used in meta-analysis | |||

Mu | SE | Sigma | SE | |||||||

Backer | 88 | PR | Chinese and international—travellers from Wuhan | 20–28 January | 6.4 | 11.1 | 1.796 | 0.077 | 0.349 | 0.045 |

Lauer | 181 | PR | Chinese and international - travellers from known affected areas | 4 January to | 5.5 | 11.5 | 1.621 | 0.064 | 0.418 | 0.069 |

Li | 10 | PR | Early cases in Wuhan | 1 December to | 5.2 | 12.5** | 1.425 | 0.240 | 0.669 | 0.141 |

Bi | 183 | PR | Shenzhen—travellers from Wuhan | 14 January to | 4.8* | 14.0 | 1.570 | 0.245 | 0.650 | 0.167 |

Jiang | 40 | PP | Location unclear | 14 December to | 4.9 | 9.7** | 1.530 | 0.066 | 0.464 | 0.046 |

Linton | 158 | PR | Cases external to Wuhan | Start of epidemic until 31 January | 5.6 | 10.8** | 1.611 | 0.070 | 0.472 | 0.048 |

Zhang | 49 | PR | China—provinces other than Hubei | Start of epidemic until 27 February | 5.2 | 10.5** | 1.540 | 0.092 | 0.470 | 0.072 |

Ma | 587 | PP | Multiple countries including China | Not specified | 7.4 | 17 | 1.857 | 0.024 | 0.547 | 0.023 |

Leung | 61† | PR | China—provinces other than Hubei | 10 January to | 7.2 | 14.6 | 1.780 | 0.353 | 0.680 | 0.248 |

*Median, **95th percentile

†Inferred from data reported.

PP, preprint, not peer reviewed; PR, published, peer reviewed.

Quality assessment (

The initial pooled estimate of mu from this data set (ie, data set 1, n=8 studies) was 1.66 (1.55, 1.76) and the pooled estimate of sigma was 0.48 (0.42, 0.54). The I^{2} values were 75% and 56% for mu and sigma, respectively. Egger’s tests for mu and sigma were not statistically significant; p=0.31 and p=0.20 for mu and sigma, respectively. However, evaluation of the funnel plots (^{2} values were 75% and 24% for mu and sigma, respectively.

Forest plot of the random effects (RE) meta-analysis of mu parameter of the lognormal distribution of incubation period.

Forest plot of the random effects (RE) meta-analysis of sigma parameter of the lognormal distribution.

Probability density function of the pooled lognormal distribution of reported incubation period with mu=1.63 and sigma=0.50.

Cumulative distribution function of pooled lognormal distribution. Each possible combination of values between the 95% CIs of mu and sigma is plotted as single black lines.

Percentiles of the pooled lognormal distribution after simulating all possible combinations of mu and sigma within the 95% CIs of the pooled estimates of both parameters

Percentile | Median (days) | Min | Max | Difference (max − min) |

2.5th | 1.92 | 1.54 | 2.38 | 0.84 |

5th | 2.24 | 1.83 | 2.75 | 0.92 |

10th | 2.69 | 2.24 | 3.23 | 0.99 |

25th | 3.64 | 3.12 | 4.25 | 1.13 |

50th | 5.10 | 4.53 | 5.75 | 1.22 |

75th | 7.15 | 6.13 | 8.34 | 2.21 |

90th | 9.69 | 8.06 | 11.60 | 3.54 |

95th | 11.60 | 9.49 | 14.20 | 4.71 |

97.5th | 13.60 | 10.9 | 16.90 | 6.00 |

The median days for each percentile are shown along with the minimum and maximum values for that percentile.

Cumulative distribution function of pooled lognormal distribution for incubation period and original input studies.

Probability density function of pooled lognormal distribution for incubation period and studies (n=2) not included in the meta-analysis because of the distribution used.

For the purpose of this study we defined incubation period as the time in days from the point of COVID-19 exposure to the onset of symptoms.

By definition, the required case data for the determination of individual incubation periods need to include both exposure (window) and onset of symptoms. Precisely estimating these events can be difficult. Symptom onset is based on case recall, whereas exposure is determined either from: movement history, thereby providing a window prior to movement of potential exposure, or a known window of exposure (from earliest to latest) to a confirmed case (close contact). However, exposure and/or symptom onset are rarely observed exactly. The methods used to deal with this include restricting the analysis to data from patients where the exposure window could be narrowed to a short window (eg, <3 days); taking a median point from the exposure window to determine the exposure time point. Alternatively, Linton

After the initial meta-analysis we decided to remove the Backer ^{2} values drop to 0% for both parameters. The corresponding mean and median are 5.48 and 4.85 days, respectively. Interestingly, removing this study also increases the precision of the estimate of the value for mu.

One of the weaknesses of our approach is that we extracted and analysed the parameters of the lognormal distribution independently. However, in reality the parameters and the initial distribution that they are fitted to are linked. We were unable to include two studies that did not fit lognormal distributions to the data. However,

It is worth noting that the parameter values from our meta-analysis are somewhat higher than previously used in modelling studies. For example, Ferguson

It is reasonable to assume that the incubation period estimated here should be relatively generalisable across different populations: unlike parameters such as serial interval, for example, incubation period depends only on the interaction between the virus and the host, which is expected to be similar across populations, and not on behavioural factors such as frequency of contacts which might be expected to vary across different countries. However, there is potential for a number of biases in these data which may impact on their external validity: in order to accurately estimate incubation period, it is possible that well-characterised cases may be preferentially chosen to reduce the impact of prolonged exposure windows. It is possible that such cases could be biased towards more severe cases. In that case, the estimate for incubation period could be biased downwards, since it is possible that the incubation period could be shorter in more severely affected individuals. Furthermore, these well-characterised cases (ie, those cases where exposure windows and dates of symptom onset are determined with a high degree of certainty) may not have been representative of all cases (often male, often younger

Based on available evidence, we find that the incubation period distribution may be modelled with a lognormal distribution with pooled mu and sigma parameters of 1.63 (1.51, 1.75) and 0.50 (0.45, 0.55), respectively. It should be noted that uncertainty increases towards the tail of the distribution (

@AndyByrneSci, @MiriamC51755360

CM conducted the eligibility screening of shortlisted studies, extracted the data and conducted the analysis with input from all authors. ÁC, KH and FB conducted the initial literature searches. CM and SJM completed the initial drafts of the manuscript. MG and LO reviewed the statistical methods. All authors (CM, ÁC, KH, AB, AWB, FB, MC, JG, EL, DM, PW, MG, LO, SJM) read and approved the final manuscript.

The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

All authors have completed the ICMJE uniform disclosure form at

Not required.

Not commissioned; externally peer reviewed.

All data relevant to the study are included in the article or uploaded as supplementary information. The data for the meta-analyses conducted are included in the manuscript.