We use Stein’s method to obtain distributional approximations of subgraph counts in the uniform attachment model or random directed acyclic graph; we provide also estimates of rates of convergence. In particular, we give uni- and multi-variate Poisson approximations to the counts of cycles and normal approximations to the counts of unicyclic subgraphs; we also give a partial result for the counts of trees. We further find a class of multicyclic graphs whose subgraph counts are a.s. bounded as $n\to \infty$.

For given positive integers $r\ge 3$, $n$ and $e\le \binom{n}{2}$, the famous Erdős–Rademacher problem asks for the minimum number of $r$-cliques in a graph with $n$ vertices and $e$ edges. A conjecture of Lovász and Simonovits from the 1970s states that, for every $r\ge 3$, if $n$ is sufficiently large then, for every $e\le \binom{n}{2}$, at least one extremal graph can be obtained from a complete partite graph by adding a triangle-free graph into one part.

In this note, we explicitly write the minimum number of $r$-cliques predicted by the above conjecture. Also, we describe what we believe to be the set of extremal graphs for any $r\ge 4$ and all large $n$, amending the previous conjecture of Pikhurko and Razborov.

Cooperative behavior constitutes a key aspect of human society and non-human animal systems, but explaining how cooperation evolves represents a major scientific challenge. It is now well established that social network structure plays a central role for the viability of cooperation. However, not much is known about the importance of the positions of cooperators in the networks for the evolution of cooperation. Here, we investigate how the spread of cooperation is affected by correlations between cooperativeness and individual social connectedness (such that cooperators occupy well-connected network positions). Using simulation models, we find that these correlations enhance cooperation in standard scale-free networks but not in standard Poisson networks. In contrast, when degree assortativity is increased such that individuals cluster with others of similar social connectedness, we find that Poisson networks can maintain high levels of cooperation, which can even exceed those of scale-free networks. We show that this is due to dynamics where bridge areas between social clusters act as barriers to the spread of defection. We also find that this positive effect on cooperation is sensitive to the presence of Trojan horses (defectors placed within cooperator clusters), which allow defection to invade. The results provide new knowledge about the conditions under which cooperation may evolve, and are also relevant to consider in regard to the design of cooperation studies.

Subacute and chronic meningitis (SCM) presents significant diagnostic challenges, with numerous infectious and non-infectious inflammatory causes. This study examined patients aged 16 and older with SCM admitted to referral centers for neuroinfections and neuroinflammations in Mashhad, Iran, between March 2015 and October 2022. Among 183 episodes, tuberculous meningitis was the most common infectious cause (46.5%), followed by Brucella meningitis (24.6%). The cause of SCM was definitively proven in 40.4%, presumptive in 35.0%, and unknown in 24.6% of cases. In-hospital mortality was 14.4%, and 30.5% of survivors experienced unfavorable outcomes (Glasgow Outcome Scale 2–4). Patients with unknown causes had a significantly higher risk of death compared to those with presumptive or proven diagnoses (risk ratio 4.18). This study emphasizes the diagnostic difficulties of SCM, with one-quarter of cases remaining undiagnosed and over one-third having only a presumptive diagnosis. Improving diagnostic methods could potentially enhance prognosis and reduce mortality.

Recent advances in clinical prediction for diarrhoeal aetiology in low- and middle-income countries have revealed that the addition of weather data to clinical data improves predictive performance. However, the optimal source of weather data remains unclear. We aim to compare the use of model estimated satellite- and ground-based observational data with weather station directly observed data for the prediction of aetiology of diarrhoea. We used clinical and etiological data from a large multi-centre study of children with moderate to severe diarrhoea cases to compare their predictive performances. We show that the two sources of weather conditions perform similarly in most locations. We conclude that while model estimated data is a viable, scalable tool for public health interventions and disease prediction, given its ease of access, directly observed weather station data is likely adequate for the prediction of diarrhoeal aetiology in children in low- and middle-income countries.

We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the random hypergraph has bounded expected degrees, we provide a spectral algorithm that outputs a partition with at least a $\gamma$ fraction of the vertices classified correctly, where $\gamma \in (0.5,1)$ depends on the signal-to-noise ratio (SNR) of the model. When the SNR grows slowly as the number of vertices goes to infinity, our algorithm achieves weak consistency, which improves the previous results in Ghoshdastidar and Dukkipati ((2017) Ann. Stat. 45(1) 289–315.) for non-uniform HSBMs.

Our spectral algorithm consists of three major steps: (1) Hyperedge selection: select hyperedges of certain sizes to provide the maximal signal-to-noise ratio for the induced sub-hypergraph; (2) Spectral partition: construct a regularised adjacency matrix and obtain an approximate partition based on singular vectors; (3) Correction and merging: incorporate the hyperedge information from adjacency tensors to upgrade the error rate guarantee. The theoretical analysis of our algorithm relies on the concentration and regularisation of the adjacency matrix for sparse non-uniform random hypergraphs, which can be of independent interest.

Leptospirosis is a bacterial zoonosis that poses an increasing global public health risk. Pacific Island communities are highly vulnerable to leptospirosis outbreaks, yet the local drivers of infection remain poorly understood. We conducted a systematic review to identify the drivers of human Leptospira infection in the Pacific Islands. There were 42 included studies from which findings were synthesized descriptively. In tropical Pacific Islands, infections were a product of sociodemographic factors such as male gender/sex, age 20 to 60 years, Indigenous ethnicity, and poverty; lifestyle factors such as swimming, gardening, and open skin wounds; and environmental factors, including seasonality, heavy rainfall, and exposure to rodents, cattle, and pigs. Possible mitigation strategies in these islands include strengthening disease reporting standards at a regional level; improving water security, rodent control, and piggery management at a community level; and information campaigns to target individual-level drivers of infection. By contrast, in New Zealand, exposures were predominantly occupational, with infections occurring in meat and farm workers. Accordingly, interventions could include adjustments to occupational practices and promoting the uptake of animal vaccinations. Given the complexity of disease transmission and future challenges posed by climate change, further action is required for leptospirosis control in the Pacific Islands.

We determine the order of the k-core in a large class of dense graph sequences. Let $G_n$ be a sequence of undirected, n-vertex graphs with edge weights $\{a^n_{i,j}\}_{i,j \in [n]}$ that converges to a graphon $W\colon[0,1]^2 \to [0,+\infty)$ in the cut metric. Keeping an edge (i,j) of $G_n$ with probability ${a^n_{i,j}}/{n}$ independently, we obtain a sequence of random graphs $G_n({1}/{n})$. Using a branching process and the theory of dense graph limits, under mild assumptions we obtain the order of the k-core of random graphs $G_n({1}/{n})$. Our result can also be used to obtain the threshold of appearance of a k-core of order n.

SARS-CoV-2 superspreading occurs when transmission is highly efficient and/or an individual infects many others, contributing to rapid spread. To better quantify heterogeneity in SARS-CoV-2 transmission, particularly superspreading, we performed a systematic review of transmission events with data on secondary attack rates or contact tracing of individual index cases published before September 2021 prior to the emergence of variants of concern and widespread vaccination. We reviewed 592 distinct events and 9,883 index cases from 491 papers. A meta-analysis of secondary attack rates identified substantial heterogeneity across 12 chosen event types/settings, with the highest transmission (25–35%) in co-living situations including households, nursing homes, and other congregate housing. Among index cases, 67% reported zero secondary cases and only 3% (287) infected >5 secondary cases (“superspreaders”). Index case demographic data were limited, with only 55% of individuals reporting age, sex, symptoms, real-time polymerase chain reaction (PCR) cycle threshold values, or total contacts. With the data available, we identified a higher percentage of superspreaders among symptomatic individuals, individuals aged 49–64 years, and individuals with over 100 total contacts. Addressing gaps in the literature regarding transmission events and contact tracing is needed to properly explain the heterogeneity in transmission and facilitate control efforts for SARS-CoV-2 and other infections.

In the transitioning era towards the COVID-19 endemic, there is still a sizable population that has never been vaccinated against COVID-19 in the Netherlands. This study employs Bayesian spatio-temporal modelling to assess the relative chances of COVID-19 vaccination uptake – first, second, and booster doses – both at the municipal and regional (public health services) levels. Incorporating ecological regression modelling to consider socio-demographic factors, our study unveils a diverse spatio-temporal distribution of vaccination uptake. Notably, the areas located in or around the Dutch main urban area (Randstad) and regions that are more religiously conservative exhibit a below-average likelihood of vaccination. Analysis at the municipal level within public health service regions indicates internal heterogeneity. Additionally, areas with a higher proportion of non-Western migrants consistently show lower chances of vaccination across vaccination dose scenarios. These findings highlight the need for tailored national and local vaccination strategies. Particularly, more regional efforts are essential to address vaccination disparities, especially in regions with elevated proportions of marginalized populations. This insight informs ongoing COVID-19 campaigns, emphasizing the importance of targeted interventions for optimizing health outcomes during the second booster phase, especially in regions with a relatively higher proportion of marginalized populations.

We consider continuous-state branching processes (CB processes) which become extinct almost surely. First, we tackle the problem of describing the stationary measures on $(0,+\infty)$ for such CB processes. We give a representation of the stationary measure in terms of scale functions of related Lévy processes. Then we prove that the stationary measure can be obtained from the vague limit of the potential measure, and, in the critical case, can also be obtained from the vague limit of a normalized transition probability. Next, we prove some limit theorems for the CB process conditioned on extinction in a near future and on extinction at a fixed time. We obtain non-degenerate limit distributions which are of the size-biased type of the stationary measure in the critical case and of the Yaglom distribution in the subcritical case. Finally we explore some further properties of the limit distributions.

Several recent studies conclude that an increase in the pathogenicity of SARS-CoV-2 cannot be ruled out. However, it should be noted that SARS-CoV-2 is a ‘direct’ respiratory virus – meaning it is usually spread by the respiratory route but does not routinely pass through the lymphatics like measles and smallpox. Providing its tropism does not change, it will be unique if its pathogenicity does not decrease until it becomes similar to common cold viruses. Ewald noted in the 1980s that respiratory viruses may evolve mildness because their spread benefits from the mobility of their hosts. This review examines factors that usually lower respiratory viruses’ severity, including heat sensitivity (which limits replication in the warmer lungs) and changes to the virus’s surface proteins. Other factors may, however, increase pathogenicity, such as replication in the lymphatic system and spreading via solid surfaces or faecal matter. Furthermore, human activities and political events could increase the harmfulness of SARS-CoV-2, including the following: large-scale testing, especially when the results are delayed; transmission in settings where people are close together and not free to move around; poor hygiene facilities; and social, political, or cultural influences that encourage sick individuals to remain active, including crises such as wars. If we can avoid these eventualities, SARS-CoV-2 is likely to evolve to be milder, although the timescale is uncertain. Observations of influenza-like pandemics suggest it may take around two decades for COVID-19 to become as mild as seasonal colds.

We are interested in the law of the first passage time of an Ornstein–Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a two-parameter family of functional transformations of a time-varying boundary. For specific values of the parameters, these transformations appear in a realisation of a standard Ornstein–Uhlenbeck bridge. We provide three different proofs of this connection. The first is based on a similar result for Brownian motion, the second uses a generalisation of the so-called Gauss–Markov processes, and the third relies on the Lie group symmetry method. We investigate the properties of these transformations and study the algebraic and analytical properties of an involution operator which is used in constructing them. We also show that these transformations map the space of solutions of Sturm–Liouville equations into the space of solutions of the associated nonlinear ordinary differential equations. Lastly, we interpret our results through the method of images and give new examples of curves with explicit first passage time densities.

In the last 10–15 years, there has been a global resurgence of scarlet fever, an infection historically associated with significant morbidity and mortality. It is unknown whether scarlet fever incidence has increased in Australia. We aimed to examine the incidence, predictors and severity of scarlet fever in the state of Victoria, Australia from 2007 to 2017, analyzing scarlet fever emergency department (ED) presentations, hospitalizations and deaths. Of the 1 578 scarlet fever cases during the study period, most occurred in children aged <10 years (1 344, 85%), in males (882, 56%), and during winter and spring months (918, 57%). There were no deaths with scarlet fever, however, 374 cases (24%) were admitted to hospital. The annual incidence of scarlet fever was stable during the study period (mean, 2.5; range, 1.9–3.1 cases per 100 000). Annual incidence was highest in children aged <5 years (19.3 per 100 000), and was 21% higher in males than females, adjusting for age and year (incidence rate ratio, 1.21, 95%CI 1.09–1.34). Whilst scarlet fever ED presentations and hospitalizations were stable in Victoria from 2007 to 2017, the recent identification of a Streptococcus pyogenes variant in Australia associated with epidemic scarlet fever overseas highlights the risk of future outbreaks.

Streptococcus pneumoniae serotype 35B, a non-vaccine type, is a major contributor to the increase in pneumococcal infection post-vaccination. We aimed to understand the mechanism of its spread by characterizing 35B. The serotype, type 1 pilus (T1P) positivity, and antimicrobial susceptibility of 319 isolates in 2018–2022 were analysed and compared with those of isolates in 2014–2017 to find the changes. 35B accounted for 40 (12.5%) isolates. T1P positivity was notably higher in 35B (87.5%) than in the other serotypes. To confirm the role of T1P, an adhesion factor, we compared adherence to A549 cells between T1P-positive 35B isolates and their T1P-deficient mutants, showing contribution of T1P to adherence. Penicillin-non-susceptible rate of 35B was 87.5%, and meropenem-resistant 35B rate was 35.0%, which increased from 14.5% of 2014–2017 (p = 0.009). Multilocus sequence typing was performed in 35B strains. Prevalence of clonal complex 558, harbouring T1P and exhibiting multidrug non-susceptibility, suggested the advantages of 35B in attachment and survival in the host. The emergence of ST156 isolates, T1P-positive and non-susceptible to β-lactams, has raised concern about expansion in Japan. The increase of serotype 35B in pneumococcal diseases might have occurred due to its predominant colonizing ability after the elimination of the vaccine-serotypes.

Seasonal influenza epidemics result in high levels of healthcare utilization. Vaccination is an effective strategy to reduce the influenza-related burden of disease. However, reporting vaccine effectiveness does not convey the population impacts of influenza vaccination. We aimed to calculate the burden of influenza-related hospitalizations and emergency department (ED) attendance averted by influenza vaccination in Victoria, Australia, from 2017 to 2019, and associated economic savings. We applied a compartmental model to hospitalizations and ED attendances with influenza-specific, and pneumonia and influenza (P&I) with the International Classification of Diseases, 10th Revision, Australian Modification (ICD-10-AM) diagnostic codes of J09-J11 and J09-J18, respectively. We estimated an annual average of 7657 (120 per 100000 population) hospitalizations and 20560 (322 per 100000 population) ED attendances over the study period, associated with A$85 million hospital expenditure. We estimated that influenza vaccination averted an annual average of 1182 [range: 556 – 2277] hospitalizations and 3286 [range: 1554 – 6257] ED attendances and reduced the demand for healthcare services at the influenza season peak. This equated to approximately A13 [range: A6 – A25] million of savings over the study period. Calculating the burden averted is feasible in Australia and auseful approach to demonstrate the health and economic benefits of influenza vaccination.

We study a system consisting of n particles, moving forward in jumps on the real line. Each particle can make both independent jumps, whose sizes have some distribution, and ‘synchronization’ jumps, which allow it to join a randomly chosen other particle if the latter happens to be ahead of it. The system state is the empirical distribution of particle locations. We consider the mean-field asymptotic regime where $n\to\infty$. We prove that $v_n$, the steady-state speed of advance of the particle system, converges, as $n\to\infty$, to a limit $v_{**}$ which can easily be found from a minimum speed selection principle. Also we prove that as $n\to\infty$, the system dynamics converges to that of a deterministic mean-field limit (MFL). We show that the average speed of advance of any MFL is lower-bounded by $v_{**}$, and the speed of a ‘benchmark’ MFL, resulting from all particles initially being co-located, is equal to $v_{**}$. In the special case of exponentially distributed independent jump sizes, we prove that a traveling-wave MFL with speed v exists if and only if $v\ge v_{**}$, with $v_{**}$ having a simple explicit form; we also show the existence of traveling waves for the modified systems with a left or right boundary moving at a constant speed v. We provide bounds on an MFL’s average speed of advance, depending on the right tail exponent of its initial state. We conjecture that these results for exponential jump sizes extend to general jump sizes.

We reviewed all diagnoses of Shigella species notified to the UK Health Security Agency from January 2016 to March 2023. An overall increase in notifications of shigellosis was seen between 2016 (n = 415/quarter) and 2023 (n = 1 029/quarter). However, notifications dramatically declined between March 2020 and September 2021 during the COVID-19 pandemic (n = 208/quarter) highlighting the impact of travel and social distancing restrictions on transmission. S. sonnei diagnoses were more affected by lockdown restrictions than S. flexneri, most likely due to a combination of species-specific characteristics and host attributes. Azithromycin resistance continued to be associated with epidemics of sexually transmissible S. flexneri (adult males = 45.6% vs. adult females = 8.7%) and S. sonnei (adult males = 59.5% vs. adult females = 14.6%). We detected resistance to ciprofloxacin in S. sonnei from adult male cases not reporting travel at a higher frequency (79.4%) than in travel-associated cases (61.7%). Extensively drug-resistant Shigella species associated with sexual transmission among men almost exclusively had ESBL encoded by blaCTX-M-27, whereas those associated with returning travellers had blaCTX-M-15. Given the increasing incidence of infections and AMR, we recommend that enhanced surveillance is used to better understand the impact of travel and sexual transmission on the acquisition and spread of MDR and XDR Shigella species.

Escherichia albertii is an emerging foodborne enteropathogen associated with infectious diarrhoea in humans. In February 2023, an outbreak of acute gastroenteric cases was reported in a junior high school located in Hangzhou, Zhejiang province, China. Twenty-two investigated patients presented diarrhoea (22/22, 100%), abdominal pain (21/22, 95.5%), nausea (6/22, 27.3%), and vomiting (3/22, 13.6%). E. albertii strains were successfully isolated from anal swabs collected from six patients. Each isolate was classified as sequence type ST2686, harboured eae-β gene, and carried both cdtB-I and cdtB-II subtypes, being serotyped as EAOg32:EAHg4 serotype. A comprehensive whole-genome phylogenetic analysis revealed that the six isolates formed a distinct cluster, separate from other strains. These isolates exhibited minimal genetic variation, differing from one another by 0 to 1 single nucleotide polymorphism, suggesting a common origin from a single clone. To the best of our knowledge, this represented the first reported outbreak of gastroenteritis attributed to E. albertii outside of Japan on a global scale.

We propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations which characterize nonlinear $\alpha$-stable Lévy processes under a sublinear expectation space with $\alpha\in(1,2)$. We further establish the error bounds for the monotone approximation scheme. This in turn yields an explicit Berry–Esseen bound and convergence rate for the $\alpha$-stable central limit theorem under sublinear expectation.