Capturing spatial dependence of COVID-19 case counts with cellphone mobility data

Abstract

Spatial dependence is usually introduced into spatial models using some measure of physical proximity. When analysing COVID-19 case counts, this makes sense as regions that are close together are more likely to have more people moving between them, spreading the disease. However, using the actual number of trips between each region may explain COVID-19 case counts better than physical proximity. In this paper, we investigate the efficacy of using telecommunications-derived mobility data to induce spatial dependence in spatial models applied to two Spanish communities' COVID-19 case counts. We do this by extending Besag York Mollié (BYM) models to include both a physical adjacency effect, alongside a mobility effect. The mobility effect is given a Gaussian Markov random field prior, with the number of trips between regions as edge weights. We leverage modern parametrizations of BYM models to conclude that the number of people moving between regions better explains variation in COVID-19 case counts than physical proximity data. We suggest that this data should be used in conjunction with physical proximity data when developing spatial models for COVID-19 case counts.

Keywords: Bayesian hierarchical model; Besag York Mollié model; COVID-19; Gaussian Markov random field; Mobility data.

Fig. 1

Number of trips greater than 500 metres (a and b) and daily case counts (c and d) in the two Communities of Spain from March to June 2020.

Fig. 2

COVID-19 cases per thousand, up to May 31 2020 for two communities in Spain. Background map ©Stamen Design.

Fig. 3

Number of trips (incoming, outgoing, and within) the 179 regions of Madrid, and 245 health zones of Castilla-Leon, for the period March 1 to March 7 2020.

Fig. 4

Log-relative risk contributions (a–d) from the movement effects (${\mathit{\gamma }}^{\ast }$) and spatial effects (${\mathit{\varphi }}^{\ast }$). The predicted cases per thousand people are also presented (e–f).

Fig. A.1

Posterior Density of the proportion of variance explained by each of the 3 spatial parameters when adjacency and movement data are included in the same model.

Fig. A.2

Posterior Density of the proportion of variance explained by spatial components when adjacency and movement data are used in separate models (model validation).

Fig. A.3

Traceplots of $\mathit{\rho }$.

Fig. B.1

Number of trips to and from Madrid City (white).

Fig. B.2

Standard deviations of predicted cases per thousand people.