Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic

Antonio Barrera, Patricia Román-Román, Juan José Serrano-Pérez and Francisco Torres-Ruiz
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Antonio Barrera: Departamento de Análisis Matemático, Estadística e Investigación Operativa y Matemática Aplicada, Facultad de Ciencias, Universidad de Málaga, Bulevar Louis Pasteur, 31, 29010 Málaga, Spain
Patricia Román-Román: Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla, 11, 18001 Granada, Spain
Juan José Serrano-Pérez: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
Francisco Torres-Ruiz: Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla, 11, 18001 Granada, Spain

Mathematics, 2021, vol. 9, issue 19, 1-29

Abstract: A proposal is made to employ stochastic models, based on diffusion processes, to represent the evolution of the SARS-CoV-2 virus pandemic. Specifically, two diffusion processes are proposed whose mean functions obey multi-sigmoidal Gompertz and Weibull-type patterns. Both are constructed by introducing polynomial functions in the ordinary differential equations that originate the classical Gompertz and Weibull curves. The estimation of the parameters is approached by maximum likelihood. Various associated problems are analyzed, such as the determination of initial solutions for the necessary numerical methods in practical cases, as well as Bayesian methods to determine the degree of the polynomial. Additionally, strategies are suggested to determine the best model to fit specific data. A practical case is developed from data originating from several Spanish regions during the first two waves of the COVID-19 pandemic. The determination of the inflection time instants, which correspond to the peaks of infection and deaths, is given special attention. To deal with this particular issue, point estimation as well as first-passage times have been considered.

Keywords: COVID-19; diffusion processes; multi-sigmoidal curves; inference in diffusion processes; first-passage times (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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