Spatio-Temporal Forecasting and Uncertainty Quantification of COVID-19 Cases in Shanghai via a Bayesian Deep Learning Approach

The outbreak of COVID-19 in Shanghai in the spring of 2022 had a serious impact on the society, economy, and daily life of residents. The spread of COVID-19 often exhibits complex non-linear dynamics influenced by environment, demographics, medical conditions, frequency of nucleic acid or antigen testing, epidemic control strategies, etc. Long-short term memory (LSTM) models with complex network structures and extensive training are widely adopted to learn and predict the spreading of epidemic. However, such a model neither explains the uncertainty in data, nor takes the influence of various covariates and heterogeneities into account. Therefore, a two-stage LSTM nested generalized Poisson regression (LNGPR) model is proposed in this paper to analyze COVID-19 infectious data in Shanghai outbroke in the Spring of 2022. In the first stage, a multi-layer LSTM network is trained to learn district-specific infectious data, then the trained LSTM is used to fit and predict the number of symptomatic COVID-19 infections. In the second stage, the predicted number of cases is modeled by a generalized Poisson regression model under a hierarchical Bayesian framework, in which the logarithm of the relative risks is modeled as a linear function of covariates and random effects with spatio-temporal heterogeneities. Facilitated by a deep learning approach, the spatio-temporal generalized Poisson regression model can forecast and quantifies uncertainty of the number of daily new symptomatic infections. Furthermore, the predictions based on the proposed Bayesian deep learning approach performs better than those based on LSTM method in virtue of borrowing strength from covariates, and spatial and temporal heterogeneity.