Crossover from weak to strong disorder regime in the duration of epidemics

We study the susceptible–infected–recovered (SIR) model in complex networks, considering that not all individuals in the population interact in the same way. 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.