@misc{10481/70930,
year = {2021},
url = {http://hdl.handle.net/10481/70930},
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.},
organization = {Ministerio de Economía, Industria y Competitividad, Spain, under Grant MTM2017-85568-P},
organization = {FEDER, Consejería de Economía y
Conocimiento de la Junta de Andalucía, Spain under Grant A-FQM-456-UGR18},
publisher = {MDPI},
keywords = {COVID-19},
keywords = {Diffusion processes},
keywords = {Multi-sigmoidal curves},
keywords = {Inference on diffusion processes},
keywords = {First-passage times},
title = {Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic},
doi = {10.3390/math9192409},
author = {Barrera, Antonio and Román Román, Patricia and Serrano Pérez, Juan José and Torres Ruiz, Francisco De Asís},
}