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

Abstract

considering that not all individuals in the population interact in the same way. Thisheterogeneity between contacts is modeled by a continuous disorder. In our model, thedisorder represents the contact time or the closeness between individuals. We find thatthe duration time of an epidemic has a crossover with the system size, from a power-lawregime to a logarithmic regime depending on the transmissibility related to the strength ofthe disorder. Using percolation theory, we find that the duration of the epidemic scales asthe average length of the branches of the infection. Our theoretical findings, supported bysimulations, explains the crossover between the two regimes.