Pertussis is a highly contagious infectious disease and remains an important cause of mortality and morbidity worldwide. Over the last decade, vaccination has greatly reduced the burden of pertussis. Yet, uncertainty in individual vaccination coverage and ineffective case surveillance systems make it difficult to estimate burden and the related quantity of population-level susceptibility, which determines population risk. These issues are more pronounced in low-income settings where coverage is often overestimated, and case numbers are under-reported. Serological data provide a direct characterisation of the landscape of susceptibility to infection; and can be combined with vaccination coverage and basic theory to estimate rates of exposure to natural infection. Here, we analysed cross-sectional data on seropositivity against pertussis to identify spatial and age patterns of susceptibility in children in Madagascar. A large proportion of individuals surveyed were seronegative; however, there were patterns suggestive of natural infection in all the regions analysed. Improvements in vaccination coverage are needed to help prevent additional burden of pertussis in the country.

We answer four questions from a recent paper of Rao and Shinkar [17] on Lipschitz bijections between functions from {0, 1}n to {0, 1}. (1) We show that there is no O(1)-bi-Lipschitz bijection from Dictator to XOR such that each output bit depends on O(1) input bits. (2) We give a construction for a mapping from XOR to Majority which has average stretch $O(\sqrt{n})$, matching a previously known lower bound. (3) We give a 3-Lipschitz embedding $\phi \colon\{0,1\}^n \to \{0,1\}^{2n+1}$ such that $${\rm{XOR }}(x) = {\rm{ Majority }}(\phi (x))$$ for all $x \in \{0,1\}^n$. (4) We show that with high probability there is an O(1)-bi-Lipschitz mapping from Dictator to a uniformly random balanced function.

Typical enteropathogenic Escherichia coli (tEPEC) infection is a major cause of diarrhoea and contributor to mortality in children <5 years old in developing countries. Data were analysed from the Global Enteric Multicenter Study examining children <5 years old seeking care for moderate-to-severe diarrhoea (MSD) in Kenya. Stool specimens were tested for enteric pathogens, including by multiplex polymerase chain reaction for gene targets of tEPEC. Demographic, clinical and anthropometric data were collected at enrolment and ~60-days later; multivariable logistic regressions were constructed. Of 1778 MSD cases enrolled from 2008 to 2012, 135 (7.6%) children tested positive for tEPEC. In a case-to-case comparison among MSD cases, tEPEC was independently associated with presentation at enrolment with a loss of skin turgor (adjusted odds ratio (aOR) 2.08, 95% confidence interval (CI) 1.37–3.17), and convulsions (aOR 2.83, 95% CI 1.12–7.14). At follow-up, infants with tEPEC compared to those without were associated with being underweight (OR 2.2, 95% CI 1.3–3.6) and wasted (OR 2.5, 95% CI 1.3–4.6). Among MSD cases, tEPEC was associated with mortality (aOR 2.85, 95% CI 1.47–5.55). This study suggests that tEPEC contributes to morbidity and mortality in children. Interventions aimed at defining and reducing the burden of tEPEC and its sequelae should be urgently investigated, prioritised and implemented.

We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particular, the proposed curvatures based on the interpretation of Haantjes definition as geodesic curvature allow us to give a network analogue of the classical local Gauss–Bonnet theorem. Furthermore, we propose even simpler and more intuitive proxies for the Haantjes curvature that allow for even faster and easier computations in large-scale networks. In addition, we also investigate the embedding properties of the proposed Ricci curvatures. Lastly, we also investigate the behavior, both on model and real-world networks, of the curvatures introduced herein with more established notions of Ricci curvature and other widely used network measures.

The prevalence of asymptomatic infection by coronavirus disease 2019 (COVID-19) as a critical measure for effectiveness of mitigation strategy has been reported to be widely varied. In this study, we aimed to determine the prevalence of asymptomatic infection using serosurvey on general population. In a cross-sectional seroprevalence survey in Guilan province, Iran, the specific antibody against COVID-19 in a representative sample was detected using rapid test kits. Among 117 seropositive subjects, prevalence of asymptomatic infection was determined based on the history of symptoms during the preceding 3 months. The design-adjusted prevalence of asymptomatic infection was 57.2% (95% confidence interval (CI) 44–69). The prevalence was significantly lower in subjects with previous contacts to COVID-19 patients (12%, 95% CI 2–49) than others without (69%, 95% CI, 46–86). The lowest prevalence was for painful body symptom (74.4%). This study revealed that more than half of the infected COVID-19 patients had no symptoms. The implications of our findings include the importance of adopting public health measures such as social distancing and inefficiency of contact tracing to interrupt epidemic transmission.

Stochastic clearing theory has wide-spread applications in the context of supply chain and service operations management. Historical application domains include bulk service queues, inventory control, and transportation planning (e.g., vehicle dispatching and shipment consolidation). In this paper, motivated by a fundamental application in shipment consolidation, we revisit the notion of service performance for stochastic clearing system operation. More specifically, our goal is to evaluate and compare service performance of alternative operational policies for clearing decisions, as quantified by a measure of timely service referred to as Average Order Delay ($AOD$). All stochastic clearing systems are subject to service delay due to the inherent clearing practice, and $\textrm {AOD}$ can be thought of as a benchmark for evaluating timely service. Although stochastic clearing theory has a long history, the existing literature on the analysis of $\textrm {AOD}$ as a service measure has several limitations. Hence, we extend the previous analysis by proposing a more general method for a generic analytical derivation of $\textrm {AOD}$ for any renewal-type clearing policy, including but not limited to alternative shipment consolidation policies in the previous literature. Our proposed method utilizes a new martingale point of view and lends itself for a generic analytical characterization of $\textrm {AOD}$, leading to a complete comparative analysis of alternative renewal-type clearing policies. Hence, we also close the gaps in the literature on shipment consolidation via a complete set of analytically provable results regarding $\textrm {AOD}$ which were only illustrated through numerical tests previously.

In this paper, we derive the asymptotic properties of the density-weighted average derivative estimator when a regressor is contaminated with classical measurement error and the density of this error must be estimated. Average derivatives of conditional mean functions are used extensively in economics and statistics, most notably in semiparametric index models. As well as ordinary smooth measurement error, we provide results for supersmooth error distributions. This is a particularly important class of error distribution as it includes the Gaussian density. We show that under either type of measurement error, despite using nonparametric deconvolution techniques and an estimated error characteristic function, we are able to achieve a $\sqrt {n}$-rate of convergence for the average derivative estimator. Interestingly, if the measurement error density is symmetric, the asymptotic variance of the average derivative estimator is the same irrespective of whether the error density is estimated or not. The promising finite sample performance of the estimator is shown through a Monte Carlo simulation.

Google's ‘Community Mobility Reports’ (CMR) detail changes in activity and mobility occurring in response to COVID-19. They thus offer the unique opportunity to examine the relationship between mobility and disease incidence. The objective was to examine whether an association between COVID-19-confirmed case numbers and levels of mobility was apparent, and if so then to examine whether such data enhance disease modelling and prediction. CMR data for countries worldwide were cross-correlated with corresponding COVID-19-confirmed case numbers. Models were fitted to explain case numbers of each country's epidemic. Models using numerical date, contemporaneous and distributed lag CMR data were contrasted using Bayesian Information Criteria. Noticeable were negative correlations between CMR data and case incidence for prominent industrialised countries of Western Europe and the North Americas. Continent-wide examination found a negative correlation for all continents with the exception of South America. When modelling, CMR-expanded models proved superior to the model without CMR. The predictions made with the distributed lag model significantly outperformed all other models. The observed relationship between CMR data and case incidence, and its ability to enhance model quality and prediction suggests data related to community mobility could prove of use in future COVID-19 modelling.

As the COVID-19 pandemic continues to escalate and place pressure on hospital system resources, a proper screening and risk stratification score is essential. We aimed to develop a risk score to identify patients with increased risk of COVID-19, allowing proper identification and allocation of limited resources. A retrospective study was conducted of 338 patients who were admitted to the hospital from the emergency room to regular floors and tested for COVID-19 at an acute care hospital in the Metropolitan Washington D.C. area. The dataset was split into development and validation sets with a ratio of 6:4. Demographics, presenting symptoms, sick contact, triage vital signs, initial laboratory and chest X-ray results were analysed to develop a prediction model for COVID-19 diagnosis. Multivariable logistic regression was performed in a stepwise fashion to develop a prediction model, and a scoring system was created based on the coefficients of the final model. Among 338 patients admitted to the hospital from the emergency room, 136 (40.2%) patients tested positive for COVID-19 and 202 (59.8%) patients tested negative. Sick contact with suspected or confirmed COVID-19 case (3 points), nursing facility residence (3 points), constitutional symptom (1 point), respiratory symptom (1 point), gastrointestinal symptom (1 point), obesity (1 point), hypoxia at triage (1 point) and leucocytosis (−1 point) were included in the prediction score. A risk score for COVID-19 diagnosis achieved area under the receiver operating characteristic curve of 0.87 (95% confidence interval (CI) 0.82–0.92) in the development dataset and 0.85 (95% CI 0.78–0.92) in the validation dataset. A risk prediction score for COVID-19 can be used as a supplemental tool to assist clinical decision to triage, test and quarantine patients admitted to the hospital from the emergency room.

We propose a new approach to mortality prediction under survival energy hypothesis (SEH). We assume that a human is born with initial energy, which changes stochastically in time and the human dies when the energy vanishes. Then, the time of death is represented by the first hitting time of the survival energy (SE) process to zero. This study assumes that SE follows a time-inhomogeneous diffusion process and defines the mortality function, which is the first hitting time distribution function of the SE process. Although SEH is a fictitious construct, we illustrate that this assumption has the potential to yield a good parametric family of cumulative probability of death, and the parametric family yields surprisingly good predictions for future mortality rates.

This study used hospital records from two time periods to understand the implication of COVID-19 on hospital-based deaths in Burundi. The place of COVID-19 symptoms was sought among deaths that occurred from January to May 2020 (during the pandemic) vs. January to May 2019 (before the pandemic). First, death proportions were tested to seize differences between mortality rates for each month in 2020 vs. 2019. In the second time, we compared mean time-to-death between the two periods using the Kaplan–Meier survival curve. Finally, a logistic regression was fitted to assess the likelihood of dying from COVID-19 symptoms between the two periods. We found statistical evidence of a higher death rate in May 2020 as compared to May 2019. Moreover, death occurred faster in 2020 (mean = 6.7 days, s.d. = 8.9) than in 2019 (mean = 7.8 days, s.d. = 10.9). Unlike in 2019, being a male was significantly associated with a much lower likelihood of dying with one or more COVID-19 symptom(s) in 2020 (odds ratio 0.35, 95% confidence interval 0.14–0.87). This study yielded some evidence for a possible COVID-19-related hospital-based mortality trend for May 2020. However, considering the time-constraint of the study, further similar studies over a longer period of time need to be conducted to trace a clearer picture on COVID-19 implication on hospital-based deaths in Burundi.

One of the largest nationwide bursts of the first COVID-19 outbreak occurred in Spain, where infection expanded in densely populated areas through March 2020. We analyse the cumulative growth curves of reported cases and deaths in all Spain and two highly populated regions, Madrid and Catalonia, identifying changes and sudden shifts in their exponential growth rate through segmented Poisson regressions. We associate these breakpoints with a timeline of key events and containment measures, and data on policy stringency and citizen mobility. Results were largely consistent for infections and deaths in all territories, showing four major shifts involving 19–71% reductions in growth rates originating from infections before 3 March and on 5–8, 10–12 and 14–18 March, but no identifiable effect of the strengthened lockdown of 29–30 March. Changes in stringency and mobility were only associated to the latter two shifts, evidencing an early deceleration in COVID-19 spread associated to personal hygiene and social distancing recommendations, followed by a stronger decrease when lockdown was enforced, leading to the contention of the outbreak by mid-April. This highlights the importance of combining public health communication strategies and hard confinement measures to contain epidemics.

We analyze a mean field game model of SIR dynamics (Susceptible, Infected, and Recovered) where players choose when to vaccinate. We show that this game admits a unique mean field equilibrium (MFE) that consists in vaccinating at a maximal rate until a given time and then not vaccinating. The vaccination strategy that minimizes the total cost has the same structure as the MFE. We prove that the vaccination period of the MFE is always smaller than the one minimizing the total cost. This implies that, to encourage optimal vaccination behavior, vaccination should always be subsidized. Finally, we provide numerical experiments to study the convergence of the equilibrium when the system is composed by a finite number of agents ($N$) to the MFE. These experiments show that the convergence rate of the cost is $1/N$ and the convergence of the switching curve is monotone.

The relationship between zoo animals, particularly nonhuman primates, and visitors is complex and varies by species. Adding complexity to this relationship is the trend for zoos to host events outside of normal operating hours. Here, we explored whether a late-night haunted-house style event influenced the behavior of spider monkeys. We conducted behavioral observations both on event nights and nights without the event. The spider monkeys were active and outside more frequently on event nights compared to the control nights indicating that their typical nighttime behavior was altered. However, it is difficult to definitively conclude whether the behavioral changes were a result of the event being aversive or enriching. Our findings suggest that zoos should conduct behavioral observations of and collect physiological data from their animals, especially if they are sensitive to environmental changes, when implementing new events, including those occurring outside of normal operating hours to ensure high levels of animal welfare.

The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a Kr+1-free graph on n vertices with e(G) > ex(n, Kr+1)– α n2, then one can remove εn2 edges from G to obtain an r-partite graph. Füredi gave a short proof that one can choose α = ε. We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.

Spatial analysis ranges from simple univariate descriptive statistics to complex multivariate analyses and is typically used to investigate spatial patterns or to identify spatially linked consumer behaviours in insurance. This paper investigates if the incorporation of publicly available spatially linked demographic census data at population level is useful in modelling customers’ lapse behaviour (i.e. stopping payment of premiums) in life insurance policies, based on data provided by an insurance company in Ireland. From the insurance company’s perspective, identifying and assessing such lapsing risks in advance permit engagement to prevent such incidents, saving money by re-evaluating customer acquisition channels and improving capital reserve calculation and preparation. Incorporating spatial analysis in lapse modelling is expected to improve lapse prediction. Therefore, a hybrid approach to lapse prediction is proposed – spatial clustering using census data is used to reveal the underlying spatial structure of customers of the Irish life insurer, in conjunction with traditional statistical models for lapse prediction based on the company data. The primary contribution of this work is to consider the spatial characteristics of customers for life insurance lapse behaviour, via the integration of reliable government provided census demographics, which has not been considered previously in actuarial literature. Company decision-makers can use the insights gleaned from this analysis to identify customer subsets to target with personalized promotions to reduce lapse rates, and to reduce overall company risk.

This paper establishes central limit theorems (CLTs) and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous microparameters estimated separately for each entity. The CLT applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. This paper studies the conditions when one can consistently estimate the asymptotic variance, and proposes a bootstrap scheme for cases when one cannot. A small simulation study illustrates performance of the asymptotic and bootstrap procedures. The results are useful for making inferences in two-step estimation procedures related to factor models, as well as in other related contexts. Our treatment avoids structural modeling of cross-sectional dependence but imposes time-series independence.

We propose a multiplex interdependent durations model and study its empirical content. The model considers an empirical stopping game of multiple agents making optimal timing decisions with incomplete information. We characterize the unique Bayesian Nash equilibrium of the stopping game in a system of simultaneous equations involving the conditional distribution of each duration with a moderate strategic interaction condition. The system of nonlinear simultaneous equations allows us to obtain constructive identification results of the interaction effects and other nonparametric model primitives. We propose two consistent semiparametric estimation methods based on different parameterizations of modeling components with right-censored duration data.

In this paper, we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary measure at a rate slower than geometric. Specifically, we consider suitably defined higher-order nonlinear autoregressions that behave similarly to a unit root process for large values of the observed series but we place almost no restrictions on their dynamics for moderate values of the observed series. Results on the subgeometric ergodicity of nonlinear autoregressions have previously appeared only in the first-order case. We provide an extension to the higher-order case and show that the autoregressions we consider are, under appropriate conditions, subgeometrically ergodic. As useful implications, we also obtain stationarity and$\beta $-mixing with subgeometrically decaying mixing coefficients.