Logistic equation and COVID-19

TL;DR

This paper applies the generalized logistic equation to model COVID-19 epidemic data across several countries, demonstrating its effectiveness in capturing overall infection trends and highlighting the importance of time-dependent coefficients.

Contribution

It introduces the use of the generalized logistic equation with time-varying coefficients to analyze COVID-19 spread, providing a more accurate description of epidemic dynamics.

Findings

Logistic model fits cumulative infection data with R^2 > 0.8

Daily infection numbers show high variability, requiring time-dependent coefficients

Spectral analysis reveals periodic peaks matching serial intervals

Abstract

The generalized logistic equation is used to interpret the COVID-19 epidemic data in several countries: Austria, Switzerland, the Netherlands, Italy, Turkey and South Korea. The model coefficients are calculated: the growth rate and the expected number of infected people, as well as the exponent indexes in the generalized logistic equation. It is shown that the dependence of the number of the infected people on time is well described on average by the logistic curve (within the framework of a simple or generalized logistic equation) with a determination coefficient exceeding 0.8. At the same time, the dependence of the number of the infected people per day on time has a very uneven character and can be described very roughly by the logistic curve. To describe it, it is necessary to take into account the dependence of the model coefficients on time or on the total number of cases. Variations, for example, of the growth rate can reach 60%. The variability spectra of the coefficients have characteristic peaks at periods of several days, which corresponds to the observed serial intervals. The use of the stochastic logistic equation is proposed to estimate the number of probable peaks in the coronavirus incidence.