Spreading Phenomena - Chapter 10
Consider the problem of the propagation of an SIS infection in two types of networks: An aggregated network , constructed by summing all contacts over the course of a week. A temporal network , in which each contact occurs only at the moment when it was recorded. The figure below shows the fraction of infected individuals I(t) over time in each network. The structural and epidemiological parameters are: Aggregated network : average degree \( \langle k \rangle = 12 \) second moment \( \langle k^2 \rangle = 260 \) Temporal network : effective average degree \( \langle k_{\text{eff}} \rangle = 5 \) effective second moment \( \langle k_{\text{eff}}^2 \rangle = 40 \) Model rates: transmission \( \beta = 0.04 \) recovery \( \mu = 0.02 \) Consider the approximate epidemic threshold for general networks: \[ \lambda_c = \frac{\mu}{\beta}\,\frac{\langle k\rangle}...