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

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.

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

10.1101/2020.03.30.20047274 ◽

2020 ◽

Cited By ~ 6

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.

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Transmission of SARS-CoV-2 in Georgia, USA, 2020

10.1101/2020.05.19.20107219 ◽

2020 ◽

Author(s):

Kamalich Muniz-Rodriguez ◽

Gerardo Chowell ◽

Jessica S. Schwind ◽

Randall Ford ◽

Sylvia K. Ofori ◽

...

Keyword(s):

Growth Phase ◽

Exponential Growth ◽

Growth Pattern ◽

Cumulative Incidence ◽

The State ◽

Control Measures ◽

Reproductive Number ◽

Initial Growth ◽

Social Distancing ◽

Dougherty County

ABSTRACTObjectiveSARS-CoV-2 has significantly impacted Georgia, USA including two major hotspots, Metro Atlanta and Dougherty County in southwestern Georgia. With government deliberations about relaxing social distancing measures, it is important to understand the trajectory of the epidemic in the state of Georgia.MethodsWe collected daily cumulative incidence of confirmed COVID-19 cases in Georgia. We estimated the reproductive number (Re) of the COVID-19 epidemic on April 18 and May 2 by characterizing the initial growth phase of the epidemic using the generalized-growth model.ResultsThe data presents a sub-exponential growth pattern in the cumulative incidence curves. On April 18, 2020, Re was estimated as 1.20 (95% CI: 1.10, 1.20) for the state of Georgia, 1.10 (95% CI: 1.00, 1.20) for Dougherty County, and 1.20 (95% CI: 1.10, 1.20) for Metro Atlanta. Extending our analysis to May 2, 2020, Re estimates decreased to 1.10 (95% CI: 1.10, 1.10) for the state of Georgia, 1.00 (95% CI: 1.00, 1.10) for Dougherty County, and 1.10 (95% CI: 1.10, 1.10) for Metro Atlanta.ConclusionsTransmission appeared to be decreasing after the implementation of social distancing measures. However, these results should be interpreted with caution when considering relaxing control measures due to low testing rates.

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Initial Model for the Impact of Social Distancing on CoVID-19 Spread

10.1101/2020.05.04.20091207 ◽

2020 ◽

Author(s):

Genghmun Eng

Keyword(s):

Exponential Growth ◽

Growth Function ◽

Worst Case ◽

Social Distancing ◽

Sick People ◽

Large Numbers ◽

The World ◽

The Usa ◽

The Impact ◽

Good Agreement

AbstractThe initial stages of the CoVID-19 coronavirus pandemic all around the world exhibit a nearly exponential rise in the number of infections with time. Planners, governments, and agencies are scrambling to figure out “How much? How bad?” and how to effectively treat the potentially large numbers of simultaneously sick people. Modeling the CoVID-19 pandemic using an exponential rise implicitly assumes a nearly unlimited population of uninfected persons (“dilute pandemic”). Once a significant fraction of the population is infected (“saturated pandemic”), an exponential growth no longer applies. A new model is developed here, which modifies the standard exponential growth function to account for factors such as Social Distancing. A Social Mitigation Parameter [SMP] αS is introduced to account for these types of society-wide changes, which can modify the standard exponential growth function, as follows: The doubling-time tdbl = (In 2)/Ko can also be used to substitute for Ko, giving a {tdbl, αS} parameter pair for comparing to actual CoVID-19 data. This model shows how the number of CoVID-19 infections can self-limit before reaching a saturated pandemic level. It also provides estimates for: (a) the timing of the pandemic peak, (b) the maximum number of new daily cases that would be expected, and (c) the expected total number of CoVID-19 cases. This model shows fairly good agreement with the presently available CoVID-19 pandemic data for several individual States, and the for the USA as a whole (6 Figures), as well as for various countries around the World (9 Figures). An augmented model with two Mitigation Parameters, αS and βS, is also developed, which can give better agreement with the daily new CoVID-19 data. Data-to-model comparisons also indicate that using αS by itself likely provides a worst-case estimate, while using both αS and βS likely provides a best-case estimate for the CoVID-19 spread.

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Initial Model for Impact of Social Distancing on CoVID-19 Spread (Preprint)

10.2196/preprints.20097 ◽

2020 ◽

Author(s):

Genghmun Eng

Keyword(s):

Exponential Growth ◽

Growth Function ◽

Worst Case ◽

Social Distancing ◽

Sick People ◽

S Parameter ◽

Large Numbers ◽

The World ◽

The Usa ◽

Good Agreement

UNSTRUCTURED The initial stages of the CoVID-19 coronavirus pandemic all around the world exhibit a nearly exponential rise in the number of infections with time. Planners, governments, and agencies are scrambling to figure out "How much? How bad?" and how to effectively treat the potentially large numbers of simultaneously sick people. Modeling the CoVID-19 pandemic using an exponential rise implicitly assumes a nearly unlimited population of uninfected persons ("dilute pandemic"). Once a significant fraction of the population is infected ("saturated pandemic"), an exponential growth no longer applies. A new model is developed here, which modifies the standard exponential growth function to account for factors such as Social Distancing. A Social Mitigation Parameter [SMP] α/s\ is introduced to account for these types of society-wide changes, which can modify the standard exponential growth function, as follows: N(t)= No exp[ +Ko t/(1 + α/s\ t)] . The doubling-time t/dbl\=(ln2)/Ko can also be used to substitute for Ko, giving a {t/dbl\, α/s\} parameter pair for comparing to actual CoVID-19 data. This model shows how the number of CoVID-19 infections can self-limit before reaching a saturated pandemic level. It also provides estimates for: (a) the timing of the pandemic peak, (b) the maximum number of new daily cases that would be expected, and (c) the expected total number of CoVID-19 cases. This model shows fairly good agreement with the presently available CoVID-19 pandemic data for several individual States, and the for the USA as a whole (6 Figures), as well as for various countries around the World (9 Figures). An augmented model with two Mitigation Parameters, α/s\ and β/s\, is also developed, which can give better agreement with the daily new CoVID-19 data. Data-to-model comparisons also indicate that using α/s\ by itself likely provides a worst-case estimate, while using both α/s\ and β/s\ likely provides a best-case estimate for the CoVID-19 spread.

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Modelling the relation between income and commuting distance

Journal of The Royal Society Interface ◽

10.1098/rsif.2016.0306 ◽

2016 ◽

Vol 13 (119) ◽

pp. 20160306 ◽

Cited By ~ 17

Author(s):

Giulia Carra ◽

Ismir Mulalic ◽

Mogens Fosgerau ◽

Marc Barthelemy

Keyword(s):

Power Law ◽

Job Search ◽

Alternative Model ◽

The Usa ◽

Quality Aspect ◽

Using Data ◽

Commuting Distances ◽

The Uk ◽

Commuting Distance

We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK and the USA, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent γ ≈ 3 and (ii) an average growing slowly as a power law with an exponent less than one that depends on the country considered. The classical theory for job search is based on the idea that workers evaluate the wage of potential jobs as they arrive sequentially through time, and extending this model with space, we obtain predictions that are strongly contradicted by our empirical findings. We propose an alternative model that is based on the idea that workers evaluate potential jobs based on a quality aspect and that workers search for jobs sequentially across space. We also assume that the density of potential jobs depends on the skills of the worker and decreases with the wage. The predicted distribution of commuting distances decays as 1/ r 3 and is independent of the distribution of the quality of jobs. We find our alternative model to be in agreement with our data. This type of approach opens new perspectives for the modelling of mobility.

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Modeling Manifest Huntington’s Disease Prevalence Using Diagnosed Incidence and Survival Time

Neuroepidemiology ◽

10.1159/000516767 ◽

2021 ◽

pp. 1-8

Author(s):

Valerie Crowell ◽

Richard Houghton ◽

Akanksha Tomar ◽

Tricia Fernandes ◽

Ferdinando Squitieri

Keyword(s):

Huntington's Disease ◽

Huntington’S Disease ◽

Disease Burden ◽

Epidemiological Data ◽

Incidence Rates ◽

Simulated Patients ◽

Published Data ◽

The Usa ◽

Probability Of Death ◽

The Uk

Introduction: Understanding the epidemiology of Huntington’s disease (HD) is key to assessing disease burden and the healthcare resources required to meet patients’ needs. We aimed to develop and validate a model to estimate the diagnosed prevalence of manifest HD by the Shoulson-Fahn stage. Methods: A literature review identified epidemiological data from Brazil, Canada, France, Germany, Italy, Spain, the UK, and the USA. Data on staging distribution at diagnosis, progression, and mortality were derived from Enroll-HD. Newly diagnosed patients with manifest HD were simulated by applying annual diagnosed incidence rates to the total population in each country, each year from 1950 onwards. The number of diagnosed prevalent patients from the previous year who remained in each stage was estimated in line with the probability of death or progression. Diagnosed prevalence in 2020 was estimated as the sum of simulated patients, from all the incident cohorts, still alive. Results: The model estimates that in 2020, there were 66,787 individuals diagnosed with HD in the 8 included countries, of whom 62–63% were in Shoulson-Fahn stages 1 and 2 (with less severely limited functional capacity than those in stages 3–5). Diagnosed prevalence is estimated to be 8.2–9.0 per 100,000 in the USA, Canada, and the 5 included European countries and 3.5 per 100,000 in Brazil. Conclusion: The modeled estimates generally accord with the previously published data. This analysis contributes to better understanding of the epidemiology of HD and highlights areas of uncertainty.

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Brain Tumor Epidemiology: Updates from USA, UK and Australia

10.20944/preprints202110.0071.v1 ◽

2021 ◽

Author(s):

Sumit Chatterjee ◽

Ranjan Roy

Keyword(s):

Brain Tumor ◽

Brain Tumors ◽

Treatment Protocol ◽

Epidemiological Data ◽

Normal Brain ◽

Threatening Condition ◽

Normal Brain Function ◽

The Usa ◽

The Uk ◽

The Brain

A brain tumor is an abnormal mass of tissue found inside the brain that consists of cells that grow and multiply without any control and unchecked by the mechanisms that regulate normal cell growth. It is one of the leading causes of death in many different regions worldwide, affecting various ages, sex, race, or ethnicities. Besides being a life-threatening condition, it can also disrupt normal brain function leading to severe cognitive morbidity. Additionally, the cost associated with active treatment and palliative care of the brain tumor most often proves to be out of reach for many people. Over the past decades, even though we have several published literature showing the epidemiology and characteristics of brain tumors, up-to-date epidemiological data is yet to be published. This review will provide comparable recent statistics regarding the incidence of brain tumors in 3 different regions; - the USA, the UK, and Australia. Also, a focus will be given to brain tumor’s key characteristics, classifications, and treatment protocol.

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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

10.1101/2020.06.01.20100461 ◽

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.

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An early mainstream economist from Hungary: István Varga (1897–1962)

Acta Oeconomica ◽

10.1556/aoecon.53.2003.2.4 ◽

2003 ◽

Vol 53 (2) ◽

pp. 195-213 ◽

Cited By ~ 1

Author(s):

K. Majoros

Keyword(s):

Austrian Economic ◽

National Income ◽

Anglo Saxon ◽

Turbulent Times ◽

The Usa ◽

New Ideas ◽

Modern Economic ◽

The Uk ◽

Economic Thinking ◽

Lasting Influence

The study introduces a Hungarian economic thinker, István Varga*, whose valuable activity has remained unexplored up to now. He became an economic thinker during the 1920s, in a country that had not long before become independent of Austria. The role played by Austria in the modern economic thinking of that time was a form of competition with the thought adhered to by the UK and the USA. Hungarian economists mainly interpreted and commented on German and Austrian theories, reasons for this being that, for example, the majority of Hungarian economists had studied at German and Austrian universities, while at Hungarian universities principally German and Austrian economic theories were taught. István Varga was familiar not only with contemporary German economics but with the new ideas of Anglo-Saxon economics as well — and he introduced these ideas into Hungarian economic thinking. He lived and worked in turbulent times, and historians have only been able to appreciate his activity in a limited manner. The work of this excellent economist has all but been forgotten, although he was of international stature. After a brief summary of Varga’s profile the study will demonstrate the lasting influence he has had in four areas — namely, business cycle research and national income estimations, the 1946 Hungarian stabilisation program, corporate profit, and consumption economics — and will go on to summarise his most important achievements.

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