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Logistic equation and COVID-19.

Efim Pelinovsky1,2,3, Andrey Kurkin1, Oxana Kurkina1

  • 1Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Minin st., 24, Nizhny Novgorod, 603950, Russian Federation.

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Summary
This summary is machine-generated.

The generalized logistic equation effectively models COVID-19 cases, showing good fit for total infections but requiring adjustments for daily new cases. Stochastic models can predict epidemic peaks.

Keywords:
COVID-19Generalized logistic modelLogistic equationMathematical modeling

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Infectious Disease Dynamics

Background:

  • The COVID-19 pandemic necessitated robust epidemiological modeling to understand transmission dynamics.
  • Logistic models are commonly used for epidemic forecasting, but their applicability to daily case fluctuations requires investigation.

Purpose of the Study:

  • To apply the generalized logistic equation to interpret COVID-19 epidemic data across multiple countries.
  • To evaluate the model's accuracy in describing both cumulative and daily new infection trends.
  • To explore methods for improving the description of daily case variations and predicting epidemic peaks.

Main Methods:

  • Utilized the generalized logistic equation to analyze COVID-19 data from Austria, Switzerland, the Netherlands, Italy, Turkey, and South Korea.
  • Calculated key model coefficients including growth rate, expected infected population, and exponent indices.
  • Assessed model fit using the coefficient of determination (R²).
  • Investigated time-dependent coefficient variations and employed stochastic logistic equations.

Main Results:

  • The logistic curve accurately described the cumulative number of COVID-19 infections over time (R² > 0.8).
  • Daily new COVID-19 infections exhibited uneven patterns, only roughly fitting the logistic curve.
  • Significant variations (up to 60%) in growth rates were observed, necessitating time-dependent coefficient adjustments.
  • Analysis revealed characteristic peaks in coefficient variability spectra, aligning with observed serial intervals.
  • Stochastic logistic equations were proposed for estimating probable peaks in coronavirus incidence.

Conclusions:

  • The generalized logistic equation provides a reliable framework for modeling cumulative COVID-19 cases.
  • Modeling daily new cases requires incorporating time-varying parameters or more advanced stochastic approaches.
  • Understanding coefficient variability is crucial for accurate epidemic forecasting and peak prediction.