In rapidly growing and high-burden urban centres, identifying tuberculosis (TB) transmission hotspots and understanding the potential impact of interventions can inform future control and prevention strategies. Using data on local demography, TB reports and patient reporting patterns in Dhaka South City Corporation (DSCC) and Dhaka North City Corporation (DNCC), Bangladesh, between 2010 and 2017, we developed maps of TB reporting rates across wards in DSCC and DNCC and identified wards with high rates of reported TB (i.e. ‘hotspots’) in DSCC and DNCC. We developed ward-level transmission models and estimated the potential epidemiological impact of three TB interventions: active case finding (ACF), mass preventive therapy (PT) and a combination of ACF and PT, implemented either citywide or targeted to high-incidence hotspots. There was substantial geographic heterogeneity in the estimated TB incidence in both DSCC and DNCC: incidence in the highest-incidence wards was over ten times higher than in the lowest-incidence wards in each city corporation. ACF, PT and combined ACF plus PT delivered to 10% of the population reduced TB incidence by a projected 7%–9%, 13%–15% and 19%–23% over five years, respectively. Targeting TB hotspots increased the projected reduction in TB incidence achieved by each intervention 1.4- to 1.8-fold. The geographical pattern of TB notifications suggests high levels of ongoing TB transmission in DSCC and DNCC, with substantial heterogeneity at the ward level. Interventions that reduce transmission are likely to be highly effective and incorporating notification data at the local level can further improve intervention efficiency.

Recurrent outbreaks of haemolytic uraemic syndrome (HUS) caused by Shiga toxin-producing Escherichia coli (STEC) serotype O55:H7 occurred in England between 2014 and 2018. We reviewed the epidemiological evidence to identify potential source(s) and transmission routes of the pathogen, and to assess the on-going risk to public health. Over the 5-year period, there were 43 confirmed and three probable cases of STEC O55:H7. The median age of cases was 4 years old (range 6 months to 69 years old) and over half of all cases were female (28/46, 61%). There were 36/46 (78.3%) symptomatic cases, and over half of all cases developed HUS (25/46, 54%), including two fatal cases. No common food or environmental exposures were identified, although the majority of cases lived in rural or semi-rural environments and reported contact with both wild and domestic animals. This investigation informed policy on the clinical and public health management of HUS caused by STEC other than serotype O157:H7 (non-O157 STEC) in England, including comprehensive testing of all household contacts and household pets and more widespread use of polymerase chain reaction assays for the rapid diagnosis of STEC-HUS.

The classical credibility theory is a cornerstone of experience rating, especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly robust in the sense that it retains the credibility estimator’s freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.

The Turán number ex(n, H) of a graph H is the maximal number of edges in an H-free graph on n vertices. In 1983, Chung and Erdős asked which graphs H with e edges minimise ex(n, H). They resolved this question asymptotically for most of the range of e and asked to complete the picture. In this paper, we answer their question by resolving all remaining cases. Our result translates directly to the setting of universality, a well-studied notion of finding graphs which contain every graph belonging to a certain family. In this setting, we extend previous work done by Babai, Chung, Erdős, Graham and Spencer, and by Alon and Asodi.

An outbreak of SARS-CoV2 infection in a Barcelona prison was studied. One hundred and forty-eight inmates and 36 prison staff were evaluated by rt-PCR, and 24.1% (40 prisoners, two health workers and four non-health workers) tested positive. In all, 94.8% of cases were asymptomatic. The inmates were isolated in prison module 4, which was converted into an emergency COVID unit. There were no deaths. Generalised screening and the isolation and evaluation of the people infected were key measures. Symptom-based surveillance must be supplemented by rapid contact-based monitoring in order to avoid asymptomatic spread among prisoners and the community at large.

Critical cascades are found in many self-organizing systems. Here, we examine critical cascades as a design paradigm for logic and learning under the linear threshold model (LTM), and simple biologically inspired variants of it as sources of computational power, learning efficiency, and robustness. First, we show that the LTM can compute logic, and with a small modification, universal Boolean logic, examining its stability and cascade frequency. We then frame it formally as a binary classifier and remark on implications for accuracy. Second, we examine the LTM as a statistical learning model, studying benefits of spatial constraints and criticality to efficiency. We also discuss implications for robustness in information encoding. Our experiments show that spatial constraints can greatly increase efficiency. Theoretical investigation and initial experimental results also indicate that criticality can result in a sudden increase in accuracy.

Monitoring and evaluation (M&E) is an essential component of public health emergency response. In the WHO African region (WHO AFRO), over 100 events are detected and responded to annually. Here we discuss the development of the M&E for COVID-19 that established a set of regional and country indicators for tracking the COVID-19 pandemic and response measures. An interdisciplinary task force used the 11 pillars of strategic preparedness and response to define a set of inputs, outputs, outcomes and impact indicators that were used to closely monitor and evaluate progress in the evolving COVID-19 response, with each pillar tailored to specific country needs. M&E data were submitted electronically and informed country profiles, detailed epidemiological reports, and situation reports. Further, 10 selected key performance indicators were tracked to monitor country progress through a bi-weekly progress scoring tool used to identify priority countries in need of additional support from WHO AFRO. Investment in M&E of health emergencies should be an integral part of efforts to strengthen national, regional and global capacities for early detection and response to threats to public health security. The development of an adaptable M&E framework for health emergencies must draw from the lessons learned throughout the COVID-19 response.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is pandemic. Prevention and control strategies require an improved understanding of SARS-CoV-2 dynamics. We did a rapid review of the literature on SARS-CoV-2 viral dynamics with a focus on infective dose. We sought comparisons of SARS-CoV-2 with other respiratory viruses including SARS-CoV-1 and Middle East respiratory syndrome coronavirus. We examined laboratory animal and human studies. The literature on infective dose, transmission and routes of exposure was limited specially in humans, and varying endpoints were used for measurement of infection. Despite variability in animal studies, there was some evidence that increased dose at exposure correlated with higher viral load clinically, and severe symptoms. Higher viral load measures did not reflect coronavirus disease 2019 severity. Aerosol transmission seemed to raise the risk of more severe respiratory complications in animals. An accurate quantitative estimate of the infective dose of SARS-CoV-2 in humans is not currently feasible and needs further research. Our review suggests that it is small, perhaps about 100 particles. Further work is also required on the relationship between routes of transmission, infective dose, co-infection and outcomes.

The global outbreak of coronavirus disease 2019 (COVID-19) is greatly threatening the public health in the world. We reconstructed global transmissions and potential demographic expansions of severe acute respiratory syndrome coronavirus 2 based on genomic information. We found that intercontinental transmissions were rare in January and early February but drastically increased since late February. After world-wide implements of travel restrictions, the transmission frequencies decreased to a low level in April. We identified a total of 88 potential demographic expansions over the world based on the star-radiative networks and 75 of them were found in Europe and North America. The expansion numbers peaked in March and quickly dropped since April. These findings are highly concordant with epidemic reports and modelling results and highlight the significance of quarantine validity on the global spread of COVID-19. Our analyses indicate that the travel restrictions and social distancing measures are effective in containing the spread of COVID-19.

Serology data are an increasingly important tool in malaria surveillance, especially in low transmission settings where the estimation of parasite-based indicators is often problematic. Existing methods rely on the use of thresholds to identify seropositive individuals and estimate transmission intensity, while making assumptions about the temporal dynamics of malaria transmission that are rarely questioned. Here, we present a novel threshold-free approach for the analysis of malaria serology data which avoids dichotomization of continuous antibody measurements and allows us to model changes in the antibody distribution across age in a more flexible way. The proposed unified mechanistic model combines the properties of reversible catalytic and antibody acquisition models, and allows for temporally varying boosting and seroconversion rates. Additionally, as an alternative to the unified mechanistic model, we also propose an empirical approach to analysis where modelling of the age-dependency is informed by the data rather than biological assumptions. Using serology data from Western Kenya, we demonstrate both the usefulness and limitations of the novel modelling framework.

The present study attempted to analyse human papillomavirus (HPV) genotype distribution and its association with cervical cytology results in women in western China. The present retrospective analysis was performed in 1089 female outpatients with a positive HPV test result who had undergone a cervical cytology test at the gynaecological clinic, West China Second Hospital, Sichuan University, China, between January 2014 and December 2016. Of the 1089 patients with HPV infection, multiple HPV genotypes were detected in 220 patients (20.20%). Among the 1368 HPV genotypes detected, 1145 (83.70%) were high-risk subtypes. The most common genotypes were HPV-52 (18.64%), HPV-16 (16.59%), HPV-58 (13.23%), HPV-18 (6.80%), HPV-56 (5.56%) and HPV-59 (5.56%). Cervical cytology revealed abnormal cells in 430 (39.49%) patients. The most common diagnoses were atypical squamous cells of undetermined significance (ASC-US; 236 cases, 54.88%), low-grade squamous intraepithelial lesions (LSIL; 151 cases, 35.12%), high-grade squamous intraepithelial lesions (HSIL; 63 cases, 14.65%) and atypical glandular cells (AGC; 21 cases, 4.88%). HPV-66 was significantly associated (P = 0.037) with ASC; HPV-52 and HPV-56 were significantly associated with LSIL (P = 0.009 and 0.026, respectively); HPV-16 (P < 0.001), HPV-33 (P = 0.014) and HPV-58 (P = 0.003) were significantly associated with HSIL; and HPV-16 (P = 0.005) was significantly associated with AGC. HPV-16, HPV-52 and HPV-58 are associated with different diagnoses in patients with positive cervical cytological findings.

In 2009, the Robert Koch Institute (RKI) and the 16 German federal state public health authorities (PHAs) established a weekly epidemiological teleconference (EpiLag) to discuss infectious disease (ID) events and foster horizontal and vertical information exchange. We present the procedure, discussed ID topics and evaluation results of EpiLag after 10 years. We analysed attendance, duration of EpiLag and the frequency of reported events. Participants (RKI and state PHA) were surveyed regarding their satisfaction with logistics, contents and usefulness of EpiLag (Likert scales). Between 2009 and 2018, RKI hosted 484 EpiLag conferences with a mean duration of 25 min (range: 4–60) and high participation (range: 9–16; mean: 15 PHAs). Overall, 2975 ID events (39% international, 9% national and 52% subnational) were presented (mean: 6.1 per EpiLag), most frequently on measles (18%), salmonellosis (8%) and influenza (5%). All responding participants (14/16 PHAs and 9/9 at RKI) were satisfied with the EpiLag's organization and minutes and deemed EpiLag useful for an overview and information distribution on ID events relevant to Germany. EpiLag is time efficient, easily applicable and useful for a low-threshold event communication. It supports PHAs in crises and strengthens the network of surveillance stakeholders. We recommend its implementation to other countries or sectors.

In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

Erdős asked if, for every pair of positive integers g and k, there exists a graph H having girth (H) = k and the property that every r-colouring of the edges of H yields a monochromatic cycle Ck. The existence of such graphs H was confirmed by the third author and Ruciński.

We consider the related numerical problem of estimating the order of the smallest graph H with this property for given integers r and k. We show that there exists a graph H on R10k2; k15k3 vertices (where R = R(Ck; r) is the r-colour Ramsey number for the cycle Ck) having girth (H) = k and the Ramsey property that every r-colouring of the edges of H yields a monochromatic Ck Two related numerical problems regarding arithmetic progressions in subsets of the integers and cliques in graphs are also considered.

The integration of Artificial Neural Networks (ANNs) and Feature Extraction (FE) in the context of the Sample- Partitioning Adaptive Reduced Chemistry approach was investigated in this work, to increase the on-the-fly classification accuracy for very large thermochemical states. The proposed methodology was firstly compared with an on-the-fly classifier based on the Principal Component Analysis reconstruction error, as well as with a standard ANN (s-ANN) classifier, operating on the full thermochemical space, for the adaptive simulation of a steady laminar flame fed with a nitrogen-diluted stream of n-heptane in air. The numerical simulations were carried out with a kinetic mechanism accounting for 172 species and 6,067 reactions, which includes the chemistry of Polycyclic Aromatic Hydrocarbons (PAHs) up to C$ {}_{20} $. Among all the aforementioned classifiers, the one exploiting the combination of an FE step with ANN proved to be more efficient for the classification of high-dimensional spaces, leading to a higher speed-up factor and a higher accuracy of the adaptive simulation in the description of the PAH and soot-precursor chemistry. Finally, the investigation of the classifier’s performances was also extended to flames with different boundary conditions with respect to the training one, obtained imposing a higher Reynolds number or time-dependent sinusoidal perturbations. Satisfying results were observed on all the test flames.

We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the ‘winding’ technology devised by McQuillan [CoRR abs/1301.2880 (2013)] and developed by Huang, Lu and Zhang [Proc. 27th Symp. on Disc. Algorithms (SODA16), 514–527]. We show that exact computation of the partition function is #P-hard, even for line graphs, indicating that an approximation algorithm is the best that can be expected. We also show that Glauber dynamics for the Ising model is rapidly mixing on line graphs, an example being the kagome lattice.