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

TL;DR

This paper investigates how the duration of epidemics in complex networks transitions from a power-law to a logarithmic scaling with system size, influenced by contact heterogeneity modeled as disorder.

Contribution

It introduces a model incorporating continuous disorder to represent contact heterogeneity and explains the epidemic duration crossover using percolation theory.

Findings

Epidemic duration exhibits a crossover from power-law to logarithmic scaling.

The crossover depends on the transmissibility related to contact heterogeneity.

Theoretical results are supported by simulation data.

Abstract

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.