Measurability of the epidemic reproduction number in data-driven contact networks

Liu, Quan-Hui; Ajelli, Marco; Aleta, Alberto; Merler, Stefano; Moreno, Yamir; Vespignani, Alessandro

Also, regarding T g evolution over time, the annealed configuration model and the annealed data-driven model show the same behavior as the homogeneous mixing model (see Fig. S10C ). The quenched configuration model shows a decrease of T g only immediately before the epidemic peak, when the number of individuals that are infectious at the same time is higher and thus the competition to find susceptible nodes to infect is also higher (Fig. S10C) . This is fairly different from the dynamics of the data-driven model that, mainly due to the consistently high competition in households, workplaces, and schools, shows a clear shortening of T g since the beginning of the epidemic (see Fig. S10C and D) . Similarly to what we saw for R(t), none of the T g(t) patterns observed for the data-driven model are present when the configuration is annealed (Fig. S10D) , although in the annealed data-driven model the contact structure is preserved. and of three null models for the scenario representing the spread of a "uncharacterized" future influenza pandemic in the Italian population. B As A, however R(t) is broken down in the four layers. C As A, but for T g(t). D As B, but for T g(t). Figure S11 shows the comparison between R(t) as inferred from the time-series of cases and as resulting from the microsimulation data of the transmission chain for two stochastic model realizations. Tg empirical distribution over time directly estimated from the transmission tree inferred from incidence data (mean, 95% CI) directly estimated from the transmission tree inferred from incidence data (mean, 95% CI) A B Figure S11 : A Daily R(t) as inferred from the daily incidence of new infections for one stochastic model realization. T g is assumed to be: exponentially distributed with average 3 days (top); the distribution of T g has been derived from the analysis of the transmission tree of the selected model simulation (middle); the distribution of T g over time as derived from the analysis of the transmission tree of the selected model simulation (bottom). B as A, but for another stochastic realization. The two stochastic realizations used to produce this figure as well as Fig. 5 of the main text are randomly selected among the simulations run for scenario "Uncharacterized future influenza pandemic in Italy".