Nonlinear Growth Models with Lockdown Periods for Analyzing Cumulative and Daily COVID-19 Outbreak Data

The COVID−19 pandemic has caused widespread devastation across the world, with over 600 million cases and 6 million deaths recorded as of March 25th, 2023 [25]. Real-time monitoring of transmission is crucial to accurately estimate the number of real-time effective COVID−19 infections during the early stages of an outbreak, and to predict the daily new cases in many countries. Mathematical models have been employed in various studies to forecast the evolution of effective infected cases during epidemic outbreaks in different countries. This paper aims to analysis of the reported data and examines several phenomenological logistic-type models and their practical applications for forecasting the progression of infected cases. Observe that, in the presence of multiple waves the classical logistic model is not directly compatible with the available data. We introduce new models that take into account the epidemiological conditions, government measures and human behavior. This model utilize a generalized logistic growth model with time varying parameters to describe the fatality curves of COVID-19 for countries that have experienced multiple waves of infections. For instances of two waves, the model parameters change over time according to a logistic function, with the two extreme values characterizing the first and second waves for early and late times, respectively.