Realized generation times: contraction and impact of infectious period, reproduction number and population size

Andrea Torneri; Amin Azmon; Christel Faes; Eben Kenah; Gianpaolo Scalia Tomba; Jacco Wallinga; Niel Hens

The simulated data are analyzed in R; generations resulting from the first n non-extinct simulations are merge together in a unique data file and we predict the value of a loess regression to express the evolution over time of mean forward or backward generation time. This analysis required a huge computational memory, limiting the number of simulations that can be considered. However, this R function allows us to construct a confidence interval to quantify the variability of the loess regression used. In Another important aspect in the loess regression is the considered span. The fitting is done locally and the considered neighbourhood of a point x is based on the value of the span, parameter that has to be given as input in the loess function. In S4 Fig we report the evolution over time of the mean forward generation time for R = 1.5 in the vaccination scenario for three different values of the span parameter: 0.5, 0.75(default value) and 1.5 in the case of exponential infectious period. The plot shows differences between the curves in the last part of the outbreak after the vaccination time where few generations are registered. This is probably due to the little number of generations that happen after the vaccination time. We want to remark that the result of contraction holds independently on the type of span considered. Lastly, we want to show the evolution over time of the mean forward generation time for different population sizes. In S5 Fig we report this quantity for population of size N = 100, 500 and 1000 in the case of exponential infectious period. We notice that one plot is the re-scaling of the others; the general evolution of the forward generation intervals is not affect by the population size. The same results apply for the backward generation interval.