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

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.

Comparing Short-Term Univariate and Multivariate Time-Series Forecasting Models in Infectious Disease Outbreak

“… 2021 ; Katris 2021 ; Benítez et al. 2020 ) to explain, evaluate and estimate further values (forecast) the behavior of some variable like outbreak disease cases, deaths, or transmission rate all over the time.…”

“…( 2020 ) 2020 – – – EEMD – 01/01/07 to 31/12/18 3 m mca Brazil (5 states) Mul Meningitis Benítez et al. ( 2020 ) 2020 – GML, GMR Gaussian model – – 65 to 104 d 10 d dca, dde, dadhosp, dishosp Spain, Sierra Leone and Colombia Uni COVID-19, Ebola and zika virus Khan et al. ( 2020 ) 2020 VAR – – – – 08/03/20 to 27/06/20 50 d dca, dde, dre Iran Mul COVID-19 Deng et al.…”

A phenomenological model for COVID‐19 data taking into account neighboring‐provinces effect and random noise

“…Phenomenological models may also incorporate stochastic effects, to deal with the uncertainty associated to data collection and the phenomenon itself (Smith, 2013 ). For the COVID‐19 disease, some examples include a frequentist approach for the derivative of the logistic map with Gaussian error (Shen, 2020 ), a Bayesian approach for the Gompertz curve (Berihuete, Sánchez‐Sánchez, & Suárez‐Llorens, 2021 ), and a phenomenological model based on the spatiotemporal evolution of a Gaussian probability density function (Benítez et al, 2020 ).…”