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

• Published in: Physica A Vol. 391; no. 16; pp. 4181 - 4185
• Main Authors: Buono, C., Lagorio, C., Macri, P.A., Braunstein, L.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.08.2012
• Subjects: Complex systems; Crossovers; Disorder; Disorders; Epidemic; Epidemics; Heterogeneity; Networks; Percolation; Population (statistical); Simulation; Statistical mechanics; Epidemic; Percolation; Complex systems; Disorder
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2012.04.002

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. ► We study the behavior of the duration of a disease in presence of disorder. ► The duration of a disease goes as the length of the branches of the infection. ► The duration of a disease has a transition from a weak disorder regime to a strong disorder regime.