We consider a class of processes describing a population consisting of k types of individuals. The process is almost surely absorbed at the origin within finite time, and we study the expected time taken for such extinction to occur. We derive simple and precise asymptotic estimates for this expected persistence time, starting either from a single individual or from a quasi-equilibrium state, in the limit as a system size parameter N tends to infinity. Our process need not be a Markov process on $ {\mathbb Z}_+^k$; we allow the possibility that individuals’ lifetimes may follow more general distributions than the exponential distribution.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron variant (B.1.1.529) rapidly replaced Delta (B.1.617.2) to become dominant in England. Our study assessed differences in transmission between Omicron and Delta using two independent data sources and methods. Omicron and Delta cases were identified through genomic sequencing, genotyping and S-gene target failure in England from 5–11 December 2021. Secondary attack rates for named contacts were calculated in household and non-household settings using contact tracing data, while household clustering was identified using national surveillance data. Logistic regression models were applied to control for factors associated with transmission for both methods. For contact tracing data, higher secondary attack rates for Omicron vs. Delta were identified in households (15.0% vs. 10.8%) and non-households (8.2% vs. 3.7%). For both variants, in household settings, onward transmission was reduced from cases and named contacts who had three doses of vaccine compared to two, but this effect was less pronounced for Omicron (adjusted risk ratio, aRR 0.78 and 0.88) than Delta (aRR 0.62 and 0.68). In non-household settings, a similar reduction was observed only in contacts who had three doses vs. two doses for both Delta (aRR 0.51) and Omicron (aRR 0.76). For national surveillance data, the risk of household clustering, was increased 3.5-fold for Omicron compared to Delta (aRR 3.54 (3.29–3.81)). Our study identified increased risk of onward transmission of Omicron, consistent with its successful global displacement of Delta. We identified a reduced effectiveness of vaccination in lowering risk of transmission, a likely contributor for the rapid propagation of Omicron.

This article comments on the paper “Less-expensive long-term annuities linked to mortality, cash and equity” by Kevin Fergusson and Eckard Platen, appearing in this issue of the Annals of Actuarial Science. It adds two perspectives to their thought-provoking contribution. The first is a similarity to some recent work in quantitative finance on “deep hedging” that leverages machine learning models to find the cheapest replication strategy for a derivative payoff in a largely model-free setting. The second perspective engages with some of the interesting implications of their approach and draws parallels to literature in asset pricing and macro-finance. These perspectives point to the potential need for more fundamental shifts than the authors of the paper are advertising.

This study examined relationships between foodborne outbreak investigation characteristics, such as the epidemiological methods used, and the success of the investigation, as determined by whether the investigation identified an outbreak agent (i.e. pathogen), food item and contributing factor. This study used data from the Centers for Disease Control and Prevention's (CDC) National Outbreak Reporting System and National Environmental Assessment Reporting System to identify outbreak investigation characteristics associated with outbreak investigation success. We identified investigation characteristics that increase the probability of successful outbreak investigations: a rigorous epidemiology investigation method; a thorough environmental assessment, as measured by number of visits to complete the assessment; and the collection of clinical samples. This research highlights the importance of a comprehensive outbreak investigation, which includes epidemiology, environmental health and laboratory personnel working together to solve the outbreak.

Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation.

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\varepsilon$ ($\varepsilon>0$). It is known (Bertoin and Martínez, 2005) that the empirical measure of these fragments converges in law, under some renormalization. Hoffmann and Krell (2011) showed a bound for the rate of convergence. Here, we show a central limit theorem, under some assumptions. This gives us an exact rate of convergence.

When two waves interact within a rock sample, the interaction strength depends strongly on the sample’s microstructural properties, including the orientation of the sample layering. The study that established this dependence on layering speculated that the differences were caused by cracks aligned with the layers in the sample. To test this, we applied a uniaxial load to similar samples of Crab Orchard Sandstone and measured the nonlinear interaction as a function of the applied load and layer orientation. We show that the dependence of the nonlinear signal changes on applied load is exponential, with a characteristic load of 11.4–12.5 MPa that is independent of sample orientation and probe wavetype (P or S); this value agrees with results from the literature, but does not support the cracks hypothesis.

This paper proposes a testof the single equilibrium in the data assumption commonly maintained when estimating static discrete games of incomplete information. By allowing for discrete common knowledge payoff-relevant unobserved heterogeneity, the test generalizes existing methods attributing all correlation betweenplayers’ decisions to multiple equilibria. It does not require the estimation of payoffs and is therefore useful in empirical applications leveraging multiple equilibria to identify the model’s primitives. The procedure boils down to testing the emptiness of the set of data generating processes that can rationalize the sample through a single equilibrium and a finite mixture over unobserved heterogeneity. Under verifiable conditions, this testable implication is generically sufficient for degenerate equilibrium selection. The main identifying assumption is the existence of an observable variable that plays the role of a proxy for the unobservable heterogeneity. Examples of such proxies are provided based on empirical applications from the existing literature.

We consider a sequential treatment problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision-maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socioeconomic functional such as an inequality, welfare, or poverty measure. We develop expected regret lower bounds for this problem and construct a near minimax optimal sequential assignment policy.

This paper studies control function (CF) approaches in endogenous threshold regression where the threshold variable is allowed to be endogenous. We first use a simple example to show that the structural threshold regression (STR) estimator of the threshold point in Kourtellos, Stengos and Tan (2016, Econometric Theory 32, 827–860) is inconsistent unless the endogeneity level of the threshold variable is low compared to the threshold effect. We correct the CF in the STR estimator to generate our first CF estimator using a method that extends the two-stage least squares procedure in Caner and Hansen (2004, Econometric Theory 20, 813–843). We develop our second CF estimator which can be treated as an extension of the classical CF approach in endogenous linear regression. Both these approaches embody threshold effect information in the conditional variance beyond that in the conditional mean. Given the threshold point estimates, we propose new estimates for the slope parameters. The first is a by-product of the CF approach, and the second type employs generalized method of moment (GMM) procedures based on two new sets of moment conditions. Simulation studies, in conjunction with the limit theory, show that our second CF estimator and confidence interval for the threshold point together with the associated second GMM estimator and confidence interval for the slope parameter dominate the other methods. We further apply the new estimation methodology to an empirical application from international trade to illustrate its usefulness in practice.

Syndromic surveillance was originally developed to provide early warning compared to laboratory surveillance, but it is increasing used for real-time situational awareness. When a potential threat to public health is identified, a rapid assessment of its impact is required for public health management. When threats are localised, analysis is more complex as local trends need to be separated from national trends and differences compared to unaffected areas may be due to confounding factors such as deprivation or age distributions. Accounting for confounding factors usually requires an in-depth study, which takes time. Therefore, a tool is required which can provide a rapid estimate of local incidents using syndromic surveillance data.

Here, we present ‘DiD IT?’, a new investigation tool designed to measure the impact of local threats to public health. ‘DiD IT?’ uses a difference-in-differences statistical approach to account for temporal and spatial confounding and provide a direct estimate of impact due to incidents. Temporal confounding differences are estimated by comparing unaffected locations during and outside of exposure periods. Whilst spatial confounding differences are estimated by comparing unaffected and exposed locations outside of the exposure period. Any remaining differences can be considered to be the direct effect of the local incident.

We illustrate the potential utility of the tool through four examples of localised health protection incidents in England. The examples cover a range of data sources including general practitioner (GP) consultations, emergency department (ED) attendances and a telehealth call and online health symptom checker; and different types of incidents including, infectious disease outbreak, mass-gathering, extreme weather and an industrial fire. The examples use the UK Health Security Agency's ongoing real-time syndromic surveillance systems to show how results can be obtained in near real-time.

The tool identified 700 additional online difficulty breathing assessments associated with a severe thunderstorm, 53 additional GP consultations during a mumps outbreak, 2–3 telehealth line calls following an industrial fire and that there was no significant increase in ED attendances during the G7 summit in 2021.

DiD IT? can provide estimates for the direct impact of localised events in real-time as part of a syndromic surveillance system. Thus, it has the potential for enhancing surveillance and can be used to evaluate the effectiveness of extending national surveillance to a more granular local surveillance.

This study aimed to evaluate the contrast-enhanced ultrasound (CEUS) features of ureteral tuberculosis (UTB) and ureteral malignant tumour and to explore its application value in the differentiation of UTB from ureteral tumour. The ultrasound (US) and CEUS imaging features of 33 and 12 cases of pathologically confirmed UTB and ureteral malignant tumour, respectively, were retrospectively evaluated, and echo of the ureteral wall, abnormal echo of the lumen, degree of ureteral dilation and CEUS patterns of the two diseases were statistically analysed. The results revealed that the lumen echo of UTB was hyperechoic or anechoic, whereas that of ureteral tumour lesions was hypoechoic (χ2 = 28.22, P < 0.001). The wall echo of the obstruction site differed between the two diseases; in UTB, the ureteral wall was thickened but the outer wall remained intact, whereas in ureteral tumour, both the malignant tumour wall and outer wall were irregular (χ2 = 30.25, P < 0.001). CEUS of UTB revealed nonenhancement or heterogeneous enhancement in the lumen, whereas that of ureteral tumours revealed significant homogeneous enhancement (χ2 = 30.25, P < 0.001). Thus, CEUS can reveal lesion microcirculation and be used to evaluate blood supply characteristics in the lesion, indicating that it has high potential for differentiating the two diseases.

In this paper, we introduce the 3-step hedge-based valuation for the valuation of hybrid claims. We consider an insurance portfolio which is exposed to traded risks, diversifiable risks and non-traded systematic risks. The class of 3-step hedge-based valuations is equivalent with the class of fair valuations. Closed-form solutions are derived for a portfolio of unit-linked contracts under the assumption of independence between financial and non-financial risks. We also consider the additive 3-step valuation and show that this additive valuation is a member of the more general class of 3-step hedge-based valuations.

Despite promising steps towards the elimination of hepatitis C virus (HCV) in the UK, several indicators provide a cause for concern for future disease burden. We aimed to improve understanding of geographical variation in HCV-related severe liver disease and historic risk factor prevalence among clinic attendees in England and Scotland. We used metadata from 3829 HCV-positive patients consecutively enrolled into HCV Research UK from 48 hospital centres in England and Scotland during 2012–2014. Employing mixed-effects statistical modelling, several independent risk factors were identified: age 46–59 y (ORadj 3.06) and ≥60 y (ORadj 5.64) relative to <46 y, male relative to female sex (ORadj 1.58), high BMI (ORadj 1.73) and obesity (ORadj 2.81) relative to normal BMI, diabetes relative to no diabetes (ORadj 2.75), infection with HCV genotype (GT)-3 relative to GT-1 (ORadj 1.75), route of infection through blood products relative to injecting drug use (ORadj 1.40), and lower odds were associated with black ethnicity (ORadj 0.31) relative to white ethnicity. A small proportion of unexplained variation was attributed to differences between hospital centres and local health authorities. Our study provides a baseline measure of historic risk factor prevalence and potential geographical variation in healthcare provision, to support ongoing monitoring of HCV-related disease burden and the design of risk prevention measures.

We prove some estimates for the variations of transition probabilities of the (1+1)-affine process. From these estimates we deduce the strong Feller and the ergodic properties of the total variation distance of the process. The key strategy is the pathwise construction and analysis of several Markov couplings using strong solutions of stochastic equations.

This paper proposes a two-phase deep reinforcement learning approach, for hedging variable annuity contracts with both GMMB and GMDB riders, which can address model miscalibration in Black-Scholes financial and constant force of mortality actuarial market environments. In the training phase, an infant reinforcement learning agent interacts with a pre-designed training environment, collects sequential anchor-hedging reward signals, and gradually learns how to hedge the contracts. As expected, after a sufficient number of training steps, the trained reinforcement learning agent hedges, in the training environment, equally well as the correct Delta while outperforms misspecified Deltas. In the online learning phase, the trained reinforcement learning agent interacts with the market environment in real time, collects single terminal reward signals, and self-revises its hedging strategy. The hedging performance of the further trained reinforcement learning agent is demonstrated via an illustrative example on a rolling basis to reveal the self-revision capability on the hedging strategy by online learning.

Ross River virus (RRV) is the most common mosquito-borne infection in Australia. RRV disease is characterised by joint pain and lethargy, placing a substantial burden on individual patients, the healthcare system and economy. This burden is compounded by a lack of effective treatment or vaccine for the disease. The complex RRV disease ecology cycle includes a number of reservoirs and vectors that inhabit a range of environments and climates across Australia. Climate is known to influence humans, animals and the environment and has previously been shown to be useful to RRV prediction models. We developed a negative binomial regression model to predict monthly RRV case numbers and outbreaks in the Darling Downs region of Queensland, Australia. Human RRV notifications and climate data for the period July 2001 – June 2014 were used for model training. Model predictions were tested using data for July 2014 – June 2019. The final model was moderately effective at predicting RRV case numbers (Pearson's r = 0.427) and RRV outbreaks (accuracy = 65%, sensitivity = 59%, specificity = 73%). Our findings show that readily available climate data can provide timely prediction of RRV outbreaks.

Hand, foot and mouth disease (HFMD) is a common infection in the world, and its epidemics result in heavy disease burdens. Over the past decade, HFMD has been widespread among children in China, with Shanxi Province being a severely affected northern province. Located in the temperate monsoon climate, Shanxi has a GDP of over 2.5 trillion yuan. It is important to have a comprehensive understanding of the basic features of HFMD in those areas that have similar meteorological and economic backgrounds to northern China. We aimed to investigate epidemiological characteristics, identify spatial clusters and predict monthly incidence of HFMD. All reported HFMD cases were obtained from the Shanxi Center for Disease Control and Prevention. Overall HFMD incidence showed a significant downward trend from 2017 to 2020, increasing again in 2021. Children aged < 5 years were primarily affected, with a high incidence of HFMD in male patients (relative risk: 1.316). The distribution showed a seasonal trend, with major peaks in June and July and secondary peaks in October and November with the exception of 2020. Other enteroviruses were the predominant causative agents of HFMD in most years. Areas with large numbers of HFMD cases were primarily in central Shanxi, and spatial clusters in 2017 and 2018 showed a positive global spatial correlation. Local spatial autocorrelation analysis showed that hot spots and secondary hot spots were concentrated in Jinzhong and Yangquan in 2018. Based on monthly incidence from September 2021 to August 2022, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) of the long short-term memory (LSTM) and seasonal autoregressive integrated moving average (SARIMA) models were 386.58 vs. 838.25, 2.25 vs. 3.08, and 461.96 vs. 963.13, respectively, indicating that the predictive accuracy of LSTM was better than that of SARIMA. The LSTM model may be useful in predicting monthly incidences of HFMD, which may provide early warnings of HFMD epidemics.