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

Abstract

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.

An Analysis of the Reliability of Reported COVID-19 Data in Western Balkan Countries

“…We must emphasize that the data after 14 December are made public only on weekly basis from this source. As observed from Figure 2 above the epidemic growths in some of the countries naturally follow an exponential family distribution which may be a suspicious that the data may follow Benford Law [9]. The new cases time series for Serbia show a rapid increase in the figures especially after September 2020.…”

“…In their work with the data (up to June 2020), [9] found that in countries where the precautions and interventions were made to control the expansion of the COVID-19 pandemic the reported data satisfied Benford Law. Based on this result and considering the fact that all the Western Balkan countries took measures until quarantine (period that ended in early June) we studied the reported data if they should satisfied Benford Law.…”

“…The reporting process was studied by [8], who observed the number of infections in China, USA and Italy and confirmed that the reported numbers match the distribution expected in Benford's Law. An epidemic growth model that could capture the intrussion efforts in different countries in order to obtain a better understanding ofthe growth rate for COVID-19 infections was proposed by [9]. In their work they showed that epidemic growths without intervention are likely to satisfy Benford Law.…”

Dynamical SPQEIR model assesses the effectiveness of non-pharmaceutical interventions against COVID-19 epidemic outbreaks

“…However, across the analysed countries, the share of positive tests was similar (see e.g. [ 27 ]), and no significant deviation from expected dynamics was observed by studies applying Benford’s law [ 28 , 29 ], possibly indicating that these data still capture to a reasonable extent the dynamics of the epidemic wave. In addition, the analysed countries were selected based on the fact that they sufficiently met the other model assumptions, e.g.…”

Evaluación comparativa de la vigilancia en salud pública de COVID-19 en Colombia: primer semestre

“…Análisis como el que aquí se presenta han tenido gran acogida durante la pandemia de COVID-19. Es así como varios estudios han usado la ley de Benford para detectar posibles fraudes en los datos de la pandemia (19,20), establecer las características comunes de los países que no cumplen la ley de Benford (21) e, incluso, usar la distribución de Benford como criterio para definir si hay "aplanamiento" o no de la curva epidémica (22). En todos estos casos, los autores refieren que la objetividad del método es su mayor fortaleza.…”