IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i19p2409-d644801.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla, 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

  • Patricia Román-Román

    (Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla, 11, 18001 Granada, Spain
    Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Juan José Serrano-Pérez

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Francisco Torres-Ruiz

    (Instituto de Matemáticas de la Universidad de Granada (IMAG), Calle Ventanilla, 11, 18001 Granada, Spain
    Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Antonio Barrera & Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic," Mathematics, MDPI, vol. 9(19), pages 1-29, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2409-:d:644801
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/19/2409/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/19/2409/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. F. Javier Girón & M. Lina Martínez & Elías Moreno & Francisco Torres, 2006. "Objective Testing Procedures in Linear Models: Calibration of the p‐values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 765-784, December.
    2. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2018. "Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors," Mathematics, MDPI, vol. 6(5), pages 1-13, May.
    3. Maleki, Mohsen & Mahmoudi, Mohammad Reza & Heydari, Mohammad Hossein & Pho, Kim-Hung, 2020. "Modeling and forecasting the spread and death rate of coronavirus (COVID-19) in the world using time series models," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2019. "A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    5. Román-Román, P. & Torres-Ruiz, F., 2015. "A stochastic model related to the Richards-type growth curve. Estimation by means of simulated annealing and variable neighborhood search," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 579-598.
    6. Juan Carlos Mora & Sandra Pérez & Alla Dvorzhak, 2020. "Application of a Semi-Empirical Dynamic Model to Forecast the Propagation of the COVID-19 Epidemics in Spain," Forecasting, MDPI, vol. 2(4), pages 1-18, October.
    7. Román, P. & Serrano, J.J. & Torres, F., 2008. "First-passage-time location function: Application to determine first-passage-time densities in diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4132-4146, April.
    8. Chénangnon Frédéric Tovissodé & Bruno Enagnon Lokonon & Romain Glèlè Kakaï, 2020. "On the use of growth models to understand epidemic outbreaks with application to COVID-19 data," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-14, October.
    9. Andrew B Lawson & Joanne Kim, 2021. "Space-time covid-19 Bayesian SIR modeling in South Carolina," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-14, March.
    10. Luz-Sant’Ana, Istoni & Román-Román, Patricia & Torres-Ruiz, Francisco, 2017. "Modeling oil production and its peak by means of a stochastic diffusion process based on the Hubbert curve," Energy, Elsevier, vol. 133(C), pages 455-470.
    11. Jasper Verschuur & Elco E Koks & Jim W Hall, 2021. "Global economic impacts of COVID-19 lockdown measures stand out in high-frequency shipping data," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-16, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xenikos, D.G. & Constantoudis, V., 2023. "Weibull dynamics and power-law diffusion of epidemics in small world 2D networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Antonio Di Crescenzo & Paola Paraggio & Patricia Román-Román & Francisco Torres-Ruiz, 2023. "Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean," Statistical Papers, Springer, vol. 64(5), pages 1391-1438, October.
    2. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "Hyperbolastic Models from a Stochastic Differential Equation Point of View," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    3. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2018. "Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors," Mathematics, MDPI, vol. 6(5), pages 1-13, May.
    4. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    5. Patricia Román-Román & Sergio Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Using First-Passage Times to Analyze Tumor Growth Delay," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    6. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    7. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2020. "Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior," Mathematics, MDPI, vol. 8(2), pages 1-20, January.
    8. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2019. "A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    9. Hwang, Eunju, 2022. "Prediction intervals of the COVID-19 cases by HAR models with growth rates and vaccination rates in top eight affected countries: Bootstrap improvement," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. J. Cano & C. Carazo & D. Salmerón, 2013. "Bayesian model selection approach to the one way analysis of variance under homoscedasticity," Computational Statistics, Springer, vol. 28(3), pages 919-931, June.
    11. J. Verschuur & E. E. Koks & J. W. Hall, 2022. "Ports’ criticality in international trade and global supply-chains," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    12. Eunju Hwang, 2023. "Improvement on Forecasting of Propagation of the COVID-19 Pandemic through Combining Oscillations in ARIMA Models," Forecasting, MDPI, vol. 6(1), pages 1-18, December.
    13. Mike K. P. So & Lupe S. H. Chan & Amanda M. Y. Chu, 2021. "Financial Network Connectedness and Systemic Risk During the COVID-19 Pandemic," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(4), pages 649-665, December.
    14. Pramesti Getut, 2023. "Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process," Monte Carlo Methods and Applications, De Gruyter, vol. 29(1), pages 1-32, March.
    15. Nawaz, Muhammad Zahid & Nawaz, Shahid & Guzmán, Francisco & Plotkina, Daria, 2023. "The aftermath of Covid-19: The rise of pandemic animosity among consumers and its scale development," Journal of Business Research, Elsevier, vol. 157(C).
    16. Warren S. Vaz, 2022. "COVID-19 Impact on the Energy Sector in the United States (2020)," Energies, MDPI, vol. 15(21), pages 1-23, October.
    17. Mike Tsionas & Mikael A. Martins & Almas Heshmati, 2023. "Effects of the vaccination and public support on covid-19 cases and number of deaths in Sweden," Operational Research, Springer, vol. 23(3), pages 1-28, September.
    18. Guido Consonni & Roberta Paroli, 2017. "Objective Bayesian Comparison of Constrained Analysis of Variance Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 589-609, September.
    19. Isra Al-Turaiki & Fahad Almutlaq & Hend Alrasheed & Norah Alballa, 2021. "Empirical Evaluation of Alternative Time-Series Models for COVID-19 Forecasting in Saudi Arabia," IJERPH, MDPI, vol. 18(16), pages 1-19, August.
    20. Rui Wang & Xingzhong Xu, 2021. "A Bayesian-motivated test for high-dimensional linear regression models with fixed design matrix," Statistical Papers, Springer, vol. 62(4), pages 1821-1852, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2409-:d:644801. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.