The Gompertz Model in the Modeling of Limited Growth Phenomena: Interdisciplinary Applications in Context

Abstract

The Gompertz model is known for its extraordinary versatility in modeling phenomena that exhibit limited growth. This asymmetric sigmoid function describes processes that begin with slow growth, then enter an exponential acceleration phase, and subsequently decelerate as they approach an upper limit (carrying capacity, K). Originally proposed in 1825 to describe the law of human mortality, today the model finds rigorous applications in demography, biology, medicine, economics, biotechnology, and epidemiology. In the context of public health in Mexico, the Gompertz model has been crucial for forecasting and analyzing disease behavior. This work presents a comparative and descriptive analysis of the growth dynamics of three distinct phenomena using the Gompertz model: the HIV/AIDS epidemic in Mexico (1983-2020), the COVID-19 pandemic in Mexico (accumulated cases, including analysis in Zacatecas), and the in vitro proliferation of HeLa cancer cells. In all cases studied, the Gompertzian model showed a satisfactory fit to the observed data (high determination coefficients R2), confirming its empirical utility for characterizing the growth rate and estimating
the system's carrying capacity.