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Updated: Oct 21, 2025

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[Mathematical models to understand pandemics].

Fernando González-Fuenzalida1, Francisca González-Cohens2

  • 1Facultad de Medicina, Hospital del Salvador, Universidad de Chile, Santiago, Chile.

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|September 3, 2021
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Summary

Understanding epidemic spread requires specific mathematical models. This study explains the Gompertz curve for epidemic growth and the gamma curve for contagiousness, aiding comprehension of the SARS-CoV-2 pandemic.

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Public Health

Background:

  • The SARS-CoV-2 pandemic led to a rapid increase in cases requiring intensive care and mechanical ventilation.
  • Misunderstanding of epidemic behavior concepts by the public and medical community complicates pandemic response.
  • Accurate mathematical modeling is crucial for understanding and managing epidemic spread.

Purpose of the Study:

  • To clarify key mathematical concepts essential for understanding epidemic dynamics.
  • To explain epidemic spread using Gompertz curves instead of exponential models.
  • To introduce the gamma curve for modeling contagiousness periods.

Main Methods:

  • Descriptive analysis of epidemic spread patterns.
  • Application of Gompertz curves to model epidemic growth.
  • Utilization of gamma curves to represent contagiousness duration.
  • Graphical and simplified explanations of mathematical concepts.

Main Results:

  • Epidemic spread is more accurately modeled by a Gompertz curve than an exponential curve.
  • The period of contagiousness can be effectively described using a gamma curve.
  • Contagion magnitude and rate are quantifiable and modelable mathematical concepts.

Conclusions:

  • Understanding Gompertz and gamma curves enhances comprehension of epidemic spread and contagiousness.
  • Simplified explanations of these mathematical models can improve public and medical understanding of pandemics like SARS-CoV-2.
  • Accurate modeling is vital for effective public health strategies during infectious disease outbreaks.