Generalized logistic model with time-varying parameters to analyze COVID-19 outbreak data

Accurately estimating the number of infections that actually occur in the earliest phases of an outbreak and predicting the number of new cases per day in various countries is crucial for real-time monitoring of COVID-19 transmission. Numerous studies have used mathematical models to predict the progression of infection rates in several countries following the appearance of epidemiological outbreaks. In this study, we analyze the data reported and then study several logistical-type phenomenological models and their application in practice for forecasting infection evolution. When several epidemic waves follow one another, it is important to stress that a traditional logistic model cannot necessarily be fully adapted to the data made available. New models are being introduced to simultaneously take account of human behavior, measures taken by the government, and epidemiological conditions. This research used a generalized logistic model based on parameters that vary over time to describe trends in COVID-19-infected cases in countries that have undergone several waves. In two-wave scenarios, the parameters of the model evolve dynamically over time following a logistic function, where the first and second waves are characterized by two extreme values for the early period and the late one, respectively.