scholarly journals Patterns of the COVID19 epidemic spread around the world: exponential vs power laws

2020 ◽  
Author(s):  
Natalia L. Komarova ◽  
Dominik Wodarz
Keyword(s):  
Power Law ◽  
Growth Pattern ◽  
Growth Dynamics ◽  
Power Laws ◽  
Epidemiological Data ◽  
Social Distancing ◽  
Spatially Distributed ◽  
Best Fitting ◽  
Epidemic Development ◽  
The Uk

AbstractWe have analyzed the COVID19 epidemic data of more than 174 countries (excluding China) in the period between January 22 and March 28, 2020. We found that some countries (such as the US, the UK, and Canada) follow an exponential epidemic growth, while others (like Italy and several other European countries) show a power law like growth. At the same time, regardless of the best fitting law, most countries can be shown to follow a trajectory similar to that of Italy, but with varying degrees of delay. We found that countries with “younger” epidemics tend to exhibit more exponential like behavior, while countries that are closer behind Italy tend to follow a power law growth. We hypothesize that there is a universal growth pattern of this infection that starts off as exponential and subsequently becomes more power law like. Although it cannot be excluded that this growth pattern is a consequence of social distancing measures, an alternative explanation is that it is an intrinsic epidemic growth law, dictated by a spatially distributed community structure, where the growth in individual highly mixed communities is exponential but the longer term, local geographical spread (in the absence of global mixing) results in a power-law. This is supported by computer simulations of a metapopulation model that gives rise to predictions about the growth dynamics that are consistent with correlations found in the epidemiological data. Therefore, seeing a deviation from straight exponential growth may not be a consequence of working non-pharmaceutical interventions (except for, perhaps, restricting the air travel). Instead, this is a normal course of raging infection spread. On the practical side, this cautions us against overly optimistic interpretations of the countries epidemic development and emphasizes the need to continue improving the compliance with social distancing behavior recommendations.

scholarly journals Patterns of the COVID-19 pandemic spread around the world: exponential versus power laws

2020 ◽  
Vol 17 (170) ◽  
pp. 20200518 ◽  
Author(s):  
Natalia L. Komarova ◽  
Luis M. Schang ◽  
Dominik Wodarz
Keyword(s):  
Power Law ◽  
Exponential Growth ◽  
Growth Pattern ◽  
Growth Dynamics ◽  
Power Laws ◽  
Epidemiological Data ◽  
Social Distancing ◽  
Spatially Distributed ◽  
The Usa ◽  
The Uk

We have analysed the COVID-19 epidemic data of more than 174 countries (excluding China) in the period between 22 January and 28 March 2020. We found that some countries (such as the USA, the UK and Canada) follow an exponential epidemic growth, while others (like Italy and several other European countries) show a power law like growth. Regardless of the best fitting law, many countries can be shown to follow a common trajectory that is similar to Italy (the epicentre at the time of analysis), but with varying degrees of delay. We found that countries with ‘younger’ epidemics, i.e. countries where the epidemic started more recently, tend to exhibit more exponential like behaviour, while countries that were closer behind Italy tend to follow a power law growth. We hypothesize that there is a universal growth pattern of this infection that starts off as exponential and subsequently becomes more power law like. Although it cannot be excluded that this growth pattern is a consequence of social distancing measures, an alternative explanation is that it is an intrinsic epidemic growth law, dictated by a spatially distributed community structure, where the growth in individual highly mixed communities is exponential but the longer term, local geographical spread (in the absence of global mixing) results in a power law. This is supported by computer simulations of a metapopulation model that gives rise to predictions about the growth dynamics that are consistent with correlations found in the epidemiological data. Therefore, seeing a deviation from straight exponential growth may be a natural progression of the epidemic in each country. On the practical side, this indicates that (i) even in the absence of strict social distancing interventions, exponential growth is not an accurate predictor of longer term infection spread, and (ii) a deviation from exponential spread and a reduction of estimated doubling times do not necessarily indicate successful interventions, which are instead indicated by a transition to a reduced power or by a deviation from power law behaviour.

scholarly journals Determining the optimal strategy for reopening schools, work and society in the UK: balancing earlier opening and the impact of test and trace strategies with the risk of occurrence of a secondary COVID-19 pandemic wave

2020 ◽  
Author(s):  
Jasmina Panovska-Griffiths ◽  
Cliff Kerr ◽  
Robyn Margaret Stuart ◽  
Dina Mistry ◽  
Daniel Klein ◽  
...  
Keyword(s):  
Large Scale ◽  
Reproduction Number ◽  
Epidemiological Data ◽  
Contact Tracing ◽  
Cumulative Number ◽  
Social Distancing ◽  
Uk Government ◽  
The Uk ◽  
The Impact ◽  
Pandemic Wave

Background In order to slow down the spread of SARS-CoV-2, the virus causing the COVID-19 pandemic, the UK government has imposed strict physical distancing (lockdown) measures including school 'dismissals' since 23 March 2020. As evidence is emerging that these measures may have slowed the spread of the pandemic, it is important to assess the impact of any changes in strategy, including scenarios for school reopening and broader relaxation of social distancing. This work uses an individual-based model to predict the impact of a suite of possible strategies to reopen schools in the UK, including that currently proposed by the UK government. Methods We use Covasim, a stochastic agent-based model for transmission of COVID-19, calibrated to the UK epidemic. The model describes individuals' contact networks stratified as household, school, work and community layers, and uses demographic and epidemiological data from the UK. We simulate a range of different school reopening strategies with a society-wide relaxation of lockdown measures and in the presence of different non-pharmaceutical interventions, to estimate the number of new infections, cumulative cases and deaths, as well as the effective reproduction number with different strategies. To account for uncertainties within the stochastic simulation, we also simulated different levels of infectiousness of children and young adults under 20 years old compared to older ages. Findings We found that with increased levels of testing of people (between 25% and 72% of symptomatic people tested at some point during an active COVID-19 infection depending on scenarios) and effective contact-tracing and isolation for infected individuals, an epidemic rebound may be prevented across all reopening scenarios, with the effective reproduction number (R) remaining below one and the cumulative number of new infections and deaths significantly lower than they would be if testing did not increase. If UK schools reopen in phases from June 2020, prevention of a second wave would require testing 51% of symptomatic infections, tracing of 40% of their contacts, and isolation of symptomatic and diagnosed cases. However, without such measures, reopening of schools together with gradual relaxing of the lockdown measures are likely to induce a secondary pandemic wave, as are other scenarios for reopening. When infectiousness of <20 year olds was varied from 100% to 50% of that of older ages, our findings remained unchanged. Interpretation To prevent a secondary COVID-19 wave, relaxation of social distancing including reopening schools in the UK must be implemented alongside an active large-scale population-wide testing of symptomatic individuals and effective tracing of their contacts, followed by isolation of symptomatic and diagnosed individuals. Such combined measures have a greater likelihood of controlling the transmission of SARS-CoV-2 and preventing a large number of COVID-19 deaths than reopening schools and society with the current level of implementation of testing and isolation of infected individuals.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals Impact of Relaxing Covid-19 Social Distancing Measures on Rural North Wales: A Simulation Analysis

2020 ◽  
Vol 8 ◽  
Author(s):  
Rhodri P. Hughes ◽  
Dyfrig A. Hughes
Keyword(s):  
Simulation Analysis ◽  
Model Averaging ◽  
Incidence Rates ◽  
Mortality Data ◽  
Rural Regions ◽  
Social Distancing ◽  
North Wales ◽  
The Uk ◽  
Sigmoidal Growth ◽  
Related Mortality

Background: Social distancing policies aimed to limit Covid-19 across the UK were gradually relaxed between May and August 2020, as peak incidences passed. Population density is an important driver of national incidence rates; however peak incidences in rural regions may lag national figures by several weeks. We aimed to forecast the timing of peak Covid-19 mortality rate in rural North Wales.Methods: Covid-19 related mortality data up to 7/5/2020 were obtained from Public Health Wales and the UK Government. Sigmoidal growth functions were fitted by non-linear least squares and model averaging used to extrapolate mortality to 24/8/2020. The dates of peak mortality incidences for North Wales, Wales and the UK; and the percentage of predicted mortality at 24/8/2020 were calculated.Results: The peak daily death rates in Wales and the UK were estimated to have occurred on the 14/04/2020 and 15/04/2020, respectively. For North Wales, this occurred on the 07/05/2020, corresponding to the date of analysis. The number of deaths reported in North Wales on 07/05/2020 represents 33% of the number predicted to occur by 24/08/2020, compared with 74 and 62% for Wales and the UK, respectively.Conclusion: Policies governing the movement of people in the gradual release from lockdown are likely to impact significantly on areas–principally rural in nature–where cases of Covid-19, deaths and immunity are likely to be much lower than in populated areas. This is particularly difficult to manage across jurisdictions, such as between England and Wales, and in popular holiday destinations.

scholarly journals Power Laws in Economics: An Introduction

2016 ◽  
Vol 30 (1) ◽  
pp. 185-206 ◽  
Author(s):  
Xavier Gabaix
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Power Laws ◽  
Economic Fluctuations ◽  
Formal Definition ◽  
Empirical Power

Many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. However a series of power laws in economics do count as true and nontrivial quantitative laws—and they are not only established empirically, but also understood theoretically. I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock market. I summarize some of the theoretical explanations that have been proposed. I suggest that power laws help us explain many economic phenomena, including aggregate economic fluctuations. I hope to clarify why power laws are so special, and to demonstrate their utility. In conclusion, I list some power-law-related economic enigmas that demand further exploration. A formal definition may be useful.

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

scholarly journals POWER LAWS IN REAL ESTATE PRICES DURING BUBBLE PERIODS

2012 ◽  
Vol 16 ◽  
pp. 61-81 ◽  
Author(s):  
TAKAAKI OHNISHI ◽  
TAKAYUKI MIZUNO ◽  
CHIHIRO SHIMIZU ◽  
TSUTOMU WATANABE
Keyword(s):  
Real Estate ◽  
Power Law ◽  
House Price ◽  
Power Laws ◽  
Cross Sectional ◽  
Price Distribution ◽  
Before And After ◽  
Real Estate Prices ◽  
Using Data ◽  
The U.S

How can we detect real estate bubbles? In this paper, we propose making use of information on the cross-sectional dispersion of real estate prices. During bubble periods, prices tend to go up considerably for some properties, but less so for others, so that price inequality across properties increases. In other words, a key characteristic of real estate bubbles is not the rapid price hike itself but a rise in price dispersion. Given this, the purpose of this paper is to examine whether developments in the dispersion in real estate prices can be used to detect bubbles in property markets as they arise, using data from Japan and the U.S. First, we show that the land price distribution in Tokyo had a power-law tail during the bubble period in the late 1980s, while it was very close to a lognormal before and after the bubble period. Second, in the U.S. data we find that the tail of the house price distribution tends to be heavier in those states which experienced a housing bubble. We also provide evidence suggesting that the power-law tail observed during bubble periods arises due to the lack of price arbitrage across regions.

Transmission dynamics and mechanisms of endemicity of scrapie in the UK sheep population

2008 ◽  
Vol 137 (6) ◽  
pp. 762-774 ◽  
Author(s):  
J. E. TRUSCOTT ◽  
N. M. FERGUSON
Keyword(s):  
Structural Diversity ◽  
Epidemiological Data ◽  
Transmissible Spongiform Encephalopathies ◽  
Spongiform Encephalopathies ◽  
Sheep Population ◽  
Mean Values ◽  
The United Kingdom ◽  
The Family ◽  
The Uk

SUMMARYScrapie is a fatal neurological disease of sheep which is endemic in the United Kingdom. It is one of the family of transmissible spongiform encephalopathies (TSEs) that includes BSE. In this paper, we developed a micro-simulation model for scrapie in the UK sheep population, incorporating the genetic and structural diversity of the population and infectious contact between flocks through trading. The simulation was fitted to epidemiological data from a range of sources. We found a detection/reporting probability of 16% (95% CI 12–17) for animals dying of scrapie. Prevalence of infected animals in the population was about 0·15%. Infected individuals were found in 9% of flocks overall, rising to 60% in Shetland and 75% in Swaledale flocks. Mean values of R0 for flocks varied with breed from 2·43 (Shetland) to 0·21 (Suffolk). We also examined the possible long-term persistence of scrapie in the UK flock in the absence of any intervention.

scholarly journals Economic Freedom: The Top, the Bottom, and the Reality. I. 1997–2007

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 38
Author(s):  
Marcel Ausloos ◽  
Philippe Bronlet
Keyword(s):  
Gross Domestic Product ◽  
Power Law ◽  
Economic Freedom ◽  
Power Laws ◽  
Domestic Product ◽  
Berlin Wall ◽  
Data Points ◽  
Transitional Point ◽  
Exponential Behaviour ◽  
Stable Exponent

We recall the historically admitted prerequisites of Economic Freedom (EF). We have examined 908 data points for the Economic Freedom of the World (EFW) index and 1884 points for the Index of Economic Freedom (IEF); the studied periods are 2000–2006 and 1997–2007, respectively, thereby following the Berlin wall collapse, and including 11 September 2001. After discussing EFW index and IEF, in order to compare the indices, one needs to study their overlap in time and space. That leaves 138 countries to be examined over a period extending from 2000 to 2006, thus 2 sets of 862 data points. The data analysis pertains to the rank-size law technique. It is examined whether the distributions obey an exponential or a power law. A correlation with the country’s Gross Domestic Product (GDP), an admittedly major determinant of EF, follows, distinguishing regional aspects, i.e., defining 6 continents. Semi-log plots show that the EFW-rank relationship is exponential for countries of high rank (≥20); overall the log–log plots point to a behaviour close to a power law. In contrast, for the IEF, the overall ranking has an exponential behaviour; but the log–log plots point to the existence of a transitional point between two different power laws, i.e., near rank 10. Moreover, log–log plots of the EFW index relationship to country GDP are characterised by a power law, with a rather stable exponent (γ≃0.674) as a function of time. In contrast, log–log plots of the IEF relationship with the country’s gross domestic product point to a downward evolutive power law as a function of time. Markedly the two studied indices provide different aspects of EF.

scholarly journals Investigating the roots of the nonlinear Luttinger liquid phenomenology

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Lisa Markhof ◽  
Mikhail Pletyukov ◽  
Volker Meden
Keyword(s):  
Spectral Function ◽  
Power Law ◽  
Single Particle ◽  
Structure Factor ◽  
Particle Interaction ◽  
Luttinger Liquid ◽  
Power Laws ◽  
Second Order ◽  
Dynamical Structure ◽  
Momentum Dependence

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and used to compute the single-particle spectral function. This forms the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order perturbative contribution to the structure factor was so far not studied. We first close this gap and show that it is consistent with the conjectured power law. Secondly, we critically assess the steps leading to the mobile impurity Hamiltonian. We show that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This dependence was recently shown to spoil power laws in the single-particle spectral function which previously were believed to be part of the Tomonaga-Luttinger liquid universality. Although our second order results for the structure factor are consistent with power-law scaling, this raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal. We conclude that more work is required to clarify this.

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