Common power laws for cities and spatial fractal structures

Mori, Tomoya; Smith, Tony; Hsu, Wen‐Tai

doi:10.1073/pnas.1913014117

Cited by 44 publications

(32 citation statements)

References 31 publications

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“…The system mimics the observed city size distribution which is fairly close to the Zipf law [20]. The random distribution of smaller cities is not entirely naturalistic, since evidence suggests that real cities are organised in a fractal pattern [21, 22]. A figure using a city distribution closer to a fractal can be found in the supplement.…”

Section: Resultsmentioning

confidence: 61%

COVID-19 superspreading in cities versus the countryside

Eilersen

Sneppen

2020

Preprint

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So far, the COVID-19 pandemic has been characterised by an initial rapid rise in new cases followed by a peak and a more erratic behaviour that varies between regions. This is not easy to reproduce with traditional SIR models, which predict a more symmetric epidemic. Here, we argue that superspreaders and population heterogeneity are the core factors explaining this discrepancy. We do so through an agent-based lattice model of a disease spreading in a heterogeneous population.We predict that an epidemic driven by superspreaders will spread rapidly in cities, but not in the countryside where the sparse population limits the maximal number of secondary infections. This suggests that mitigation strategies should include restrictions on venues where people meet a largenumber of strangers. Furthermore, mitigating the epidemic in cities and in the countryside may require different levels of restrictions.

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Section: Resultsmentioning

confidence: 61%

COVID-19 superspreading in cities versus the countryside

Eilersen

Sneppen

2020

Preprint

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“…Fostered by a recent deluge of highly-detailed city data, researchers from diverse disciplines such as geography, economics, or physics have devoted ongoing efforts in identifying and understanding fundamental principles and regularities underlying urban systems [ 1 , 6 , 12 – 14 ]. While most of these works are either concerned with Zipf’s law [ 15 – 25 ] or urban scaling [ 26 – 34 ], very few have tackled the relationship between both. Zipf’s law and urban scaling have mostly been studied independently because it is commonly assumed that both laws are independent descriptions of urban systems across countries.…”

Section: Introductionmentioning

confidence: 99%

Association between population distribution and urban GDP scaling

et al. 2021

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Urban scaling and Zipf’s law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about the connection between these two laws using population and GDP data from almost five thousand consistently-defined cities in 96 countries. We empirically demonstrate that both laws are tied to each other and derive an expression relating the urban scaling and Zipf exponents. This expression captures the average tendency of the empirical relation between both exponents, and simulations yield very similar results to the real data after accounting for random variations. We find that while the vast majority of countries exhibit increasing returns to scale of urban GDP, this effect is less pronounced in countries with fewer small cities and more metropolises (small Zipf exponent) than in countries with a more uneven number of small and large cities (large Zipf exponent). Our research puts forward the idea that urban scaling does not solely emerge from intra-city processes, as population distribution and scaling of urban GDP are correlated to each other.

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“…We revealed herein that the multifractal scaling of the population and Covid-19 cases operated over the same range of spatial scales. Power-law scaling was also reported for several properties of urban systems such as city sizes ( 32 ). Signatures of multifractal characteristics are routinely detected using the convexity of the so-called moment scaling function K ( q ) for moment order q .…”

Section: Resultsmentioning

confidence: 72%

A kernel-modulated SIR model for Covid-19 contagious spread from county to continent

Geng

Katul

Gerges

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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The tempo-spatial patterns of Covid-19 infections are a result of nested personal, societal, and political decisions that involve complicated epidemiological dynamics across overlapping spatial scales. High infection “hotspots” interspersed within regions where infections remained sporadic were ubiquitous early in the outbreak, but the spatial signature of the infection evolved to affect most regions equally, albeit with distinct temporal patterns. The sparseness of Covid-19 infections in the United States was analyzed at scales spanning from 10 to 2,600 km (county to continental scale). Spatial evolution of Covid-19 cases in the United States followed multifractal scaling. A rapid increase in the spatial correlation was identified early in the outbreak (March to April). Then, the increase continued at a slower rate and approached the spatial correlation of human population. Instead of adopting agent-based models that require tracking of individuals, a kernel-modulated approach is developed to characterize the dynamic spreading of disease in a multifractal distributed susceptible population. Multiphase Covid-19 epidemics were reasonably reproduced by the proposed kernel-modulated susceptible–infectious–recovered (SIR) model. The work explained the fact that while the reproduction number was reduced due to nonpharmaceutical interventions (e.g., masks, social distancing, etc.), subsequent multiple epidemic waves still occurred; this was due to an increase in susceptible population flow following a relaxation of travel restrictions and corollary stay-at-home orders. This study provides an original interpretation of Covid-19 spread together with a pragmatic approach that can be imminently used to capture the spatial intermittency at all epidemiologically relevant scales while preserving the “disordered” spatial pattern of infectious cases.

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Common power laws for cities and spatial fractal structures

Cited by 44 publications

References 31 publications

COVID-19 superspreading in cities versus the countryside

COVID-19 superspreading in cities versus the countryside

Association between population distribution and urban GDP scaling

A kernel-modulated SIR model for Covid-19 contagious spread from county to continent

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