Our analyses have provided quantitative support for the long-held belief that the serial interval of pertussis is long, in the order of several weeks (Anderson and May, 1992 and Vynnycky and White, 2010). Our results have furthermore uncovered significant differences in the time scales of particular transmission events in the household. Specifically, while for most transmission routes the mean of the generation interval is approximately 19 days (95%CI: 15–21 days), an infection of the infant by the father or a sibling typically takes more than a week longer (28 days; 95%CI: 23–33 days). These differences are statistically significant and the means of the serial interval distributions can be estimated with fair precision. However, it should be noted that the estimated variances are large. As a consequence, variability in individual serial intervals can be substantial (Fig. 2).
A number of key assumptions need scrutiny. First, we have based the analyses on a method that has been widely used to estimate serial intervals (Hens et al., 2012, te Beest et al., 2013 and Vink et al., 2013). The method is intuitively appealing, but makes the simplifying assumption that the time to infection of a susceptible person does not depend on the number of infectious persons in the household in the at-risk period. In other words, there is no competition between infectious persons for infection of susceptible persons, and we assume that the phenomenon called generation interval contraction plays a minor role (Svensson, 2007, Kenah et al., 2008 and Kenah, 2011). This was done in order to avoid introduction of estimands such as the latent period (i.e. the period from infection to a person becoming infectious) and the incubation period (i.e. the period from infection to onset of symptoms) that cannot be estimated directly from the data. As a consequence, our finding that infection of the infant by the father or a sibling takes longer than transmission through other pathways may be attributable to fathers and siblings being less infectious to their children than mothers (i.e. having less or less intense contacts, having lower bacterial loads, or both), to fathers/siblings having a more prolonged latent period than mothers, or to fathers/siblings becoming symptomatic earlier after infection than mothers. If direct evidence were available on the infectiousness over time of infected persons (e.g., by bacterial culturing or PCR of tracheal swabs), one could envisage meaningful extensions of the methods employed here to relate the onset of symptoms to the moment of infection and the onset of the infectious period (Kenah, 2011 and Cauchemez and Ferguson, 2012).
Second, the analyses are based on the premise that serial interval durations are independent of the households in which the transmission events occur. In essence, this amounts to assuming that there is no household clustering of serial interval durations, i.e. some households having shorter serial interval...