Fractional Growth Model Applied to COVID-19 Data

Abstract

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<β≤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 R2>0.999.

Nonexistence of Global Solutions to Higher-Order Time-Fractional Evolution Inequalities with Subcritical Degeneracy

“…Suppose that u is a global weak solution to (3)- (2). By (9), for a sufficiently large T, and all ϕ ∈ Φ T :…”

“…Due to the usefulness of fractional derivatives in modeling various phenomena from science and engineering (as can be seen in, e.g., [6][7][8][9]), the study of fractional partial differential equations (as well as fractional differential equations) becomes a subject of increasing concern. The study of the nonexistence of global solutions to time-fractional evolution equations and inequalities has been initiated by Kirane and their collaborators (as can be seen in, e.g., [10][11][12][13][14]).…”

Hybrid Fibonacci wavelet method to solve fractional‐order logistic growth model

“…Power series representation of the solution of the fractional logistic equation and the existence of solution is discussed in Area and Nieto [10]. The WHO classified COVID-19, a recent illness brought on by the SARS-CoV-2 virus, a public health emergency of major global import on January 30, 2020 [14][15][16]. Since then, several nations have created sophisticated models to comprehend the dynamics of this phenomenon and enable prediction [14].…”

“…Since then, several nations have created sophisticated models to comprehend the dynamics of this phenomenon and enable prediction [14]. Basic models like logistics and Gompertz are still used for these difficult modeling problems since they accurately depict totals deaths and cases that have been confirmed [14,15]. The carrying capacity is included in the logistic equation as a moderating effect on the growth rate.…”

“…The carrying capacity is included in the logistic equation as a moderating effect on the growth rate. The fractional logistic model is one of the mathematical models that has piqued the interest of several researchers [15]. The logistic (Verhulst) growth models have received extensive study and have been resolved using a variety of techniques, some of which are Legendre collocation methods [17], a collocation method for the numerical solution of fractional order [17], differential quadrature method [18], Dickson polynomial and spectral tau techniques [19], modified Eulerian numbers [20], Adomian decomposition method, and successive approximation method [7,8].…”