Infection time

Given a realization of the infection process, for each m∈[0,|V|], let

The random variable t(m) denotes the first time in which at least m nodes are infected. Given a realization of the SI process on a time-varying network, let t(m) = ∞ for M>I(|T|). In what follows, the notation t_A(m) indicates that nodes on a specific network A are considered (e.g. A can be the friendship or the encounter network, even if the infection spreads on the encounter network).