Estimation of the critical points of an epidemic by means of a logistic growth model

Abstract Epidemiological models have become a very important tool in understanding an epidemic’s development, mainly because they help researchers find more efficient strategies in their fight against its spread. Several models have been proposed up to now: some use fractional calculus to solve differential equations while others use applications from other areas such as predatorprey models. The SIR and SEIR models, among others, mainly focus on the variable response and on epidemiological parameters such as the basic reproduction number (R0) and infection rate per unit of time, nevertheless they do not focus on the variable ‘time’. We propose the use of the variable time, as the main variable, by using a reparametrization in the logistic model since it will lead to the understanding of the epidemic as it goes along the time. Moreover, this model is important because it allows the estimation of the points of acceleration and deceleration, the point of maximum growth and the asymptotic point of the epidemic. This is only possible by getting an stable epidemic curve with an ‘S’ shape. In this work we use the variable ‘accumulated cases’ of COVID-19 of China and Italy and point out the main socioeconomic facts that occurred in each period of the estimated critical points from the logistic growth model.