  We study the Susceptible-Infected-Recovered model in complex networks,
considering that not all individuals in the population interact in the same way
between them. This heterogeneity between contacts is modeled by a continuous
disorder. In our model the disorder represents the contact time or the
closeness between individuals. We find that the duration time of an epidemic
has a crossover with the system size, from a power law regime to a logarithmic
regime depending on the transmissibility related to the strength of the
disorder. Using percolation theory, we find that the duration of the epidemic
scales as the average length of the branches of the infection. Our theoretical
findings, supported by simulations, explains the crossover between the two
regimes.
