Dose-response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi-mechanistic models known as single-hit models, such as the exponential and the exact beta-Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single-hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so-called single-hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single-hit models. Further analysis of the model framework is facilitated by formulating the single-hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single-hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model-consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model-consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model-consistent expression for the mean per-exposure dose that produces the correct total risk from repeated exposures is developed.
Climate change is expected to lead to an increased frequency and intensity of extreme precipitation events. For urban drainage, the primary adverse effects are more frequent and severe sewer overloading and flooding in urban areas, and higher discharges through combined sewer overflows (CSO). For assessing the possible effects of climate change, urban drainage models are run with climate-change-adjusted input data. However, current climate models are run on a spatial–temporal scale that is too coarse to resolve processes relevant to urban drainage modelling, in particular convective precipitation events. In the work reported here the delta-change method was used to develop a high-resolution time series of precipitation for the period 2071–2100 based on a recently produced climate model precipitation time series for Oslo. The present and future performance of the sewer networks was determined using MOUSE software. The simulations indicated future increases in annual CSO discharge of 33% when comparing years of maximum annual runoff. There is also an 83% increase in annual CSO discharge when comparing years of maximum annual precipitation. In addition, there are increases in the flooding of manholes and increased levels of backwater in pipes, which translates into more flooding of basements.
Detection and quantification of tread wear particles in the environment have been a challenge owing to lack of a robust method. This study investigated the applicability of a combination of Simultaneous Thermal Analysis (STA), Fourier Transform Infra-Red (FTIR), and Parallel Factor Analysis (PARAFAC) in the detection and quantification of tire particles from formulated sediments. FTIR spectral data were obtained by heating 20 samples in STA. Among the 20 samples, 12 were tire granules in formulated sediments (TGIS) containing 1%, 2%, 5%, and 10% by mass of tire granules, while the remaining eight contained 0.5, 1, 2.5, and 5 mg of tire granules only (TGO). The PARAFAC models decomposed the trilinear data into three components. Tire rubber materials in tire granules (RM) and a combination of water and carbon dioxide were the components identified in all samples. The linear regression analysis of score values from the PARAFAC models showed that the RM quantity predicted were comparable to measured values in both TGIS and TGO. Decomposing the overlying components in the spectral data into different components, and predicting unknown quantity in both sample types, the method proves robust in identifying and quantifying tire particles from sediments.
Spatial and/or temporal clustering of pathogens will invalidate the commonly used assumption of Poisson-distributed pathogen counts (doses) in quantitative microbial risk assessment. In this work, the theoretically predicted effect of spatial clustering in conventional "single-hit" dose-response models is investigated by employing the stuttering Poisson distribution, a very general family of count distributions that naturally models pathogen clustering and contains the Poisson and negative binomial distributions as special cases. The analysis is facilitated by formulating the dose-response models in terms of probability generating functions. It is shown formally that the theoretical single-hit risk obtained with a stuttering Poisson distribution is lower than that obtained with a Poisson distribution, assuming identical mean doses. A similar result holds for mixed Poisson distributions. Numerical examples indicate that the theoretical single-hit risk is fairly insensitive to moderate clustering, though the effect tends to be more pronounced for low mean doses. Furthermore, using Jensen's inequality, an upper bound on risk is derived that tends to better approximate the exact theoretical single-hit risk for highly overdispersed dose distributions. The bound holds with any dose distribution (characterized by its mean and zero inflation index) and any conditional dose-response model that is concave in the dose variable. Its application is exemplified with published data from Norovirus feeding trials, for which some of the administered doses were prepared from an inoculum of aggregated viruses. The potential implications of clustering for dose-response assessment as well as practical risk characterization are discussed.
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