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A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function

Author

Listed:
  • Domingo Benítez

    (SIANI Research Institute, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain)

  • Gustavo Montero

    (SIANI Research Institute, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain)

  • Eduardo Rodríguez

    (SIANI Research Institute, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain)

  • David Greiner

    (SIANI Research Institute, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain)

  • Albert Oliver

    (SIANI Research Institute, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain)

  • Luis González

    (SIANI Research Institute, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain)

  • Rafael Montenegro

    (SIANI Research Institute, University of Las Palmas de Gran Canaria, Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain)

Abstract

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

Suggested Citation

  • Domingo Benítez & Gustavo Montero & Eduardo Rodríguez & David Greiner & Albert Oliver & Luis González & Rafael Montenegro, 2020. "A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2000-:d:442322
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. Fanelli, Duccio & Piazza, Francesco, 2020. "Analysis and forecast of COVID-19 spreading in China, Italy and France," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Sylvia Richardson & Laurent Leblond & Isabelle Jaussent & Peter J. Green, 2002. "Mixture models in measurement error problems, with reference to epidemiological studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 549-566, October.
    4. Raymond J. Carroll & Kathryn Roeder & Larry Wasserman, 1999. "Flexible Parametric Measurement Error Models," Biometrics, The International Biometric Society, vol. 55(1), pages 44-54, March.
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    Cited by:

    1. Julia Calatayud & Marc Jornet & Jorge Mateu, 2023. "A phenomenological model for COVID‐19 data taking into account neighboring‐provinces effect and random noise," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 146-155, May.

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