During the coronavirus disease 2019 (COVID-19) pandemic, many countries opted for strict public health measures, including closing schools. After some time, they have started relaxing some of those restrictions. To avoid overwhelming health systems, predictions for the number of new COVID-19 cases need to be considered when choosing a school reopening strategy. Using a computer simulation based on a stochastic compartmental model that includes a heterogeneous and dynamic network, we analyse different strategies to reopen schools in the São Paulo Metropolitan Area, including one similar to the official reopening plan. Our model allows us to describe different types of relations between people, each type with a different infectiousness. Based on our simulations and model assumptions, our results indicate that reopening schools with all students at once has a big impact on the number of new COVID-19 cases, which could cause a collapse of the health system. On the other hand, our results also show that a controlled school reopening could possibly avoid the collapse of the health system, depending on how people follow sanitary measures. We estimate that postponing the schools' return date for after a vaccine becomes available may save tens of thousands of lives just in the São Paulo Metropolitan Area compared to a controlled reopening considering a worst-case scenario. We also discuss our model constraints and the uncertainty of its parameters.

The notion of the capacity of a polynomial was introduced by Gurvits around 2005, originally to give drastically simplified proofs of the van der Waerden lower bound for permanents of doubly stochastic matrices and Schrijver’s inequality for perfect matchings of regular bipartite graphs. Since this seminal work, the notion of capacity has been utilised to bound various combinatorial quantities and to give polynomial-time algorithms to approximate such quantities (e.g. the number of bases of a matroid). These types of results are often proven by giving bounds on how much a particular differential operator can change the capacity of a given polynomial. In this paper, we unify the theory surrounding such capacity-preserving operators by giving tight capacity preservation bounds for all nondegenerate real stability preservers. We then use this theory to give a new proof of a recent result of Csikvári, which settled Friedland’s lower matching conjecture.

In this paper, we consider multi-state coherent systems that can be regarded as a series/parallel/recurrent connection of multi-state modules with binary/multi-state components. The multi-state (survival) signatures of such systems are presented in terms of multi-state (survival) signatures of related modules based on the structures. For a recurrent structure, the multi-state survival signature of the structure is also needed. The results established here are finally illustrated with a number of examples.

Student's t test is valid for statistical inference under the normality assumption or asymptotically. By contrast, although the bootstrap t test was proposed in 1993, it is seldom adopted in medical research. We aim to demonstrate that the bootstrap t test outperforms Student's t test under normality in data. Using random data samples from normal distributions, we evaluated the testing performance, in terms of true-positive rate (TPR) and false-positive rate and diagnostic abilities, in terms of the area under the curve (AUC), of the bootstrap t test and Student's t test. We explore the AUC of both tests with varying sample size and coefficient of variation. We compare the testing outcomes using the COVID-19 serial interval (SI) data in Shenzhen and Hong Kong, China, for demonstration. With fixed TPR, the bootstrap t test maintained the equivalent accuracy in TPR, but significantly improved the true-negative rate from the Student's t test. With varying TPR, the diagnostic ability of bootstrap t test outperformed or equivalently performed as Student's t test in terms of the AUC. The equivalent performances are possible but rarely occur in practice. We find that the bootstrap t test outperforms by successfully detecting the difference in COVID-19 SI, which is defined as the time interval between consecutive transmission generations, due to sex and non-pharmaceutical interventions against the Student's t test. We demonstrated that the bootstrap t test outperforms Student's t test, and it is recommended to replace Student's t test in medical data analysis regardless of sample size.

The outbreak of pneumonia-like respiratory disorder at China and its rapid transmission world-wide resulted in public health emergency, which brought lineage B betacoronaviridae SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) into spotlight. The fairly high mutation rate, frequent recombination and interspecies transmission in betacoronaviridae are largely responsible for their temporal changes in infectivity and virulence. Investigation of global SARS-CoV-2 genotypes revealed considerable mutations in structural, non-structural, accessory proteins as well as untranslated regions. Among the various types of mutations, single-nucleotide substitutions are the predominant ones. In addition, insertion, deletion and frame-shift mutations are also reported, albeit at a lower frequency. Among the structural proteins, spike glycoprotein and nucleocapsid phosphoprotein accumulated a larger number of mutations whereas envelope and membrane proteins are mostly conserved. Spike protein and RNA-dependent RNA polymerase variants, D614G and P323L in combination became dominant world-wide. Divergent genetic variants created serious challenge towards the development of therapeutics and vaccines. This review will consolidate mutations in different SARS-CoV-2 proteins and their implications on viral fitness.

This paper derives the limit distribution of the rescaled sum of the absolute value of an integrated process with continuously distributed innovations raised to a negative power less than $-$1, and of the analogous statistic that is obtained using the same function of an integrated process but only considering positive values of the integrated process. We show that the limit behavior of this statistic is determined by the values of the integrated process that are closest to 0, and find the limit behavior of the values of the integrated process that are closest to 0.

Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in=\in (m) < 1$$; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

Susceptible S-Infected I-Recovered R-Death D (SIRD) compartmental models are often used for modelling of infectious diseases. On the basis of the analogy between SIRD and compartmental models in hydrology, this study makes mathematical formulations developed in hydrology available for modelling in epidemiology. We adapt the Hayami model solution of the diffusive wave equation generally used in hydrological modelling to compartmental I–R–D models in epidemiology by simulating the relationships between the number of infectious I(t), the number of recoveries R(t) and the number of deaths D(t). The Hayami model is easy-to-use, robust and parsimonious. We compare the empirical one-parameter exponential model usually used in SIRD models to the two-parameter Hayami model. Applications were implemented on the recent Covid-19 pandemic. The application on data from 24 countries shows that both models give comparable performances for modelling the I–D relationship. However, for modelling the I–R relationship and the active cases, the exponential model gives fair performances whereas the Hayami model substantially improves the model performances. The Hayami model also presents the advantage that its parameters can be easily estimated from the analysis of the data distributions of I(t), R(t) and D(t). The Hayami model is parsimonious with only two parameters which are useful to compare the temporal evolution of recoveries and deaths in different countries based on different contamination rates and recoveries strategies. This study highlights the interest of knowledge transfer between different scientific disciplines in order to model different processes.

Since 2015, the incidence of invasive meningococcal disease (IMD) caused by serogroup W (MenW) has increased in Sweden, due to the introduction of the 2013 strain belonging to clonal complex 11. The aim of this study was to describe the clinical presentation of MenW infections, in particular the 2013 strain, including genetic associations. Medical records of confirmed MenW IMD cases in Sweden during the years 1995–2019 (n = 113) were retrospectively reviewed and the clinical data analysed according to strain. Of all MenW patients, bacteraemia without the focus of infection was seen in 44%, bacteraemic pneumonia in 26%, meningitis in 13% and epiglottitis in 8%, gastrointestinal symptoms in 48% and 4% presented with petechiae. Phylogenetic analysis was used for possible links between genetic relationship and clinical picture. The 2013 strain infections, particularly in one cluster, were associated with more severe disease compared with other MenW infections. The patients with 2013 strain infections (n = 68) were older (52 years vs. 25 years for other strains), presented more often with diarrhoea as an atypical presentation (P = 0.045) and were more frequently admitted for intensive care (P = 0.032). There is a risk that the atypical clinical presentation of MenW infections, with predominantly gastrointestinal or respiratory symptoms rather than neck stiffness or petechiae, may lead to delay in life-saving treatment.

Systemic risk (SR) is considered as the risk of collapse of an entire system, which has played a significant role in explaining the recent financial turmoils from the insurance and financial industries. We consider the asymptotic behavior of the SR for portfolio losses in the model allowing for heavy-tailed primary losses, which are equipped with a wide type of dependence structure. This risk model provides an ideal framework for addressing both heavy-tailedness and dependence. As some extensions, several simulation experiments are conducted, where an insurance application of the asymptotic characterization to the determination and approximation of related SR capital has been proposed, based on the SR measure.

Raw mortality data often exhibit irregular patterns due to randomness. Graduation refers to the act of smoothing crude mortality rates. In this paper, we propose a flexible and robust methodology for graduating mortality rates using adaptive P-splines. Since the observed data at high ages are often sparse and unreliable, we use an exponentially increasing penalty. We use mortality data of England and Wales and model male and female mortality rates jointly by means of penalties, achieving borrowing of information between the two sexes.

Conflicting results have been obtained through meta-analyses for the role of obesity as a risk factor for adverse outcomes in patients with coronavirus disease-2019 (COVID-19), possibly due to the inclusion of predominantly multimorbid patients with severe COVID-19. Here, we aimed to study obesity alone or in combination with other comorbidities as a risk factor for short-term all-cause mortality and other adverse outcomes in Mexican patients evaluated for suspected COVID-19 in ambulatory units and hospitals in Mexico. We performed a retrospective observational analysis in a national cohort of 71 103 patients from all 32 states of Mexico from the National COVID-19 Epidemiological Surveillance Study. Two statistical models were applied through Cox regression to create survival models and logistic regression models to determine risk of death, hospitalisation, invasive mechanical ventilation, pneumonia and admission to an intensive care unit, conferred by obesity and other comorbidities (diabetes mellitus (DM), chronic obstructive pulmonary disease, asthma, immunosuppression, hypertension, cardiovascular disease and chronic kidney disease). Models were adjusted for other risk factors. From 24 February to 26 April 2020, 71 103 patients were evaluated for suspected COVID-19; 15 529 (21.8%) had a positive test for SARS-CoV-2; 46 960 (66.1%), negative and 8614 (12.1%), pending results. Obesity alone increased adjusted mortality risk in positive patients (hazard ratio (HR) = 2.7, 95% confidence interval (CI) 2.04–2.98), but not in negative and pending-result patients. Obesity combined with other comorbidities further increased risk of death (DM: HR = 2.79, 95% CI 2.04–3.80; immunosuppression: HR = 5.06, 95% CI 2.26–11.41; hypertension: HR = 2.30, 95% CI 1.77–3.01) and other adverse outcomes. In conclusion, obesity is a strong risk factor for short-term mortality and critical illness in Mexican patients with COVID-19; risk increases when obesity is present with other comorbidities.

Financial literacy is a core life skill for participating in modern society. But how many of us have been educated about money; the importance of budgeting and saving for a rainy day; how bank accounts and debt work and when it makes sense to save for a pension? Our brief research to date indicates a shockingly low level of financial literacy in the general population. And, it does not look like this will get better soon; regarding improving financial literacy, the Financial Services Authority stated in 2003 that “Never has the need been so great or so urgent”. And yet many children will go through school without an hour spent studying financial literacy. Furthermore, efforts to improve financial literacy at older ages are either non-existent or piecemeal at best.

The consequences of poor financial literacy are especially damaging for vulnerable people. Vulnerable groups of people are most at risk of making poor financial decisions throughout their lives, which has negative consequences for saving, home ownership, debt levels, retirement and financial inclusion. In this paper, we consider various mechanisms to protect such financial customers, whilst recognising that improving financial literacy is not a silver bullet to improve customer outcomes from financial products.

Financial literacy cannot be brought to a point where the public can understand many financial products without support and advice. But surely, awareness of basic financial literacy principles can be raised, including the most important: when to seek support and advice before undertaking important financial decisions. The paper suggests some key principles for financial literacy and will also consider methods and tools to allow the public to access much-needed support and advice.

Although vaccines have become available, emergence and rapid transmission of new variants have added new paradigm in the coronavirus disease-2019 (COVID-19) pandemic. Weather, population and host immunity have been detected as the regulatory elements of COVID-19. This study aims to investigate the effects of weather, population and host factors on the outcome of COVID-19 and mutation frequency in Japan. Data were collected during January 2020 to February 2021. About 92% isolates were form GR clades. Variants 501Y.V1 (53%) and 452R.V1 (24%) were most prevalent in Japan. The strongest correlation was detected between fatalities and population density (rs = 0.81) followed by total population (rs = 0.72). Relative humidity had the highest correlation (rs = −0.71) with the case fatality rate. Cluster mutations namely N501Y (45%), E484K (30%), N439K (16%), K417N (6%) and T478I (3%) at spike protein have increased during January to February 2021. Above 90% fatality was detected in patients aged >60 years. The ratio of male to female patients of COVID-19 was 1.35:1. This study will help to understand the seasonality of COVID-19 and impact of weather on the outcome which will add knowledge to reduce the health burden of COVID-19 by the international organisations and policy makers.

This paper provides a method to assess the risk relief deriving from a foreign expansion by a life insurance company. We build a parsimonious continuous-time model for longevity risk that captures the dependence across different ages in domestic versus foreign populations. We calibrate the model to portray the case of a UK annuity portfolio expanding internationally toward Italian policyholders. The longevity risk diversification benefits of an international expansion are sizable, in particular when interest rates are low. The benefits are judged based on traditional measures, such as the Risk Margin or volatility reduction, and on a novel measure, the Diversification Index.

Hospital healthcare workers (HCWs) are at increased risk of contracting COVID-19 infection. We aimed to determine the seroprevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antibodies in HCWs in Ireland. Two tertiary referral hospitals in Irish cities with diverging community incidence and seroprevalence were identified; COVID-19 had been diagnosed in 10.2% and 1.8% of staff respectively by the time of the study (October 2020). All staff of both hospitals (N = 9038) were invited to participate in an online questionnaire and blood sampling for SARS-CoV-2 antibody testing. Frequencies and percentages for positive SARS-CoV-2 antibody were calculated and adjusted relative risks (aRR) for participant characteristics were calculated using multivariable regression analysis. In total, 5788 HCWs participated (64% response rate). Seroprevalence of antibodies to SARS-CoV-2 was 15% and 4.1% in hospitals 1 and 2, respectively. Thirty-nine percent of infections were previously undiagnosed. Risk for seropositivity was higher for healthcare assistants (aRR 2.0, 95% confidence interval (CI) 1.4–3.0), nurses (aRR: 1.6, 95% CI 1.1–2.2), daily exposure to patients with COVID-19 (aRR: 1.6, 95% CI 1.2–2.1), age 18–29 years (aRR: 1.4, 95% CI 1.1–1.9), living with other HCWs (aRR: 1.3, 95% CI 1.1–1.5), Asian background (aRR: 1.3, 95% CI 1.0–1.6) and male sex (aRR: 1.2, 95% CI 1.0–1.4). The HCW seroprevalence was six times higher than community seroprevalence. Risk was higher for those with close patient contact. The proportion of undiagnosed infections call for robust infection control guidance, easy access to testing and consideration of screening in asymptomatic HCWs. With emerging evidence of reduction in transmission from vaccinated individuals, the authors strongly endorse rapid vaccination of all HCWs.

Estimating the lengths-of-stay (LoS) of hospitalised COVID-19 patients is key for predicting the hospital beds’ demand and planning mitigation strategies, as overwhelming the healthcare systems has critical consequences for disease mortality. However, accurately mapping the time-to-event of hospital outcomes, such as the LoS in the intensive care unit (ICU), requires understanding patient trajectories while adjusting for covariates and observation bias, such as incomplete data. Standard methods, such as the Kaplan-Meier estimator, require prior assumptions that are untenable given current knowledge. Using real-time surveillance data from the first weeks of the COVID-19 epidemic in Galicia (Spain), we aimed to model the time-to-event and event probabilities of patients’ hospitalised, without parametric priors and adjusting for individual covariates. We applied a non-parametric mixture cure model and compared its performance in estimating hospital ward (HW)/ICU LoS to the performances of commonly used methods to estimate survival. We showed that the proposed model outperformed standard approaches, providing more accurate ICU and HW LoS estimates. Finally, we applied our model estimates to simulate COVID-19 hospital demand using a Monte Carlo algorithm. We provided evidence that adjusting for sex, generally overlooked in prediction models, together with age is key for accurately forecasting HW and ICU occupancy, as well as discharge or death outcomes.

No previous studies have examined Mycobacterium avium complex pulmonary disease (MAC-PD) in only elderly patients ⩾75 years old. Here, we investigated the exacerbating factors of MAC-PD in elderly patients and clarified cases that can be followed up without MAC medication. From April 2011 to March 2019, 126 advanced aged patients at our institute were newly diagnosed with MAC-PD, and could be observed based on radiological findings for over a year. Their medical records were retrospectively examined for clinical and radiological findings at the time of diagnosis and 1 year later. To identify the predictors of exacerbation, clinical characteristics of 109 treatment-naïve patients were compared between exacerbated and unchanged groups. Additionally, the unchanged group was followed for one more year. In the current study, positive acid-fast bacilli smears from the sputum test, the presence of cavitary lesions and extensive radiological findings, particularly abnormal shadows in ⩾3 lobes, were predictive of exacerbation among treatment-naïve elderly MAC-PD patients. In the unchanged group, <10% showed exacerbation of radiological findings within the subsequent year. In conclusion, if the sputum smear is negative, no cavitary lesions are present, and abnormal shadows are restricted to ⩽2 lobes, elderly patients with MAC-PD may remain untreated for a few years.

The study aims to estimate and compare the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) seroprevalence, the fraction of asymptomatic or subclinical infections in the population, determine the demographic risk factors and analyse the antibody development at different time points among adults in Bhubaneswar city, India. This was a serial three-round cross-sectional, community-based study where participants were selected from the residents of Bhubaneswar city using multi-stage random sampling. Blood samples were collected during household visits along with demographic and clinical data from every participant. Total anti-SARS-CoV-2 antibody present in serum was assessed using the electro-chemiluminescence immunoassay platform. Temporal comparisons of the community seroprevalence were performed against the detected number of cumulative cases, active cases, recoveries and deaths. A total of 3693 participants were enrolled in this study with a cumulative non-response rate of 18.33% in all the three rounds. The gender-weighted seroprevalence for the city in the first round was 1.55% (95% confidence interval (CI) 0.84–2.58), second round was 5.27% (95% CI 4.13–6.59) and in the third round was 49.04% (95% CI 46.39–51.68). In the first round, the seroprevalence was found to be highest in the elderly population, whereas the seroprevalence for the second and third phases was highest in the age group of 30–39 years. Seroprevalence showed an increasing trend over the three time periods, with the highest seropositivity rates among individuals sampled between 16 and 18 September 2020. By the third round, 93.93% of those who had previously been tested positive by real-time reverse transcription polymerase chain reaction had seroconversion and 46.57% of those who had been tested negative also showed seroconversion. Infection to case ratio during first round was 27.05, for second round and third round it was 5.62 and 17.91, respectively.