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Wastewater-based epidemiology (WBE) has proven to be a powerful tool for the population-level monitoring of pathogens, particularly severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). For assessment, several wastewater sampling regimes and methods of viral concentration have been investigated, mainly targeting SARS-CoV-2. However, the use of passive samplers in near-source environments for a range of viruses in wastewater is still under-investigated. To address this, near-source passive samples were taken at four locations targeting student hall of residence. These were chosen as an exemplar due to their high population density and perceived risk of disease transmission. Viruses investigated were SARS-CoV-2 and its variants of concern (VOCs), influenza viruses, and enteroviruses. Sampling was conducted either in the morning, where passive samplers were in place overnight (17 h) and during the day, with exposure of 7 h. We demonstrated the usefulness of near-source passive sampling for the detection of VOCs using quantitative polymerase chain reaction (qPCR) and next-generation sequencing (NGS). Furthermore, several outbreaks of influenza A and sporadic outbreaks of enteroviruses (some associated with enterovirus D68 and coxsackieviruses) were identified among the resident student population, providing evidence of the usefulness of near-source, in-sewer sampling for monitoring the health of high population density communities.
Extreme precipitation events are occurring more intensely in Canada. This can contaminate water sources with enteric pathogens, potentially increasing the risk of acute gastrointestinal illness. This study aimed to investigate the relationship between extreme precipitation and emergency department (ED) visits for acute gastrointestinal illness in Toronto from 2012 to 2022. Distributed lag non-linear models were constructed on ED visit counts with a Quasi Poisson distribution. Extreme precipitation was modelled as a 21-day lag variable, with a linear relationship assumed at levels ≧95th percentile. Separate models were also conducted on season-specific data sets. Daily precipitation and gastrointestinal illness ED visits ranged between 0 to 126 mm, and 12 to 180 visits respectively. Overall, a 10-mm increase in precipitation >95th percentile had no significant relationship with the risk of ED visits. However, stratification by seasons revealed significant relationships during spring (lags 1–19, peak at lag 14 RR = 1.04; 95% CI: 1.03, 1.06); the overall cumulative effect across the 21-day lag was also significant (RR = 1.94; 95% CI: 1.47, 2.57). Extreme precipitation has a seasonal effect on gastrointestinal health outcomes in Toronto city, suggesting varying levels of enteric pathogen exposures through drinking water or other environmental pathway during different seasons.
In this chapter we draw motivation from real-world networks and formulate random graph models for them. We focus on some of the models that have received the most attention in the literature, namely, Erdos–Rényi random graphs, inhomogeneous random graphs, configuration models, and preferential attachment models. We follow Volume 1, both for the motivation as well as for the introduction of the random graph models involved. Furthermore, we add some convenient additional results, such as degree-truncation for configuration models and switching techniques for uniform random graphs with prescribed degrees. We also discuss preliminaries used in the book, for example concerning power-law distributions.
In this chapter we investigate the small-world structure in rank-1 and general inhomogeneous random graphs. For this, we develop path-counting techniques that are interesting in their own right.
In this chapter we discuss local convergence, which describes the intuitive notion that a finite graph, seen from the perspective of a typical vertex, looks like a certain limiting graph. Local convergence plays a profound role in random graph theory. We give general definitions of local convergence in several probabilistic senses. We then show that local convergence in its various forms is equivalent to the appropriate convergence of subgraph counts. We continue by discussing several implications of local convergence, concerning local neighborhoods, clustering, assortativity, and PageRank. We further investigate the relation between local convergence and the size of the giant, making the statement that the giant is “almost local” precise.
This study examined the association between the number of nursing staff in intensive care units (ICUs) and hospital-acquired pneumonia (HAP) among surgical patients in South Korea. Data were obtained between 2008 and 2019 from the Korean National Health Insurance Service Cohort Database; 37,706 surgical patients who received critical care services were included in the analysis. Patients with a history of pneumonia 1 year prior to surgery or those who had undergone lung-related surgery were excluded. The ICU nursing management fee is an admission fee that varies based on the grading determined by nurse-to-bed ratio. Using this grading system, we classified four groups from the highest to the lowest level based on the proportion of beds to nurses (high, high-mid, mid-low, and low group). HAP was defined by the International Classification of Disease, 10th revision (ICD-10) code. Multilevel logistic regression was used to investigate the relationship between the level of ICU nurse staffing and pneumonia, controlling for variables at the individual and hospital levels. Lower levels of nurse staffing were associated with a greater incidence of HAP than higher levels of nurse staffing (mid-high, OR: 1.33, 95% CI: 1.12–1.57; mid-low, OR: 1.61, 95% CI: 1.27–2.04; low, OR: 2.13, 95% CI: 1.67–2.71). The intraclass correlation coefficient value was 0.177, and 17.7% of the variability in HAP was accounted for by the hospital. Higher ICU nursing management fee grades (grade 5 and above) in general and hospital settings were significantly associated with an increased risk of HAP compared to grade 1 admissions. Similarly, in tertiary hospitals, grade 2 and higher ICU nursing management fees were significantly associated with an increased risk of HAP compared to grade 1 admissions. Especially, a lower level of nurse staffing was associated with bacterial pneumonia but not pneumonia due to aspiration. In conclusion, this study found an association between the level of ICU nurse staffing and HAP among surgical patients. A lower level of nurse staffing in the ICU was associated with increased rates of HAP among surgical patients. This indicates that having fewer beds assigned to nurses in the ICU setting is a significant factor in preventing HAP, regardless of the size of the hospital.
In this chapter we investigate the local limit of the configuration model, we identify when it has a giant component and find its size and degree structure. We give two proofs, one based on a “the giant is almost local” argument, and another based on a continuous-time exploration of the connected components in the configuration model. Further results include its connectivity transition.
We formulate a centrally planned portfolio selection problem with the investor and the manager having S-shaped utilities under a recently popular first-loss contract. We solve for the closed-form optimal portfolio, which shows that a first-loss contract can sometimes behave like an option contract. We propose an asymptotic approach to investigate the portfolio. This approach can be adopted to illustrate economic insights, including the fact that the portfolio under a convex contract becomes more conservative when the market state is better. Furthermore, we discover a means of Pareto improvement by simultaneously considering the investor’s utility and increasing the manager’s incentive rate. This is achieved by establishing the collection of Pareto points of a single contract, proving that it is a strictly decreasing and strictly concave frontier, and comparing the Pareto frontiers of different contracts. These results may be helpful for the illustration of risk choices and the design of Pareto-optimal contracts.
In this chapter we introduce the general setting of inhomogeneous random graphs that are generalizations of the Erdos–Rényi and generalized random graphs. In inhomogeneous random graphs, the status of edges is independent with unequal edge-occupation probabilities. While these edge probabilities are moderated by vertex weights in generalized random graphs, in the general setting they are described in terms of a kernel. The main results in this chapter concern the degree structure, the multi-type branching process local limits, and the phase transition in these inhomogeneous random graphs. We also discuss various examples, and indicate that they can have rather different structure.
In this chapter we discuss some related random graph models that have been studied in the literature. We explain their relevance, as well as some of the properties in them. We discuss directed random graphs, random graphs with local and global community structures, as well as spatial random graphs.
We provide general expressions for the joint distributions of the k most significant b-ary digits and of the k leading continued fraction (CF) coefficients of outcomes of arbitrary continuous random variables. Our analysis highlights the connections between the two problems. In particular, we give the general convergence law of the distribution of the jth significant digit, which is the counterpart of the general convergence law of the distribution of the jth CF coefficient (Gauss-Kuz’min law). We also particularise our general results for Benford and Pareto random variables. The former particularisation allows us to show the central role played by Benford variables in the asymptotics of the general expressions, among several other results, including the analogue of Benford’s law for CFs. The particularisation for Pareto variables—which include Benford variables as a special case—is especially relevant in the context of pervasive scale-invariant phenomena, where Pareto variables occur much more frequently than Benford variables. This suggests that the Pareto expressions that we produce have wider applicability than their Benford counterparts in modelling most significant digits and leading CF coefficients of real data. Our results may find practical application in all areas where Benford’s law has been previously used.
This study sought to establish the elements that constitute comprehensive legal and regulatory landscape for successful digital identity system establishment and implementation. Subsequently, the study sought to assess whether these elements were present in the establishment and implementation of the National Integrated Identity Management System (NIIMS) in Kenya. The study adopted a qualitative approach, data was obtained firstly, through literature review that provided background information to the study. Secondly, semi structured interviews were undertaken on purposively selected key informants. The study established that the elements that constitute a robust legal and regulatory framework for digital identity (ID) establishment and implementation include presence of a constitutional provision on the right to privacy; existence of a digital ID law governing the establishment of the system; amendment of laws relating to the registration of persons; existence of a data protection law; existence of an overarching law governing the digital economy among others. Largely, most of these elements were present in Kenya. However, the legislative approach adopted in crafting digital ID law in Kenya was wanting. This has undermined effective implementation of the NIIM system by among other things eroding public confidence in the system. The study concluded that effective operation of the system hinged on the existence of a robust and comprehensive legal and regulatory framework that will engender users’ trust in the system. In this regard, the study recommended review of the existing legal framework to ensure that it underpins both the foundational and functional aspects of the NIIM system.