In this paper we consider the workload of a storage system with the unconventional feature that the arrival times, rather than the interarrival times, are independent and identically distributed samples from a given distribution. We start by analyzing the ‘base model’ in which the arrival times are exponentially distributed, leading to a closed-form characterization of the queue’s workload at a given moment in time (i.e. in terms of Laplace–Stieltjes transforms), assuming the initial workload was 0. Then we consider four more general models, each of them having a specific additional feature: (a) the initial workload being allowed to have any arbitrary non-negative value, (b) an additional stream of Poisson arrivals, (c) phase-type arrival times, (d) balking customers. For all four variants the transform of the transient workload is identified in closed form.

A numerical method is proposed for a class of one-dimensional stochastic control problems with unbounded state space. This method solves an infinite-dimensional linear program, equivalent to the original formulation based on a stochastic differential equation, using a finite element approximation. The discretization scheme itself and the necessary assumptions are discussed, and a convergence argument for the method is presented. Its performance is illustrated by examples featuring long-term average and infinite horizon discounted costs, and additional optimization constraints.

We investigate some aspects of the problem of the estimation of birth distributions (BDs) in multi-type Galton–Watson trees (MGWs) with unobserved types. More precisely, we consider two-type MGWs called spinal-structured trees. This kind of tree is characterized by a spine of special individuals whose BD $\nu$ is different from the other individuals in the tree (called normal, and whose BD is denoted by $\mu$). In this work, we show that even in such a very structured two-type population, our ability to distinguish the two types and estimate $\mu$ and $\nu$ is constrained by a trade-off between the growth-rate of the population and the similarity of $\mu$ and $\nu$. Indeed, if the growth-rate is too large, large deviation events are likely to be observed in the sampling of the normal individuals, preventing us from distinguishing them from special ones. Roughly speaking, our approach succeeds if $r\lt \mathfrak{D}(\mu,\nu)$, where r is the exponential growth-rate of the population and $\mathfrak{D}$ is a divergence measuring the dissimilarity between $\mu$ and $\nu$.

We aimed to estimate the secondary attack rate of mpox among UK household contacts and determine factors associated with transmission to inform public health management of contacts, during the global outbreak in 2022. Information was collected via NHS and public health services and included age, gender, place of residence, setting, and type of contact. Aggregate information was summarized for the UK. Record level data was combined for England, Wales and Northern Ireland, and multivariable logistic regression was used to determine factors associated with transmission. The secondary attack rate among UK household mpox contacts was 4% (60/1 526). Sexual contact with the index case was associated with a 11-fold increase in adjusted odds of becoming a case in England, Wales, and Northern Ireland (95% CI 5.5–22, p < 0.001). Household contacts outside of London had increased odds compared to London residents (adjusted OR 2.9, 95%CI 1.6–5.4, p < 0.001), while female contacts had reduced odds of becoming a case (aOR: 0.41, 95% CI: 0.15–0.95). We found a low overall secondary attack rate among household mpox contacts with strong evidence of increased transmission risk associated with sexual contact. This evidence will inform the risk assessment of contacts and support prioritization of those with close intimate contact for follow up.

Contact tracing for COVID-19 in England operated from May 2020 to February 2022. The clinical, demographic and exposure information collected on cases and their contacts offered a unique opportunity to study secondary transmission. We aimed to quantify the relative impact of host factors and exposure settings on secondary COVID-19 transmission risk using 550,000 sampled transmission links between cases and their contacts. Links, or ‘contact episodes’, were established where a contact subsequently became a case, using an algorithm accounting for incubation period, setting, and contact date. A mixed-effects logistic regression model was used to estimate adjusted odds of transmission. Of sampled episodes, 8.7% resulted in secondary cases. Living with a case (71% episodes) was the most significant risk factor (aOR = 2.6, CI = 1.9–3.6). Other risk factors included unvaccinated status (aOR = 1.2, CI = 1.2–1.3), symptoms, and older age (66–79 years; aOR = 1.4, CI = 1.4–1.5). Whilst global COVID-19 strategies emphasized protection outside the home, including education, travel, and gathering restrictions, this study evidences the relative importance of household transmission. There is a need to reconsider the contribution of household transmission to future control strategies and the requirement for effective infection control within households.

The Strength of Weak Ties is among the most influential social theories of the past 50 years. However, its prediction that weak ties are especially useful for obtaining novel information is sometimes not supported. To understand why, I investigate whether social networks typically satisfy the theory’s assumptions, and whether the theory’s prediction is robust to violations of its assumptions. First, examining a diverse corpus of 56 empirical social networks, I show that empirical social networks (nearly) satisfy some but not all of the theory’s assumptions. Second, using a simulation of information diffusion, I show that the predicted utility of weak ties is not robust to violations of these assumptions. When the assumptions of the theory are violated, as is common in social networks, access to novel information depends on bridging ties, regardless of their strength. Moreover, when they exist, strong bridges (i.e., bridges with high bandwidth) are more useful than weak bridges (i.e., bridges with low bandwidth). I conclude by recommending that research applying this theory should first consider whether its assumptions are satisfied, and that a tie’s strength and bridgeness should be measured and modeled independently.

Globally, there is seasonal variation in tuberculosis (TB) incidence, yet the biological and behavioural or social factors driving TB seasonality differ across countries. Understanding season-specific risk factors that may be specific to the UK could help shape future decision-making for TB control. We conducted a time-series analysis using data from 152,424 UK TB notifications between 2000 and 2018. Notifications were aggregated by year, month, and socio-demographic covariates, and negative binomial regression models fitted to the aggregate data. For each covariate, we calculated the size of the seasonal effect as the incidence risk ratio (IRR) for the peak versus the trough months within the year and the timing of the peak, whilst accounting for the overall trend. There was strong evidence for seasonality (p < 0.0001) with an IRR of 1.27 (95% CI 1.23–1.30). The peak was estimated to occur at the beginning of May. Significant differences in seasonal amplitude were identified across age groups, ethnicity, site of disease, latitude and, for those born abroad, time since entry to the UK. The smaller amplitude in older adults, and greater amplitude among South Asians and people who recently entered the UK may indicate the role of latent TB reactivation and vitamin D deficiency in driving seasonality.

Influenza and other acute respiratory viral infections (ARVIs) are among the most common human diseases. In recent decades, the discovery of cytokines and their significance in the pathogenesis of diseases has led to extensive research on these compounds in various pathologies including ARVIs. The aim of the research was to study the cytokine profile in patients with ARVIs. The cases of 30 patients were investigated. Etiological diagnosis was performed by polymerase chain reaction. Different classes of cytokines in the serum were defined by the enzyme-linked immunosorbent assay (ELISA). The level of cytokines depended on the number of pathogens. The highest levels of pro-inflammatory interleukins and the lowest levels of anti-inflammatory IL-4 were observed in patients with a combination of five or more viruses compared to those with a monoinfection. Analysis of the data showed that in the acute phase, the levels of all studied pro-inflammatory cytokines – IL-2, IL-6, and TNF-α – increased by 8, 39, and 9 times, respectively, compared to those in healthy individuals. In the acute phase of ARVI, the levels of pro-inflammatory cytokines were significantly higher and depended on the severity of the disease. The imbalance of cytokines in the serum has been established in cases of ARVIs, depending on the severity of the disease.

In December 2018, an outbreak of Salmonella Enteritidis infections was identified in Canada by whole-genome sequencing (WGS). An investigation was initiated to identify the source of the illnesses, which proved challenging and complex. Microbiological hypothesis generation methods included comparisons of Salmonella isolate sequence data to historical domestic outbreaks and international repositories. Epidemiological hypothesis generation methods included routine case interviews, open-ended centralized re-interviewing, thematic analysis of open-ended interview data, collection of purchase records, a grocery store site visit, analytic comparison to healthy control groups, and case–case analyses. Food safety hypothesis testing methods included food sample collection and analysis, and traceback investigations. Overall, 83 cases were identified across seven provinces, with onset dates from 6 November 2018 to 7 May 2019. Case ages ranged from 1 to 88 years; 60% (50/83) were female; 39% (22/56) were hospitalized; and three deaths were reported. Brand X profiteroles and eclairs imported from Thailand were identified as the source of the outbreak, and eggs from an unregistered facility were hypothesized as the likely cause of contamination. This study aims to describe the outbreak investigation and highlight the multiple hypothesis generation methods that were employed to identify the source.

An investigation into an outbreak of Salmonella Newport infections in Canada was initiated in July 2020. Cases were identified across several provinces through whole-genome sequencing (WGS). Exposure data were gathered through case interviews. Traceback investigations were conducted using receipts, invoices, import documentation, and menus. A total of 515 cases were identified in seven provinces, related by 0–6 whole-genome multi-locus sequence typing (wgMLST) allele differences. The median age of cases was 40 (range 1–100), 54% were female, 19% were hospitalized, and three deaths were reported. Forty-eight location-specific case sub-clusters were identified in restaurants, grocery stores, and congregate living facilities. Of the 414 cases with exposure information available, 71% (295) had reported eating onions the week prior to becoming ill, and 80% of those cases who reported eating onions, reported red onion specifically. The traceback investigation identified red onions from Grower A in California, USA, as the likely source of the outbreak, and the first of many food recall warnings was issued on 30 July 2020. Salmonella was not detected in any tested food or environmental samples. This paper summarizes the collaborative efforts undertaken to investigate and control the largest Salmonella outbreak in Canada in over 20 years.

In epidemiological investigations, pathogen genomics can provide insights and test epidemiological hypotheses that would not have been possible through traditional epidemiology. Tools to synthesize genomic analysis with other types of data are a key requirement of genomic epidemiology. We propose a new ‘phylepic’ visualization that combines a phylogenomic tree with an epidemic curve. The combination visually links the molecular time represented in the tree to the calendar time in the epidemic curve, a correspondence that is not easily represented by existing tools. Using an example derived from a foodborne bacterial outbreak, we demonstrated that the phylepic chart communicates that what appeared to be a point-source outbreak was in fact composed of cases associated with two genetically distinct clades of bacteria. We provide an R package implementing the chart. We expect that visualizations that place genomic analyses within the epidemiological context will become increasingly important for outbreak investigations and public health surveillance of infectious diseases.

Varicella is a vaccine-preventable infectious disease. Since 1 December 2018, the varicella vaccine has been included in the local Expanded Programme on Immunization (EPI) in Wuxi, China, and children born after 1 December 2014 are eligible for free vaccination. To evaluate the effect of varicella vaccination in Wuxi city, we selected 382 397 children born from 2012 to 2016 as subjects. Their disease data were obtained from the Chinese Disease Prevention and Control Information System, and their vaccination data were obtained from the Jiangsu Province Vaccination Integrated Service Management Information System. The incidence of breakthrough varicella cases increased in the first 4 years and reached the peak in the fifth year. With the increase of vaccination rate, the incidence of varicella decreased significantly. The vaccine effectiveness (VE) was found to be 88.17%–95.78% for one dose and 98.65%–99.93% for two doses. Although the VE per dose decreased from 99.57% in the first year to 93.04% in the eighth year, it remained high. These findings confirmed the effectiveness of varicella vaccination in children, supported the use of a two-dose varicella vaccination strategy to achieve better protection, and provided important insights into the optimal vaccination strategy for varicella prevention in children.

We hypothesized that the incubation for urethral gonorrhoea would be longer for men with oropharyngeal gonorrhoea than those without oropharyngeal gonorrhoea. We conducted a chart review of men who have sex with men with urethral gonorrhoea symptoms at a sexual health clinic between 2019 and 2021. The incubation period was defined as the number of days between men’s last sexual contact and onset of symptoms. We used a Mann–Whitney U test to compare differences in the median incubation for urethral gonorrhoea between men with and men without oropharyngeal gonorrhoea. There were 338 men with urethral symptoms (median age = 32 years; IQR: 28–39), and of these, 307 (90.1%) were tested for oropharyngeal gonorrhoea, of whom 124 (40.4%, 95% CI: 34.9–46.1) men had oropharyngeal and urethral gonorrhoea. We analyzed incubation data available for 190 (61.9%) of the 307 men, with 38.9% (74/190) testing positive for oropharyngeal gonorrhoea. The incubation for urethral gonorrhoea did not differ between 74 men (39%) with oropharyngeal gonorrhoea (median = 4 days; IQR: 2–6) and 116 men (61%) without oropharyngeal gonorrhoea (median = 2.5 days; IQR: 1–5) (p = 0.092). Research is needed to investigate gonorrhoea transmission from the oropharynx to the urethra.

Since early 2022, routine testing for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) based on symptoms and exposure history has largely ceased in Canada. Consequently, seroprevalence studies, particularly longitudinal studies, have become critical for monitoring the rate of incident SARS-CoV-2 infections and the proportion of the population with evidence of immunity. EnCORE is a longitudinal SARS-CoV-2 seroprevalence study comprising five rounds of serology testing from October 2020 to June 2023, in a sample of 2- to 17-year-olds (at baseline), recruited from daycares and schools in four neighbourhoods of Montreal, Canada. We report on SARS-CoV-2 incidence and seroprevalence among the 509 participants in the fifth and final round of the study. Seroprevalence of antibodies from either infection or vaccination was 98% (95 per cent confidence interval [CI]: 97, 99). The infection-acquired seroprevalence was 78% (95% CI: 73–82), and the incidence rate was 113 per 100 person-years (95% CI: 94–132), compared to the seroprevalence of 58% and the incidence rate of 133 per 100 person-years, respectively, in the fourth round of testing (mid–late 2022). Of the 131 participants newly seropositive for infection in Round 4, only 18 were seronegative for infection in Round 5 (median follow-up: 326 days).

On 19 January 2020, the first case of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection was identified in the United States, with the first cases in South Carolina confirmed on 06 March 2020. Due to initial limited testing capabilities and potential for asymptomatic transmission, it is possible that SARS-CoV-2 may have been present earlier than previously thought, while the immune status of at-risk populations was unknown. Saliva from 55 South Carolina emergency healthcare workers (EHCWs) was collected from September 2019 to March 2020, pre- and post-healthcare shifts, and stored frozen. To determine the presence of SARS-CoV-2-reactive antibodies, saliva-acquired post-shift was analysed by enzyme-linked immunosorbent assay (ELISA) with a repeat of positive or inconclusive results and follow-up testing of pre-shift samples. Two participants were positive for SARS-CoV-2 N/S1-reactive IgG, confirmed by follow-up testing, with S1 receptor binding domain (RBD)-specific IgG present in one individual. Positive samples were collected from medical students working in emergency medical services (EMSs) in October or November 2019. The presence of detectable anti-SARS-CoV-2 antibodies in 2019 suggests that immune responses to the virus existed in South Carolina, and the United States, in a small percentage of EHCWs prior to the earliest documented coronavirus disease 2019 (COVID-19) cases. These findings suggest the feasibility of saliva as a noninvasive tool for surveillance of emerging outbreaks, and EHCWs represent a high-risk population that should be the focus of infectious disease surveillance.

The second smallest eigenvalue of the Laplacian matrix, known as algebraic connectivity, determines many network properties. This paper investigates the optimal design of interconnections that maximizes algebraic connectivity in multilayer networks. We identify an upper bound for maximum algebraic connectivity for total weight below a threshold, independent of interconnections pattern, and only attainable with a particular regularity condition. For efficient numerical approaches in regions of no analytical solution, we cast the problem into a convex framework and an equivalent graph embedding problem associated with the optimum diffusion phases in the multilayer. Allowing more general settings for interconnections entails regions of multiple transitions, giving more diverse diffusion phases than the more studied one-toone interconnection case. When there is no restriction on the interconnection pattern, we derive several analytical results characterizing the optimal weights using individual Fiedler vectors. We use the ratio of algebraic connectivity and layer sizes to explain the results. Finally, we study the placement of a limited number of interlinks heuristically, guided by each layer’s Fiedler vector components.

We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. The result covers both matrices over finite fields with independent non-zero entries and $\{0,1\}$-matrices over the rationals. The sufficient condition is generally necessary as well.

This paper studies a bi-dimensional compound risk model with quasi-asymptotically independent and consistently varying-tailed random numbers of claims and establishes an asymptotic formula for the finite-time sum-ruin probability. Additionally, some results related to tail probabilities of random sums are presented, which are of significant interest in their own right. Some numerical studies are carried out to check the accuracy of the asymptotic formula.