Monitoring wastewater concentrations of SARS-CoV-2 yields a low-cost, noninvasive method for tracking disease prevalence and provides early warning signs of upcoming outbreaks in the serviced communities. There is tremendous clinical and public health interest in understanding the exact dynamics between wastewater viral loads and infection rates in the population. As both data sources may contain substantial noise and missingness, in addition to spatial and temporal dependencies, properly modeling this relationship must address these numerous complexities simultaneously while providing interpretable and clear insights. We propose a novel Bayesian functional concurrent regression model that accounts for both spatial and temporal correlations while estimating the dynamic effects between wastewater concentrations and positivity rates over time. We explicitly model the time lag between the two series and provide full posterior inference on the possible delay between spikes in wastewater concentrations and subsequent outbreaks. We estimate a time lag likely between 5 to 11 days between spikes in wastewater levels and reported clinical positivity rates. Additionally, we find a dynamic relationship between wastewater concentration levels and the strength of its association with positivity rates that fluctuates between outbreaks and non-outbreaks.

翻译：监测污水中SARS-CoV-2的浓度提供了一种低成本、非侵入性的疾病流行追踪方法，并为服务社区的疫情暴发提供早期预警信号。临床与公共卫生领域对理解污水病毒载量与人群感染率之间的确切动态关系具有重大兴趣。由于两类数据源均可能存在显著噪声与缺失值，并兼具时空依赖性，准确建模这种关系必须同时处理这些复杂性问题，同时提供可解释的清晰结论。我们提出了一种新颖的贝叶斯函数并发回归模型，该模型在估计污水浓度与阳性率随时间变化的动态效应时，同时考虑了空间与时间相关性。我们显式建模了两个时间序列间的滞后效应，并对污水浓度峰值与后续疫情暴发间的可能延迟提供了完整的后验推断。我们估计污水浓度峰值与临床报告阳性率峰值间的时间滞后约为5至11天。此外，我们发现污水浓度水平与其阳性率关联强度之间存在动态关系，这种关联在疫情暴发期与非暴发期呈现波动特征。