Fractional Growth Model Applied to COVID-19 Data

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order 0< beta <= 1, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination R-2>0.999.

Automated summary

A new growth model is proposed, incorporating Logistics and Gompertz models and including Caputo-type fractional derivative, with non-fixed inflection point. The model can also describe multiple sigmoidal behaviors and multiple inflection points.