COVID-19 Epidemics Monitored Through the Logarithmic Growth Rate and SIR Model

Abstract

The SIR model is often used to analyse and forecast an epidemic. In this model, the number of patients exponentially increases and decreases in the early and late phases; hence the logarithmic growth rate K is constant at the phases. However, in the case of COVID-19 epidemics, K never remains constant but increases and decreases linearly. Simulation showed that a situation in which smaller epidemics were repeated with short time intervals makes the changes in K; it also showed relationship between K to the mean infectious time τ and the basic reproduction number R0. Using this relationship, we analysed epidemic data from 279 countries and regions. The changes in K represented the state of the epidemics and were several weeks to a month ahead of the changes in the number of confirmed cases. If the negative peaks of K could not be reduced to 0.1, the number of patients remained high. To control the epidemic, it was important to observe K daily, not to allow K to remain positive continuously and to terminate a peak with a series of K-negative days. To accomplish this, it was necessary to shorten τ by finding and isolating a patient earlier.