Evolution of Scaling Emergence in Large-Scale Spatial Epidemic Spreading

Abstract

BackgroundZipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified.Methodology/Principal FindingsIn this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.Conclusions/SignificanceThe analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.

Statistical physics of vaccination

“…These networks include spatial network (whose nodes occupy a precise position in two or three-dimensional Euclidean space, and whose edges are real physical connections) [214][215][216][217], adaptive networks [218], temporal or time-varying networks [219][220][221] (for more details, please also see Section 11).…”

An environment aware epidemic spreading model and immune strategy in complex networks

“…However, they only considered the case of the network models with constant recruitment rate. Recently, there are a few studies on heterogeneous transmission rink [18][19][20][21][22][23][24]. In [18], Miller provided the analytical results of disease outbreaks in large random networks with heterogeneous susceptibility and infectivity, where the transmission of infections is addressed on static networks.…”

Avalanche duration time in a simple heterogeneous Olami–Feder–Christensen model

“…The criticality is characterized by a power-law distribution of the sizes of relaxation events without any fine tuning external parameters. SOC [3] has been empirically observed in diverse complex systems, e.g., fractal theory [4], chemical reactions [5], evolutionary population dynamics [6][7][8][9][10][11][12], forest burns [13], epidemics [14][15][16], heart attacks [17], market crashes [18], opinion formation [19], languages behavior [20], and more close of the topic in this article, earthquake [21][22][23][24][25].…”