Network-based time series modeling for COVID-19 incidence in the Republic of Ireland

Abstract

Network-based time series models have experienced a surge in popularity over the past years due to their ability to model temporal and spatial dependencies, arising from the spread of infectious disease.The generalised network autoregressive (GNAR) model conceptualises time series on the vertices of a network; it has an autoregressive component for temporal dependence and a spatial autoregressive component for dependence between neighbouring vertices in the network. Consequently, the choice of underlying network is essential.This paper assesses the performance of GNAR models on different networks in predicting COVID-19 cases for the 26 counties in the Republic of Ireland, over two distinct pandemic phases (restricted and unrestricted), characterised by inter-county movement restrictions.Ten static networks are constructed, in which vertices represent counties, and edges are built upon neighbourhood relations, such as railway lines. We find that a GNAR model based on the fairly sparse Queen's contiguity network explains the data best for the restricted pandemic phase while the fairly dense 21-nearest neighbour network performs best for the unrestricted phase.Across phases, GNAR models have higher predictive accuracy than standard ARIMA models which ignore the network structure. For county-specific predictions, in pandemic phases with more lenient or no COVID-19 regulation, the network effect is not quite as pronounced. The results indicate some robustness to the precise network architecture as long as the densities of the networks are similar.An analysis of the residuals justifies the model assumptions for the restricted phase but raises questions regarding their validity for the unrestricted phase.While outperforming ARIMA models which ignore network effects, the GNAR model warrants further development to better model complex infectious diseases, including COVID-19. 2020 Mathematics Subject Classification: 62M10, 05C82, 91D30 Network-based time series, COVID-19, spatial models, networks