Wastewater-based epidemiology (WBE) is an effective tool for tracking community circulation of respiratory viruses. We address estimating the effective reproduction number ($R_t$) and the relative number of infections from wastewater viral load. Using weekly Houston data on respiratory syncytial virus (RSV), we implement a parsimonious Bayesian renewal model that links latent infections to measured viral load through biologically motivated generation and shedding kernels. The framework yields estimates of $R_t$ and relative infections, enabling a coherent interpretation of transmission timing and phase. We compare two input strategies-(i) raw viral-load measurements with a log-scale standard deviation, and (ii) state-space-filtered load estimates with time-varying variances-and find no practically meaningful differences in inferred trajectories or peak timing. Given this equivalence, we report the filtered input as a pragmatic default because it embeds week-specific variances while leaving epidemiological conclusions unchanged.

翻译：基于废水的流行病学监测是一种追踪社区呼吸道病毒传播的有效工具。本研究旨在通过废水病毒载量数据估算有效再生数（$R_t$）及相对感染规模。利用休斯顿地区呼吸道合胞病毒的周度监测数据，我们构建了一个简约的贝叶斯更新模型，该模型通过生物学驱动的世代间隔与病毒脱落核函数将潜在感染与实测病毒载量相关联。该框架可同步估计$R_t$与相对感染数，从而实现对传播时序与阶段的连贯解读。我们比较了两种数据输入策略：（i）采用对数尺度标准差的原始病毒载量测量值，以及（ii）结合时变方差的状态空间滤波载量估计值，发现两者在推断的传播轨迹与峰值时序上未呈现具有实际意义的差异。鉴于这种等效性，我们推荐将滤波输入作为默认实践方案，因其在保持流行病学结论不变的同时，能纳入周度特异性方差信息。