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Recent studies have produced inconsistent findings regarding the association between community social vulnerability and COVID-19 incidence and death rates. This inconsistency may be due, in part, to the fact that these studies modeled cases and deaths separately, ignoring their inherent association and thus yielding imprecise estimates. To improve inferences, we develop a Bayesian multivariate negative binomial model for exploring joint spatial and temporal trends in COVID-19 infections and deaths. The model introduces smooth functions that capture long-term temporal trends, while maintaining enough flexibility to detect local outbreaks in areas with vulnerable populations. Using multivariate autoregressive priors, we jointly model COVID-19 cases and deaths over time, taking advantage of convenient conditional representations to improve posterior computation. As such, the proposed model provides a general framework for multivariate spatiotemporal modeling of counts and rates. We adopt a fully Bayesian approach and develop an efficient posterior Markov chain Monte Carlo algorithm that relies on easily sampled Gibbs steps. We use the model to examine incidence and death rates among counties with high and low social vulnerability in the state of Georgia, USA, from 15 March to 15 December 2020. [ABSTRACT FROM AUTHOR]