Power law behaviour in the saturation regime of fatality curves of the COVID-19 pandemic

Abstract

We apply a versatile growth model, whose growth rate is given by a generalised beta distribution, to describe the complex behaviour of the fatality curves of the COVID-19 disease for several countries in Europe and North America. We show that the COVID-19 epidemic curves not only may present a subexponential early growth but can also exhibit a similar subexponential (power-law) behaviour in the saturation regime. We argue that the power-law exponent of the latter regime, which measures how quickly the curve approaches the plateau, is directly related to control measures, in the sense that the less strict the control, the smaller the exponent and hence the slower the diseases progresses to its end. The power-law saturation uncovered here is an important result, because it signals to policymakers and health authorities that it is important to keep control measures for as long as possible, so as to avoid a slow, power-law ending of the disease. The slower the approach to the plateau, the longer the virus lingers on in the population, and the greater not only the final death toll but also the risk of a resurgence of infections.

Modeling the Epidemic Growth of Preprints on COVID-19 and SARS-CoV-2

“…In particular, we note that in the first subphase, i.e., for t < t − j , the GRM predicts a polynomial growth of the form [20]…”

“…In contradistinction, early exponential growth is obtained only for q = 1, in which case one has N(t) ≈ N 0 exp(rt). Similarly, in the late-time dynamics, i.e., for t > t + j , the GRM predicts an exponential rise to the plateau of the form [20]:…”

“…The availability of an exact solution also has the advantage that it allows us to compute explicitly the location of certain key characteristic points of the growth profile, as indicated below. For example, the inflection point t c of the curve N(t), wherë N(t c ) = 0, is given by [20]…”

“…To this end, we employ a generalized logistic growth model to describe the time evolution of the cumulative number of preprints deposited on preprint repositories. Since the pioneering work by Verhulst on the standard logistic model [16], phenomenological growth models have been successfully applied to many growth processes, ranging from human [16] and animal [17] population dynamics to epidemics [18], including the COVID-19 epidemic itself [19,20]. It is thus natural to expect that growth models should also be applicable to this "epidemic in an epidemic, " as the rapid surge of preprints on COVID-19 has been referred to in [13].…”

Standard and anomalous waves of COVID-19: A multiple-wave growth model for epidemics

“…In this paper, we depart from previous approaches and propose to model second-wave effects in the COVID-19 epidemic in terms of a generalised logistic model with time-dependent parameters. More specifically, we consider an extension of the so-called beta logistic model (BLM) 21 , where we assume that each parameter of the model (see below) is allowed to vary continuously and smoothly in time between two well defined values, representing the first and second waves of the epidemic dynamics, respectively. We apply the model to study the fatality curves of COVID-19, as represented by the cumulative number of deaths as a function of time, for several selected countries that display second wave effects, namely: Australia, Austria, Brazil, Germany, Iran, Italy, Japan, Morocco, Serbia, and US.…”