Spatiotemporal Transmission Dynamics of COVID-19 in Spain

Mathematical modelling of infectious diseases is an interdisciplinary area of increasing interest. Tracking and forecasting the full spatio-temporal evolution of an epidemic can help public health officials to plan their emergency response and health care. We present advanced methods of spatial data assimilation to epidemiology, in this case to the ebb and flow of COVID-19 across the landscape of Spain. Data assimilation is a general Bayesian technique for repeatedly and optimally updating an estimate of the current state of a dynamic model. We present a stochastic spatial Susceptible-Exposed-Infectious-Recovered-Dead (S-E-I-R-D) compartmental model to capture the transmission dynamics and the spatial spread of the ongoing COVID-19 outbreak in Spain. In this application the machinery of data assimilation acts to integrate incoming daily incidence data into a fully spatial population model, within a Bayesian framework for the tracking process. For the current outbreak in Spain we use registered data (CCAA-wide daily counts of total COVID-19 cases, recovered, hospitalized, and confirmed dead) from the Instituto de Salud Carlos III (ISCIII) situation reports. Our simulations show good correspondences between the stochastic model and the available sparse empirical data. A comparison between daily incidence data set and our SEIRD model coupled with Bayesian data assimilation highlights the role of a realization conditioned on all prior data and newly arrived data. In general, the SEIRD model with data assimilation gives a better fit than the model without data assimilation for the same time period. Our analyses may shed light more broadly on how the disease spreads in a large geographical area with places where no empirical data is recorded or observed. The analysis presented herein can be applied to a large class of compartmental epidemic models. It is important to remember that the model type is not particularly crucial for data assimilation, the Bayesian framework is the key. Data assimilation neither requires nor presupposes that the model of the infectious disease be in the family of S-I-R compartmental models. The projected number of newly infected and death cases up to August 1, 2020 are estimated and presented.