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

In Figs 1 and 2 we show the evolution over time of the mean forward and backward 208 generation times in a population of size N = 1000, respectively, for R 0 = 1.5, 2, 3, 4, 5 209 and for the infectious period distributions specified before. The mean forward 210 generation interval contracts as the reproduction number increases but still slightly even 211 for low values of the reproduction number. In the backward observation, the generation 212 time shows an increasing trend that is steeper for high value of the reproduction number 213 and for higher variance of the infectious period. The evolution over time for both the 214 forward and the backward generation intervals show a similar pattern for the different 215 infectious period distributions though we notice that a higher variability is observed for 216 scenarios in which the infectious period distribution has larger variance. Lastly, we observe that the different population sizes do not affect considerably the 217 average value of the forward and backward generation time (Table 1 ). In Fig S5 we show 218 that also the evolution over time is similar for the different sizes considered in the paper. 219 Results reported in Table 2 show that when the reproduction number increases, also 226 the number of generations affected by competition and the mean number of competitors 227 increase. Furthermore, p c is stable for the tested population size, while the depletion 228 intensity is more accentuated in small population. Average values of the proportion of generations affected by competition (p c ), the mean number of competitors (µ c ) and the depletion intensity (ϕ). In the vaccination scenario individuals are vaccinated at a precise time during the 238 epidemic. In Table 3 Average values of duration (T max ), final size (F S), mean forward (ω f ) and mean backward (ω b ) generation times together with the proportion of generations affected by competition (p c ), mean number of competitors (µ c ) and depletion intensity (ϕ).