Division of Epidemiology, College of Public Health, The Ohio State University, United States of America; Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, United States of America.
Mathematical Biosciences Institute and College of Public Health, The Ohio State University, United States of America.
Math Biosci. 2024 Nov;377:109257. doi: 10.1016/j.mbs.2024.109257. Epub 2024 Aug 22.
Environmental pathogen surveillance is a promising disease surveillance modality that has been widely adopted for SARS-CoV-2 monitoring. The highly variable nature of environmental pathogen data is a challenge for integrating these data into public health response. One source of this variability is heterogeneous infection both within an individual over the course of infection as well as between individuals in their pathogen shedding over time. We present a mechanistic modeling and estimation framework for connecting environmental pathogen data to the number of infected individuals. Infected individuals are modeled as shedding pathogen into the environment via a Poisson process whose rate parameter λ varies over the course of their infection. These shedding curves λ are themselves random, allowing for variation between individuals. We show that this results in a Poisson process for environmental pathogen levels with rate parameter a function of the number of infected individuals, total shedding over the course of infection, and pathogen removal from the environment. Theoretical results include determination of identifiable parameters for the model from environmental pathogen data and simple, explicit formulas for the likelihood for particular choices of individual shedding curves. We give a two step Bayesian inference framework, where the first step corresponds to calibration from data where the number of infected individuals is known, followed by an estimation step from environmental surveillance data when the number of infected individuals is unknown. We apply this modeling and estimation framework to synthetic data, as well as to an empirical case study of SARS-CoV-2 in environmental dust collected from isolation rooms housing university students. Both the synthetic data and empirical case study indicate high inter-individual variation in shedding, leading to wide credible intervals for the number of infected individuals. We examine how uncertainty in estimates of the number of infected individuals from environmental pathogen levels scales with the true number of infected individuals and model misspecification. While credible intervals for the number of infected individuals are wide, our results suggest that distinguishing between no infection and small-to-moderate levels of infection (≈10 infected individuals) may be possible, and that it is broadly possible to differentiate between moderate (≈40) and high (≈200) numbers of infected individuals.
环境病原体监测是一种很有前途的疾病监测模式，已被广泛用于 SARS-CoV-2 监测。环境病原体数据的高度可变性是将这些数据整合到公共卫生应对中的一个挑战。这种可变性的一个来源是个体在感染过程中以及个体随时间推移而排出病原体时的异质感染。我们提出了一种将环境病原体数据与感染个体数量联系起来的机制建模和估计框架。感染个体被建模为通过泊松过程将病原体排入环境，其率参数 λ 在感染过程中变化。这些排出曲线 λ 本身是随机的，允许个体之间存在差异。我们表明，这导致环境病原体水平的泊松过程，其率参数 a 是感染个体数量、感染过程中的总排出量以及病原体从环境中去除的函数。理论结果包括从环境病原体数据确定模型的可识别参数，以及对于个体排出曲线特定选择的简单、显式似然公式。我们给出了两步贝叶斯推断框架，其中第一步对应于从已知感染个体数量的数据进行校准，然后在未知感染个体数量的情况下从环境监测数据进行估计。我们将此建模和估计框架应用于合成数据以及从隔离室环境灰尘中收集的 SARS-CoV-2 的实证案例研究。合成数据和实证案例研究都表明排出的个体间差异很大，导致感染个体数量的置信区间很宽。我们研究了从环境病原体水平估计的感染个体数量的不确定性如何随真实感染个体数量和模型失配而变化。虽然感染个体数量的置信区间很宽，但我们的结果表明，区分无感染和小到中等水平的感染（≈10 个感染个体）可能是可能的，并且大致可以区分中等（≈40 个）和高（≈200 个）感染个体数量。
