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

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

Predicting infectious disease outbreak impacts on population, healthcare resources and economics and has received a special academic focus during coronavirus (COVID-19) pandemic. Focus on human disease outbreak prediction techniques in current literature, Marques et al. (Predictive models for decision support in the COVID-19 crisis. Springer, Switzerland, 2021) state that there are four main methods to address forecasting problem: compartmental models, classic statistical models, space-state models and machine learning models. We adopt their framework to compare our research with previous works. Besides being divided by methods, forecasting problems can also be divided by the number of variables that are considered to make predictions. Considering this number of variables, forecasting problems can be classified as univariate, causal and multivariate models. Multivariate approaches have been applied in less than 10% of research found. This research is the first attempt to evaluate, over real time-series data of 3 different countries with univariate and multivariate methods to provide a short-term prediction. In literature we found no research with that scope and aim. A comparison of univariate and multivariate methods has been conducted and we concluded that besides the strong potential of multivariate methods, in our research univariate models presented best results in almost all regions' predictions.

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

We model the incidence of the COVID-19 disease during the first wave of the epidemic in Castilla-Leon (Spain). Within-province dynamics may be governed by a generalized logistic map, but this lacks of spatial structure. To couple the provinces, we relate the daily new infections through a density-independent parameter that entails positive spatial correlation. Pointwise values of the input parameters are fitted by an optimization procedure. To accommodate the significant variability in the daily data, with abruptly increasing and decreasing magnitudes, a random noise is incorporated into the model, whose parameters are calibrated by maximum likelihood estimation. The calculated paths of the stochastic response and the probabilistic regions are in good agreement with the data.

A phenomenological approach to predicting tuberculosis cases with an assessment of measurement errors

BACKGROUND

Measurement errors produce bias and uncertainty. They affect the outcomes of data-fitted models. Unfortunately, tuberculosis incidence data providers do not appear to be interested in this topic.

METHOD

We use a phenomenological approach to describe and forecast tuberculosis incidence numbers in the US, and England and Wales as a function of time. We use a heuristic method to evaluate if the lack of fit of our descriptive models to the data could be explained by measurement errors.

FINDINGS

We find that if the lack of fit of our proposed models to the data is due to measurement errors, these are not so large as to make the models useless. We find numerical regularities that provide trustworthy tools to make a description and forecast the tuberculosis incidence trends.

INTERPRETATION

Measurement errors of epidemiological data collected "in the field" are probably large and could justify the lack of fit of an epidemic model to the data. Thus, to choose an appropriate model to describe an epidemic, we propose to assess the magnitude of measurement errors and apply the epidemic theory.