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

作者：Choi Wonjun; Lee Deokjae; Kertesz J; Kahng B^*

来源：PHYSICAL REVIEW E, 2018, 98(1): 012311.

DOI：10.1103/PhysRevE.98.012311

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 (N-1/3) and O (N-zeta) with the system size N on Erdos-Renyi networks, where the measured zeta 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 zeta exponents are all close to 1/4 but show model-dependence. It remains open whether or not zeta 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.

• 出版日期2018-7-19