Standard and Anomalous Waves of COVID-19: A Multiple-Wave Growth Model for Epidemics

Vasconcelos, Giovani L.; Brum, Arthur A.; Almeida, Francisco A. G.; Macêdo, Antônio M. S.; Duarte-Filho, Gerson C.; Ospina, Raydonal

We apply a generalized logistic growth model, with time-dependent parameters, to describe the fatality curves of the COVID-19 disease for several countries that exhibit multiple waves of infections. In the case of two waves only, the model parameters vary as a function of time according to a logistic function, whose two extreme values, i.e., for early and late times, characterize the first and second waves, respectively. For the multiple-wave model, the time-dependency of the parameters is likewise described by a multi-step logistic function with N intermediate plateaus, representing the N waves of the epidemic. We show that the theoretical curves are in excellent agreement with the empirical data for all countries considered here, namely: Brazil, Canada, Germany, Iran, Italy, Japan, Mexico, South Africa, Sweden, and the USA. The model also allows for predictions about the time of occurrence and severity of the subsequent waves. It is shown furthermore that the subsequent waves of COVID-19 can be generically classified into two main types, namely, standard and anomalous waves, according as to whether a given wave starts well after or well before the preceding one has subsided, respectively.