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Title: A phenomenological epidemic model based on the spatio-temporal evolution of a gaussian probability density function
Authors: Benítez, Domingo 
Montero, Gustavo 
Rodríguez, Eduardo 
Greiner, David 
Oliver, Albert 
González, Luis 
Montenegro, Rafael 
UNESCO Clasification: 120903 Análisis de datos
120914 Técnicas de predicción estadística
220510 Mecánica estadística
Keywords: Forecasts
Model fitting performance
Parameter estimation
Phenomenological epidemic models
Stochastic epidemic models
Issue Date: 2020
Project: COVID
Journal: Mathematics
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.
ISSN: 2227-7390
DOI: 10.3390/math8112000
Source: Mathematics [EISSN 2227-7390], v. 8 (11), p. 1-22, (Noviembre 2020)
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