Exponential, logistic and Gompertz growth models: A theoretical review and application to COVID-19 data

Abstract

The pandemic scenario caused by the SARS-CoV-2 coronavirus has increased the interest and divulgation of mathematical models capable of projecting the evolution of the number of cases (and/or deaths) due to COVID-19, in countries, states and/or cities. In many articles, the cumulative number of cases is modeled by a non-linear growth model, such as the exponential, logistic or Gompertz model. Motivated by this fact, in this article, we present a detailed review of these three growth models. We begin by obtaining the mathematical expression of the exponential model using a simple example of cell division. Based on the exponential model, we present in detail the mathematical development to obtain the expressions of the logistic and Gompertz models and how to obtain the coordinates of the inflection point of these two models. We also illustrate the use of these three growth models in the modeling of the cumulative number of deaths from COVID-19 recorded in the state of São Paulo in the period from} 03/17/2020 to 04/30/2021. In this modeling, we present a criterion for adjusting a piecewise model since the recorde values present a heterogeneous behaviour over time.