Two golden times in two-step contagion models: A nonlinear map approach

Wonjun Choi, Deokjae Lee, J. Kertész, B. Kahng

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

The two-step contagion model is a simple toy model for understanding pandemic outbreaks that occur in the real world. The model takes into account that a susceptible person either gets immediately infected or weakened when getting into contact with an infectious one. As the number of weakened people increases, they eventually can become infected in a short time period and a pandemic outbreak occurs. The time required to reach such a pandemic outbreak allows for intervention and is often called golden time. Understanding the size-dependence of the golden time is useful for controlling pandemic outbreak. Using an approach based on a nonlinear mapping, here we find that there exist two types of golden times in the two-step contagion model, which scale as O(N1/3) and O(Nζ) with the system size N on Erdos-Rényi networks, where the measured ζ is slightly larger than 1/4. They are distinguished by the initial number of infected nodes, o(N) and O(N), respectively. While the exponent 1/3 of the N-dependence of the golden time is universal even in other models showing discontinuous transitions induced by cascading dynamics, the measured ζ exponents are all close to 1/4 but show model-dependence. It remains open whether or not ζ reduces to 1/4 in the asymptotically large-N limit. Our method can be applied to several models showing a hybrid percolation transition and gives insight into the origin of the two golden times.

Original languageEnglish
Article number012311
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume98
Issue number1
DOIs
StatePublished - 19 Jul 2018

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