COVID-19, flattening the curve, and Benford’s law

For many countries attempting to control the fast-rising number of coronavirus cases and deaths, the race is on to “flatten the curve,” since the spread of coronavirus disease 2019 (COVID-19) has taken on pandemic proportions. In the absence of significant control interventions, the curve could be steep, with the number of COVID-19 cases growing exponentially. In fact, this level of proliferation may already be happening, since the number of patients infected in Italy closely follows an exponential trend. Thus, we propose a test. When the numbers are taken from an exponential distribution, it has been demonstrated that they automatically follow Benford’s Law (BL). As a result, if the current control interventions are successful and we flatten the curve (i.e., we slow the rate below an exponential growth rate), then the number of infections or deaths will not obey BL. For this reason, BL may be useful for assessing the effects of the current control interventions and may be able to answer the question, “How flat is flat enough?” In this study, we used an epidemic growth model in the presence of interventions to describe the potential for a flattened curve, and then investigated whether the epidemic growth model followed BL for ten selected countries with a relatively high mortality rate. Among these countries, South Korea showed a particularly high degree of control intervention. Although all of the countries have aggressively fought the epidemic, our analysis shows that all countries except for Japan satisfied BL, indicating the growth rates of COVID-19 were close to an exponential trend. Based on the simulation table in this study, BL test shows that the data from Japan is incorrect.