Keywords
Sigmoid curves
Growth models
Data fitting
Early warning
How to Cite
Abstract
S-shaped or sigmoid curves can be defined as the solutions of autonomous first-order differential equations that satisfy four conditions. Without solving the equations, we demonstrate that the solutions of the logistic family and the Smith-Birch model satisfy these conditions. We introduce two generalizations of the Smith-Birch, whose solutions are identified as S-shaped for some range of variation of the parameters. The new models introduced here predict the spread of the disease better than traditional logistic family models for time series of the cumulative number of cases for the first 61 days of the COVID-19 pandemic in some countries.
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