key: cord-0991100-8xqra1sj authors: Ejima, K.; Kim, K. S.; Ludema, C.; Bento, A. I.; Iwanami, S.; Fujita, Y.; Ohashi, H.; Koizumi, Y.; Watashi, K.; Aihara, K.; Nishiura, H.; Iwami, S. title: Estimation of the incubation period of COVID-19 using viral load data date: 2020-06-19 journal: nan DOI: 10.1101/2020.06.16.20132985 sha: e6cec7b09ee31f1bd9c04d8f9a826d0cf5dfb93c doc_id: 991100 cord_uid: 8xqra1sj The incubation period, or the time from infection to symptom onset of COVID-19 has been usually estimated using data collected through interviews with cases and their contacts. However, this estimation is influenced by uncertainty in recalling effort of exposure time. We propose a novel method that uses viral load data collected over time since hospitalization, hindcasting the timing of infection with a mathematical model for viral dynamics. As an example, we used the reported viral load data from multiple countries (Singapore, China, Germany, France, and Korea) and estimated the incubation period. The median, 2.5, and 97.5 percentiles of the incubation period were 5.23 days (95% CI: 5.17, 5.25), 3.29 days (3.25, 3.37), and 8.22 days (8.02, 8.46), respectively, which are comparable to the values estimated in previous studies. Using viral load to estimate the incubation period might be a useful approach especially when impractical to directly observe the infection event. 2 Author contributions: Conceived and designed the study: KE HN SI. Analysed the data: KE KSK SI. 25 Wrote the paper: KE KSK CL AIB SI YF YI HO YL KW KA HS SI. All authors read and approved the 26 final manuscript. 27 . 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 19, 2020. . https://doi.org/10.1101/2020.06.16.20132985 doi: medRxiv preprint 3 Abstract (144/250) 28 The incubation period, or the time from infection to symptom onset of COVID-19 has been usually estimated 29 using data collected through interviews with cases and their contacts. However, this estimation is influenced 30 by uncertainty in recalling effort of exposure time. We propose a novel method that uses viral load data 31 collected over time since hospitalization, hindcasting the timing of infection with a mathematical model for 32 viral dynamics. As an example, we used the reported viral load data from multiple countries (Singapore, China, 33 Germany, France, and Korea) and estimated the incubation period. The median, 2.5, and 97. 5 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 19, 2020. . https://doi.org/10.1101/2020.06.16.20132985 doi: medRxiv preprint The current COVID-19 outbreak is characterized by a longer incubation period (i.e., time from 45 infection to symptom onset) than that of influenza and other respiratory viruses. The median incubation period 46 of COVID-19 is estimated as 5 to 6 days (1-4), while that of influenza A and B and SARS-CoV-1 are 1.4, 0.6 47 and 4.0 days, respectively (5) . 48 Estimating the incubation period is challenging, because we rarely directly observe the time of 49 infection or the time of symptom onset (examples to the contrary in HIV infection show the intense follow up 50 needed to observe these events (6, 7)). The first study estimating the incubation period of SARS-CoV-2 was 51 Li (4), where they fit a log-binomial model to a subset of cases where detailed information about their exposure 52 to another case was available. Another set of early studies used information from cases that were identified 53 outside of Hubei province (1-3) to estimate the incubation period. In these studies, the time of exposure was 54 inferred using the duration of travel to Wuhan. Bi et al (4) added considerably to this literature by estimating 55 the incubation period from contact-based surveillance in which all the contacts of identified cases were tested 56 prospectively and a more complete chain of transmission could be documented. 57 However, even with meticulous contact tracing effort, directly observing infector-infectee pairs is a 58 time-consuming process, especially when the incubation period is lengthy. Measuring the incubation period 59 through contact tracing is more difficult if the infector-infectee pair had a lot of contact with each other, 60 leading to a wide range of tracing among suspected individuals. Indeed, Bi et al, demonstrated large 61 uncertainly (the interval of exposure was more than 10 days for about 25% of the cases) on the timing of 62 infection for COVID-19 in China (4). Although a majority of these studies (1, 2, 4) use a statistical modeling 63 technique that accounts for uncertainty both in the reports of exposure time and the time of symptom onset 64 (8), they had to inherently use a heuristic weight function for the censored information. 65 Here we propose another approach to estimate the incubation period, where we use longitudinal data 66 on viral load and hindcast the point of initial infection. Viral load data were collected at the early stage of the 67 epidemic for clinical purposes (e.g., understanding the aetiology and the pathophysiology of COVID-19) and 68 to ensure patients were no longer shedding virus (or more precisely, viral fragments) before hospital discharge. 69 . 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 19, 2020. . https://doi.org/10.1101/2020.06.16.20132985 doi: medRxiv preprint 5 The data were analysed using a mathematical model that describes the viral dynamics, which typically draw 70 a bell-shaped curve (i.e., viral load increases exponentially first until the peak where it starts declining). 71 Although the data are available only after the onset of symptoms, the timing of infection can be estimated by 72 hindcasting the model for each case. 73 74 We extracted the viral load data reported in five papers. Figure 1 shows the timing of infection for 76 each case estimated from viral load data using the virus dynamics model. The peak of viral load appears after 77 2-3 days from symptom onset. The AICs of the three models (log-normal, gamma, the Weibull distributions) 78 were, 10014.3, 10410.5, 12071.0, respectively. Thus, the lognormal distribution was preferred. The strength of this approach is that it can complement limitations that classical interview-based 90 approach has pertained to ascertain the exposure event. Our proposed approach may be applicable not only to 91 the human infectious disease and zoonoses such as influenza and COVID-19, but to animal/livestock 92 infectious diseases such as foot and mouth disease when contact recall is not possible. 93 We note that there are several studies proposed statistical approach to estimate the incubation period 94 using observed biomarkers, especially for HIV/AIDS. Shi et al. and Geskus used CD4 counts to estimate the 95 incubation period as well as residual time (i.e., time from AIDS diagnosis to current time)(9, 10). The 96 . 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 19, 2020. we used in this study did not include detailed immune response or antiviral effects given limited information. 102 The proposed approach requires collection of viral loads over time since symptom onset, which might not be 103 feasible for all patients or in resource limited contexts. Additional diagnostic testing methods are presently 104 developed to measure SARS-CoV-2 viral load in saliva, which would ease the process and mitigate the risk 105 of infection of those involved in collecting the samples(11, 12). 106 Valid estimation of incubation period is essential to mitigate risk by simplifying the process of contact 107 tracing and understanding the role pre-symptomatic infection. Unifying the proposed approach with existing 108 epidemiological methods, precise determination of the length of quarantine will be achieved. 109 110 Data 112 The viral load data from five previously published papers among hospitalized COVID-19 patients were 113 used (13-17). All cases used in our analysis presented symptoms before or after hospitalization. For 114 consistency, the viral load data from upper respiratory specimens were used in the analysis. The cases treated 115 with antivirals or with less than two data points were excluded. For all the studies from which we extracted 116 data, ethics approval was obtained from the ethics committee at each institute. Written informed consent was 117 obtained from the cases or their next of kin in the original studies. We summarized the data in Table 1 . A mathematical model for virus dynamics to estimate the day of infection establishment 120 The virus and its target cell dynamics are described by a mathematical model previously proposed 121 in (13, 18, 19 ). 122 . 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 19, 2020. calculation, using dataset when the viral load reaches the threshold. The viral load threshold for infection 131 establishment was estimated using the data of three cases whose primary cases and exposure history is known 132 (thus the day of infection establishment is known)(15), in which the start day of exposure is assumed to be 133 equal to the day of infection event. To address the uncertainty of the estimation, we resampled 100 parameter 134 sets for each individual and obtained corresponding 100 of inf . 135 136 Incubation period estimation The estimated incubation periods, inf , were fitted to three parametric distributions: Weibull, gamma, and log-138 normal distributions. Comparing the Akaike Information Criteria (AIC) for those three distributions, the best 139 model (i.e., with lowest AIC) was used for further analyses. The parametric bootstrap method was employed 140 to assess the parameter uncertainty. Specifically, the bootstrap sample was generated by resampling with 141 replacement from the all estimated inf . The proposed parametric models (i.e., Weibull, gamma, and log-142 normal distributions) were fitted to the bootstrapped data for parameter inference. We repeated this process 143 1000 times and obtained 1000 parameter sets, and the median, 2.5, and 97.5 percentiles of the distribution are 144 computed. 145 146 Viral load threshold for infection establishment 147 . 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 19, 2020. . 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 19, 2020. Gapfund Program (to S.I.); Foundation for the Fusion Of Science and Technology (to S.I.). 178 . 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 19, 2020. . https://doi.org/10.1101/2020.06.16.20132985 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 19, 2020. . https://doi.org/10.1101/2020.06.16.20132985 doi: medRxiv preprint The Incubation Period of Coronavirus Disease Publicly Reported Confirmed Cases: Estimation and Application. 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The Lancet Infectious Diseases Quantifying the effect of Vpu on the promotion of HIV-1 replication in the 218 humanized mouse model Modelling viral and immune system dynamics 179 The authors declare that they have no competing interests. 180 181 182 .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 19, 2020.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 19, 2020. 224 . 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 19, 2020. . https://doi.org/10.1101/2020.06.16.20132985 doi: medRxiv preprint