A non-central beta model to forecast and evaluate pandemics time series

Abstract

Government, researchers, and health professionals have been challenged to model, forecast, and evaluate pandemics time series (e.g. new coronavirus SARS-CoV-2, COVID-19). The main difficulty is the level of novelty imposed by these phenomena. Information from previous epidemics is only partially relevant. Further, the spread is local-dependent, reflecting a number of social, political, economic, and environmental dynamic factors. The present paper aims to provide a relatively simple way to model, forecast, and evaluate the time incidence of a pandemic. The proposed framework makes use of the non-central beta (NCB) probability density function. Specifically, a probabilistic optimisation algorithm searches for the best NCB model of the pandemic, according to the mean square error metric. The resulting model allows one to infer, among others, the general peak date, the ending date, and the total number of cases as well as to compare the level of difficult imposed by the pandemic among territories. Case studies involving COVID-19 incidence time series from countries around the world suggest the usefulness of the proposed framework in comparison with some of the main epidemic models from the literature (e.g. SIR, SIS, SEIR) and established time series formalisms (e.g. exponential smoothing - ETS, autoregressive integrated moving average - ARIMA).

Keywords: COVID-19; Forecasting; Optimisation; Pandemic models; Time series.

Fig. 1

National daily incidence time series since the first register of the COVID-19, according to Johns Hopkins University data set .

Fig. 2

The proposed framework. In the pre-processing step the time indexes (t) are normalised. It allows one to fit the corresponding incidence time series (u_t) via a NCP-based model, say ${\widehat{u}}_t,$ in the modelling step. In the forecasting step, the model ${\widehat{u}}_t$ is used to predict the time series of the pandemic incidence through the time horizon determined by the part of the analyst.

Fig. 3

Prediction of the national daily incidence of COVID-19 since the first register, according to Johns Hopkins University data set . The vertical orange dashed line separates training and test series.

Fig. 4

NCB Prediction of the national daily incidence of COVID-19 since the first register, according to Johns Hopkins University data set . The vertical dashed orange line marks the end of the available time series.

Fig. 5

Comparison of shapes of the NCB probability distributions, regarding the prediction of the national daily incidence of COVID-19 since the first register, according to Johns Hopkins University data set . In (b), one has the first two letters as mnemonics for Argentina, Brazil, China, France, Germany, India, Iran, Italy, Japan, and Spain. In turn, it was considered KS for Korea, South and UK for United Kingdom.