A new study, released on the medRxiv* preprint server, indicates that the spread of the coronavirus disease 2019 (COVID-19) is governed by power-law dynamics, suggesting that alternative modeling approaches need to be used to understand and predict its propagation.
Earlier models based on exponential growth
Most conventional modeling approaches to the transmission of COVID-19’s causative pathogen – severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) – assume that its spread follows an exponential pattern. The current study makes use of accumulating data showing that “human dynamics and clustering has power-law properties.”
Many studies of human activity show it to be governed by allometric properties (w∝Na), where N is the number of individuals and w a metric of activity). Moreover, it is important, the researchers say, to consider the effect of urban human interactions on the spread of diseases, in general, given the predominant urban location of the human population at present.
The current pandemic is characterized by chiefly asymptomatic spread. This suggests that normal human dynamics will underlie viral spread, unlike conditions of transmission that prevail when an illness is mostly symptomatic.
The studies on which power-law models of viral spread are based have come from a limited number of countries. The current study aims to understand the power-law spread of SARS-CoV-2 on a global scale.
Secondly, the researchers sought to understand if this pattern of spread at the national level is maintained at the regional level as well. They also explored the effects of reduced mobility by the population, as part of the public health policies and mandates aimed at controlling viral spread, on the power-law dynamics of viral transmission.
The study covers the spread of the virus at the onset of the pandemic. The investigators explored the total number of positives in the world at that point, and regional behavior in four countries, across three continents.
They also examined viral spread in the USA, at national, state and city levels.
The results showed that in most countries, a power-law model was indeed at work, explaining the total number of cases, at least for 30 days. This was also true for most subregional case totals, including 33 of 50 states in the USA.
In Australia, an exponential model seemed to fit better at the national level, despite 5 of 8 states showing power-law spread. This was explained by the exponential propagation seen in New South Wales, the state with the greatest population, and by the prolonged period of incubation before the virus was reported in each state.
In China, too, 19 of the 30 provinces showed power-law increase in cases, but with a slower mean propagation than at the national level. This is because the spread in Hubei, the province where the outbreak originated, dominated the national picture.
In Canada, power-law propagation was followed in 8 of 14 provinces and at the national level, because of the fact that the more populous province of British Columbia fit power-law spread, with its faster propagation.
In the USA, propagation at the national level was faster, indicating power-law dynamics at work in most of the states.
Allometric model predicts spread
It is well known that with SARS-CoV-2, most infections are asymptomatic or very mild. This means that most transmission occurs from normal-appearing individuals, unlike influenza, for instance, where most infectious individuals are symptomatic.
This means that the modeling approach used should follow the behavior of a healthy population. It is becoming evident that in a metropolitan area, the measures of community movement follow a power-law pattern, also called an allometric pattern, which moves upward in scale with the size of the population.
The allometric growth model devised by the scientists incorporating the power-law spread and the factors characterizing the early days of the pandemic was tested by extrapolating its values for another 100 days. This resulted in a better fit to the actual values than either the use of the power-law model alone or an exponential growth model.
Viral spread associated with human travel
The value of the power-law model in this pandemic is closely associated with air and vehicle travel. When lockdowns were implemented, the number of air passengers was closely linked to the virus's spread in each country.
This correlation was found to prevail even in US states where the exponential model showed a better fit. This indicates that perhaps the time constant used in these analyses could be included as part of a slower power-law spread.
The same correlation was seen in 23 of 30 of the busiest airports, which serviced the largest number of air passengers, in the USA. Thus, the magnitude of air travel plays a strong role in propagating the virus by power-law dynamics.
The same conditions were seen when the number of rural miles traveled per state was compared with the viral spread. When combined with air travel, urban, suburban and rural miles traveled made up 70% of the variance in the value of virus propagation.
What are the implications?
The power-law propagation of the virus follows the experimentally observed pattern of distribution of banknotes, used to reflect the trajectories of human travel across a variety of geographical length scales. Other studies have shown that a model which incorporates the entire civil aviation network can reproduce the spread of the virus.
Earlier, it has also been observed that mobility patterns strongly reflect reduced rates of case growth within the most badly hit US counties.
The spread of the pandemic follows power-law behavior across national and subregional scales, which in turn is linked to human movement. The allometric model could allow the direction of viral spread to be predicted several weeks in advance.
Power-law modeling would therefore enhance the predictive value of computational studies on the COVID-19 pandemic.
medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.