Anticipating the Novel Coronavirus Disease (COVID-19) Pandemic

Abstract

The COVID-19 outbreak was first declared an international public health, and it was later deemed a pandemic. In most countries, the COVID-19 incidence curve rises sharply over a short period of time, suggesting a transition from a disease-free (or low-burden disease) equilibrium state to a sustained infected (or high-burden disease) state. Such a transition is often known to exhibit characteristics of "critical slowing down." Critical slowing down can be, in general, successfully detected using many statistical measures, such as variance, lag-1 autocorrelation, density ratio, and skewness. Here, we report an empirical test of this phenomena on the COVID-19 datasets of nine countries, including India, China, and the United States. For most of the datasets, increases in variance and autocorrelation predict the onset of a critical transition. Our analysis suggests two key features in predicting the COVID-19 incidence curve for a specific country: (a) the timing of strict social distancing and/or lockdown interventions implemented and (b) the fraction of a nation's population being affected by COVID-19 at that time. Furthermore, using satellite data of nitrogen dioxide as an indicator of lockdown efficacy, we found that countries where lockdown was implemented early and firmly have been successful in reducing COVID-19 spread. These results are essential for designing effective strategies to control the spread/resurgence of infectious pandemics.

Keywords: COVID-19; critical transitions; indicators of critical slowing down; non-pharmaceutical interventions; social distancing policies.

Figure 1

Time series constructed as cumulative number of infected cases in nine different countries across the world from the onset of the epidemic in the respective countries up to April 29. (A-I): Shaded regions depict the pre-transition phase for different countries from the onset and mark the data used to compute the indicators of critical slowing down. The double-sided arrow marks the size of the moving window (up to the vertical dashed line). In the subfigures, the arrowhead on the x-axis marks the beginning of the officially recorded social-distancing and/or lockdown dates (see Table S1 in Supplementary Material).

Figure 2

Statistical estimates used to analyze the signals of a forthcoming transition in the COVID-19 incidence curve. (A-I): Figures on the left panel depicts the variance each for India, China, South Korea, USA, Singapore, Germany, Italy, UK, and Spain. (J-R): The right panel shows the lag-1 autocorrelation of the time series data analyzed in the corresponding countries. Scattered points are the estimated values of the respective slowing down indicators. Solid lines reflect the increasing/decreasing trend in the indicators and are obtained by fitting linear regression models. The shaded regions are the confidence bounds for the fitted models.

Figure 3

Statistical analysis to measure the indicators of CSD for the dataset of India up to the date of the nationwide lockdown. (A) The incidence curve depicting the fraction of people infected from January 30 up to April 29. The shaded region is the data used to calculate the changes in the generic indicators. The arrow marks the size of the rolling window used to calculate the statistical signals. The estimated values of the slowing down indicators (B) variance, (C) autocorrelation function at lag-1, (D) skewness, and (E) kurtosis. Solid lines are the fitted linear regression models to analyze the trend in the indicators along with the confidence bounds (shaded regions).

Figure 4

The sensitivity of the choice of the rolling window size and the filtering bandwidth to estimate the EWSs. (A-I): Contour plots demonstrate the effect of moving window size and the filtering bandwidth on the trends observed while calculating the changes in the variance of the time series, using the Kendall-τ test statistic. (J-R): Panels on right show the frequency distribution of the trend statistic. The inverted arrows mark the choice of the filtering bandwidth and moving window size used to capture the trends in the variance of the time series data.

Figure 5

The sensitivity of the choice of the rolling window size and the filtering bandwidth to estimate the EWSs. (A-G): Contour plots demonstrate the effect of moving window size and the filtering bandwidth on the trends observed while calculating the short term correlation pattern using ACF(1) of the time series data, using the Kendall-τ test statistic. (H-N): Panels on right show the frequency distribution of the trend statistic. The inverted triangles mark the choice of the filtering bandwidth and moving window size used to capture the trends in the ACF(1) of the time series data.

Figure 6

The probability distribution of Kendall-τ test statistic on a set of 1,000 surrogate time series generated by bootstrapping and shuffling (with replacement) the residual time series of the original data. (A-G): Histograms depict the distribution of the test statistic for the surrogate time series variance (left panels) and (H-N): autocorrelation function at lag-1 (right panels). Solid lines indicate the limit beyond which the Kendall-τ of the surrogate data is higher than the statistic observed in the ACF(1) of the original time series.

Figure 7

(A-I): Time series of triads of the population-weighted total-column NO₂ (molecules/cm²) density over the length of the study period for the nine countries considered in this work (depicted by the circular points). The solid curve in each subfigure represents a 10-triad moving window average of the time series.

Figure 8

Stochastic trajectories (marked with pink, yellow, gray, green, and blue curves) of the infected population generated using the Gillespie algorithm for: (A) India, (B) China, and (C) South Korea. The original datasets up to April 6 for the respective countries are depicted by circular (red) points for a comparison.