Spatial epidemiology of networked metapopulation: An overview

Lin WANG; Xiang Li

The Zipf's law and the Heaps' law are two representative scaling laws that usually emerge together in various complex systems, however, their joint emergence has hardly been clarified [72] . Using the data of laboratory confirmed cases of SARS, H5N1, and A(H1N1) to analyze the joint emergence of these two scalings in the evolution process of large-scale geographic transmissions, Wang et al. [70] unraveled a universal feature that the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial stage of an outbreak, while a crossover comes with their incoherence later before reaching a stable state, where the Heaps' law still presents with the wane of the strict Zipf's law. With the census populations and domestic air transportation data of the United States (US) [73, 74] , a data-driven metapopulation network model on the US country level is developed to analyze the evolution patterns of scaling emergence. In contrast with a random reshuffled model with a homogeneous structure, the data-driven heterogeneous metapopulation successfully reproduced the scaling transitions observed in the real-world pandemics. This demonstrates that the high-level heterogeneity of infrastructure plays a key role in characterizing the spatial transmission of infectious diseases, which also provides a new insight to clarifying the interdependence between the Zipf's and Heaps' scaling laws.