Covid-19 Data Logistic Growth Model in R

Introduction

The following document shows an analysis of the data associated with the coronavirus pandemic (Covid19).

The analysis is divided into two parts, the first comprises general graphs of the data and then a numerical simulation is performed using the logistic growth model (LGM) in order to forecast the possible total number of cases.

Data Repository by Johns Hopkins CSSE

Terms used

Recovery ratio

The proportion of people recovered from a specified disease among all individuals diagnosed with the disease over a certain period of time.

\[RecoveryRatio (RR) = \frac{Recovered}{Confirmed}\]

Case Fatality ratio

Case fatality rate, also called case fatality ratio, in epidemiology, the proportion of people who die from a specified disease among all individuals diagnosed with the disease over a certain period of time.

https://www.britannica.com/science/case-fatality-rate

\[Case Fatality Ratio (CFR) = \frac{Deaths}{Confirmed}\]

Logistic Growth Model (LGM)

Clark (2011) propose a new empirical model based on logistic growth models.

A nonlinear model formula including variables and parameters.

\[ProjectedCases = \frac{(K * t ^ n)}{(a + t ^ n)}\]

Where:

Cases = Projected Case
K = Carrying capacity
n = Hyperbolic exponent
a = Constant
t = Time

The best-fit nonlineal model is obtained by an iterative least-squared method.

The logistic growth model was used to determine the progression of the disease in certain countries.

There are certain countries that are included in this analysis and where the model was not used essentially because the model fails.

Projected - Confirmed Cases Ratio

Assuming that the total number of projected cases corresponds to the maximum number of cases that would occur in a given country, the projected - confirmed cases ratio is calculated using the following expression.

\[ProjectedConfirmedCases Ratio = 100 - (100 * \frac{(max(Projected Case) - max(Confirmed))}{ max(Projected Case)}\]

Global Case

Average Cases (Last three days)

Global Case Summary

Country Cases

China

Cruise Ship

The Americas

Mexico

United State (US)

Argentina

Brazil

Colombia

Chile

Venezuela

Europe

Italy

Spain

United Kingdom

France

Germany

Switzerland

Norway

Others

Japan

Korea, South

Iran

India

Russia

References

Source data: https://github.com/CSSEGISandData/COVID-19.git

Clark, A.J. (2011). “Decline Curve Analysis in Unconventional Resource Plays Using Logistic Growth Models.” M.S. Thesis, The University of Texas at Austin, August 2011.