Abstract
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.
Highlights
An outbreak of a novel coronavirus, named COVID-19, was reported in December 2019 in Wuhan, China, and has been the source of significant morbidity and mortality due to progressive pneumonia [1,2]
The cumulative confirmed COVID-19 case counts in Italy were chosen to be the example against which the growth curves in all other countries were compared, due to Italy being an epicentre of the outbreak at the time of this analysis
The analysis indicates that the countries that displayed clear evidence for exponential growth were in a relatively early phase of the epidemic, and that countries that were further along in the epidemic converged to a power law behaviour
Summary
An outbreak of a novel coronavirus, named COVID-19, was reported in December 2019 in Wuhan, China, and has been the source of significant morbidity and mortality due to progressive pneumonia [1,2] It has since spread around the world and become a pandemic, with large infection burdens reported in Europe, the USA and in other parts of the world. We find that the growth dynamics become more power law like if the epidemic is more advanced This indicates that the long-term dynamics of COVID-19 spread might be intrinsically governed by a power law, even in the absence of strict non-pharmaceutical interventions. We interpret these findings with computer simulations of a metapopulation model, which can account for an initial exponential spread phase, followed by a longer-term power law behaviour. Because power law growth results in a slow down of the infection growth rate over time even in the absence of strict interventions, these insights are important for the assessment of the developing pandemic and of the effectiveness of non-pharmaceutical interventions
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