Application of Benford’s law to COVID-19 cases in selected countries of the Caribbean and globally

Abstract

Objective To use the mathematical tool of Benford’s law to determine the efficacy of preventative measures against COVID-19 taken by Trinidad, Jamaica, Barbados, the USA and New Zealand. Benford’s law may also indicate the likelihood of fraudulent or manipulated COVID-19 data in these target countries. Method Aggregate information on the number of contracted cases of COVID-19 per day from the governments and health authorities of each target country was collected via John Hopkins’ Coronavirus Resource Center. This was used to tabulate the leading digits of each data point recorded and the frequency of appearance of each number from 1 to 9. A bar graph was then generated for each set of data alongside the expected Benford distribution for a direct comparison. Finally, a Chi-Square test, suitable for such an investigation, was carried out to statistically ascertain how close the observed distribution was to the expected Benford distribution. Results Of the five countries, the USA had a distribution which followed Benford’s law the closest due to exponential spread of the virus with a χ2 value of 12.81 (versus a critical value of 15.51). The χ2 values of New Zealand, Barbados, Jamaica and Trinidad are 161.45, 110.99, 54.26 and 52.92 respectively. These values indicated that the datasets strayed from Benford’s law. Conclusion The control interventions to mitigate the spread of the COVID-19 virus, taken by the USA were insufficient to control the proliferation of COVID-19 while those taken by the remaining countries examined during the course of the study (between the first COVID-19 case in each country to late October 2020) ranged from fairly sufficient to excellent as supported by the cumulative curves. In spite of the Benford analysis, it is unlikely that there has been any manipulation of data or fraudulent reporting occurring among the target countries.