key: cord-0741114-f9e10fow
authors: Prete, C. A.; Buss, L.; Porto, V. B.; da Silva Candido, D. A.; Ghilardi, F.; Dighe, A.; Donnelly, C. A.; Pybus, O.; Brady, O. J.; de Oliveira, W. K.; Croda, J. H. R.; Faria, N. R.; Sabino, E. C.; Nascimento, V. H.
title: Serial Interval Distribution of SARS-CoV-2 Infection in Brazil
date: 2020-06-12
journal: nan
DOI: 10.1101/2020.06.09.20127043
sha: a01219989558c14525ea21997efd47c3076ac1a6
doc_id: 741114
cord_uid: f9e10fow

Using 65 transmission pairs of SARS-CoV-2 reported to the Brazilian Ministry of Health we estimate the mean and standard deviation for the serial interval to be 2.97 and 3.29 days respectively. We also present a model for the serial interval probability distribution using only two parameters.

The severe acute respiratory syndrome novel coronavirus 2 (SARS-CoV-2) first emerged in China in December 2019 [1] and was declared a pandemic by the World Health Organization on 11 th March 2020. The transmission dynamics, such as the serial intervalthe time between symptom onset in a primary case and their secondary cases in a chain of transmission [2] are still being established. The epidemic growth rate and the serial interval jointly determine the basic reproduction number [3] , and the existence of pre-symptomatic transmission can be inferred when the serial interval is shorter than the incubation period.

Data for this analysis were provided by the Brazilian Ministry of Health following ethical approval (CONEP protocol number 30127020.0.0000.0068). All confirmed cases of SARS-CoV-2 infection notified on the REDCap system between 25 th February and 19 th March were analyzed. We received the linked pairs data (suspected and primary case) by the Brazilian Ministry of Health. We measured the serial intervals by computing the difference of dates of symptom onset.

In our dataset there were four negative serial intervals (symptom onset in the infectee preceded the infector) and seven zero-valued serial intervals (symptom onset on the same day for the infector-infectee pair). The mean (standard deviation) was 2.97 (3.29) days with a median of 3 days.

It is common to censor observed serial intervals to include only positive values; however, there is no strong theoretical justification for this. As such, we fit a serial interval probability distribution that allows for negative values by modelling the serial interval as Serial Interval = ⌊ inf,1 + Δ lat,1 + Δ lat,2 + Δ int,2 ⌋ − ⌊ inf,1 + Δ lat,1 + Δ int,1 ⌋, . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.09.20127043 doi: medRxiv preprint where ⌊⋅⌋ is the floor operator, inf,1 is a random variable uniformly distributed in the interval [0,1], (Δ lat,1 , Δ lat,2 ) are independent and identically distributed (i.i.d.) chi-squared random variables of mean 2.79 days and (Δ int,1 , Δ int,2 ) are i.i.d. chi-squared random variables of mean 1.31 days. See the Supplemental Material for theoretical motivation and method. Figure 1 shows the comparison between the measured and modelled serial intervals as well as means ± standard deviations for a number of serial interval probability distributions presented in the literature [4] [5] [6] [7] [8] [9] . We conclude that our proposed model for the serial interval probability distribution approximates well the serial intervals measured from data.

In addition, we provide two other analyses of the data in the Supplemental Material in which we i.) fit a normal distribution, and ii.) censor the data to include only positive values, best fit by a lognormal distribution.

The mean serial interval in Brazil of 2.97 days is the shortest reported to our knowledge, but we emphasize that the serial interval is not usually concentrated around the mean due to its high standard deviation (3.29 days) and non-symmetry. Du et al. [4] took an alternative approach fitting a normal distribution to 468 publicly reported serial intervals in which 12% had negative valuessee Supplemental Material for comparison with our raw data. 8.38% of the measured serial intervals are negative, which is allowed by our model. Negative serial intervals are described in the literature [2] and can occur with pre-symptomatic transmission, and a wide range for the incubation periodthe classical example being HIV.

In two transmissions clusters in Tianjin and Singapore the mean incubation periods were 9.0 and 7.1 days, respectively [5] . Our serial interval estimate is shorter than the reported incubation period, implying that the infectious period for SARS-CoV-2 begins before symptom onset. This . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.09.20127043 doi: medRxiv preprint is in line with recent observations of a large proportion of undocumented infections, complicating containment of the virus [10] .

Our estimates are based on national case notification data, and this is a strength compared to datasets complied solely from media reports. However, there are at least two important sources of bias. Firstly, there is a tendency for secondary cases to recall more recent contactsrecency or recall biasresulting in a shorter estimate of the serial interval. Similarly, contact tracing is likely to be most effective for recent contacts. Secondly, self-isolation following symptom onset will remove longer serial intervals that would have occurred due to transmission during the symptomatic phase. This second point highlights the role of contextual factorsisolation practices, population density, location of transmission, proportion of the population infected etc.

in determining the serial interval, which is not simply a biological constant of the virus. Given this consideration, it is important generate multiple estimates in different locations and stages of the epidemic. Our report is valuable as the first estimate from Brazil, and Latin America more generally.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.09.20127043 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.09.20127043 doi: medRxiv preprint

The Interval between Successive Cases of an Infectious Disease

How generation intervals shape the relationship between growth rates and reproductive numbers

The serial interval of COVID-19 from publicly reported confirmed cases

Transmission interval estimates suggest presymptomatic spread of COVID-19

Serial interval of novel coronavirus (2019-nCoV) infections. Infectious Diseases (except HIV/AIDS)

Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia

Epidemiologic characteristics of early cases with 2019 novel coronavirus (2019-nCoV) disease in Republic of Korea

Estimating the serial interval of the novel coronavirus disease (COVID-19): A statistical analysis using the public data in Hong Kong from

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

The authors declare no conflict of interest.. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.09.20127043 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2020. . https://doi.org/10.1101/2020.06.09.20127043 doi: medRxiv preprint