Authors’ response: Estimating the generation interval for COVID-19 based on symptom onset data

Abstract

To the editor: We are grateful for the comments provided by S. Bacallado, Q. Zhao and N. Ju [1]. With this reply we wish to clarify the concerns that were raised and provide some more insights. Assumption of independence between incubation period and generation time By expressing the density of the serial interval Z i as a convolution of X i and Y i , we indeed make the simplifying assumption that the incubation period of the infector, v (i) , is independent of the generation time X i = t i − t v(i). The possible correlation between the incubation period of the infector and the generation time should be taken into account. Ideally, both should be estimated from the same data. Unfortunately, we did not have these data directly available. Instead we assumed these quantities to be independent and we acknowledge that this assumption may not be realistic. However, to the best of our knowledge, the literature does not yet report clear indications of a strong relation between infectiousness and incubation period for coronavirus disease (COVID-19), with highly varying findings between studies [1]. It should be kept in mind that if our assumption of independence is not valid, our model is mis-specified as the convolution Z = X + Y is defined for independent random variables. Liu et al. [3] have investigated the impact of correlation between incubation period and serial interval on estimates of presymptomatic transmission. They found that, in the presence of active case finding and assuming a mean serial interval of 4.8 days and mean incubation period of 5.2 days, the percentage of pre-symptomatic transmission was 48% when assuming no correlation, ranging from 38% under positive correlation to 47% under negative correlation. Our estimate of the proportion of presymptomatic transmission in Singapore (i.e. 48%; where the mean serial interval was 5.21 days when allowing only positive serial intervals and assuming a mean incubation period of 5.2 days) is in line with these estimates, with the credible interval (32-67%) also covering the lower estimate.