Since December 2019, the clinical symptoms of coronavirus disease 2019 (COVID-19) and its complications are evolving. As the number of COVID patients requiring positive pressure ventilation is increasing, so is the incidence of subcutaneous emphysema (SE). We report 10 patients of COVID-19, with SE and pneumomediastinum. The mean age of the patients was 59 ± 8 years (range, 23–75). Majority of them were men (80%), and common symptoms were dyspnoea (100%), fever (80%) and cough (80%). None of them had any underlying lung disorder. All patients had acute respiratory distress syndrome on admission, with a median PaO2/FiO2 ratio of 122.5. Eight out of ten patients had spontaneous pneumomediastinum on their initial chest x-ray in the emergency department. The median duration of assisted ventilation before the development of SE was 5.5 days (interquartile range, 5–10 days). The highest positive end-expiratory pressure (PEEP) was 10 cmH2O for patients recieving invasive mechanical ventilation, while 8 cmH2O was the average PEEP in patients who had developed subcutaneous emphysema on non-invasive ventilation. All patients received corticosteroids while six also received tocilizumab, and seven received convalescent plasma therapy, respectively. Seven patients died during their hospital stay. All patients either survivor or non-survivor had prolonged hospital stay with an average of 14 days (range 8−25 days). Our findings suggest that it is lung damage secondary to inflammatory response due to COVID-19 triggered by the use of positive pressure ventilation which resulted in this complication. We conclude that the development of spontaneous pneumomediastinum and SE whenever present, is associated with poor outcome in critically ill COVID-19 ARDS patients.

Let G be a simple graph that is properly edge-coloured with m colours and let \[\mathcal{M} = \{ {M_1},...,{M_m}\} \] be the set of m matchings induced by the colours in G. Suppose that \[m \leqslant n - {n^c}\], where \[c > 9/10\], and every matching in \[\mathcal{M}\] has size n. Then G contains a full rainbow matching, i.e. a matching that contains exactly one edge from Mi for each \[1 \leqslant i \leqslant m\]. This answers an open problem of Pokrovskiy and gives an affirmative answer to a generalization of a special case of a conjecture of Aharoni and Berger. Related results are also found for multigraphs with edges of bounded multiplicity, and for hypergraphs.

Finally, we provide counterexamples to several conjectures on full rainbow matchings made by Aharoni and Berger.

Bergamo province was badly hit by the coronavirus disease 2019 (COVID-19) epidemic. We organised a public-funded, multidisciplinary follow-up programme for COVID-19 patients discharged from the emergency department or from the inpatient wards of ‘Papa Giovanni XXIII’ Hospital, the largest public hospital in the area. As of 31 July, the first 767 patients had completed the first post-discharge multidisciplinary assessment. Patients entered our programme at a median time of 81 days after discharge. Among them, 51.4% still complained of symptoms, most commonly fatigue and exertional dyspnoea, and 30.5% were still experiencing post-traumatic psychological consequences. Impaired lung diffusion was found in 19%. Seventeen per cent had D-dimer values two times above the threshold for diagnosis of pulmonary embolism (two unexpected and clinically silent pulmonary thrombosis were discovered by investigating striking D-dimer elevation). Survivors of COVID-19 exhibit a complex array of symptoms, whose common underlying pathology, if any, has still to be elucidated: a multidisciplinary approach is fundamental, to address the different problems and to look for effective solutions.

As the on-going severe acute respiratory syndrome coronavirus 2 pandemic, we aimed to understand whether economic reopening (EROP) significantly influenced coronavirus disease 2019 (COVID-19) incidence. COVID-19 data from Texas Health and Human Services between March and August 2020 were analysed. COVID-19 incidence rate (cases per 100 000 population) was compared to statewide for selected urban and rural counties. We used joinpoint regression analysis to identify changes in trends of COVID-19 incidence and interrupted time-series analyses for potential impact of state EROP orders on COVID-19 incidence. We found that the incidence rate increased to 145.1% (95% CI 8.4–454.5%) through 4th April, decreased by 15.5% (95% CI −24.4 −5.9%) between 5th April and 30th May, increased by 93.1% (95% CI 60.9–131.8%) between 31st May and 11th July and decreased by 13.2% (95% CI −22.2 −3.2%) after 12 July 2020. The study demonstrates the EROP policies significantly impacted trends in COVID-19 incidence rates and accounted for increases of 129.9 and 164.6 cases per 100 000 populations for the 24- or 17-week model, respectively, along with other county and state reopening ordinances. The incidence rate decreased sharply after 12th July considering the emphasis on a facemask or covering requirement in business and social settings.

Hispanic/Latino populations are disproportionately impacted by coronavirus disease 2019 (COVID-19) in the United States. The impact of state reopening on COVID-19 in this population after stay-at-home orders is unknown. We evaluated the incidence, prevalence and trends during reopening of severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) at a major federally qualified health centre in Providence, Rhode Island. A total of 14 505 patients were tested for SARS-CoV-2 from 19 March to 18 August 2020, of which, data on 13 318 (91.8%) patients were available; 70.0% were Hispanic/Latino, and 2905 were positive for SARS-CoV-2 infection. The urban Hispanic/Latino population was almost five times more likely to test positive for SARS-CoV-2 (risk ratio 4.97, 95% CI 2.59–9.53, P < 0.001) compared to non-Hispanic White. The positivity rates among the urban Hispanic/Latino population remained >10% during all phases of reopening. The trends of the incidence rates showed similar associations to those we observed for positivity rates. Public health interventions to address SARS-CoV-2 in Hispanic/Latino communities are urgently needed, even in latter phases of state reopening.

This study proposed a novel ensemble analysis strategy to improve hand, foot and mouth disease (HFMD) prediction by integrating environmental data. The approach began by establishing a vector autoregressive model (VAR). Then, a dynamic Bayesian networks (DBN) model was used for variable selection of environmental factors. Finally, a VAR model with constraints (CVAR) was established for predicting the incidence of HFMD in Chengdu city from 2011 to 2017. DBN showed that temperature was related to HFMD at lags 1 and 2. Humidity, wind speed, sunshine, PM10, SO2 and NO2 were related to HFMD at lag 2. Compared with the autoregressive integrated moving average model with external variables (ARIMAX), the CVAR model had a higher coefficient of determination (R2, average difference: + 2.11%; t = 6.2051, P = 0.0003 < 0.05), a lower root mean-squared error (−24.88%; t = −5.2898, P = 0.0007 < 0.05) and a lower mean absolute percentage error (−16.69%; t = −4.3647, P = 0.0024 < 0.05). The accuracy of predicting the time-series shape was 88.16% for the CVAR model and 86.41% for ARIMAX. The CVAR model performed better in terms of variable selection, model interpretation and prediction. Therefore, it could be used by health authorities to identify potential HFMD outbreaks and develop disease control measures.

Ranked set sampling (RSS) and some of its variants are sampling designs that are applied widely in different areas. When the underlying population contains different subpopulations, we can use stratified ranked set sampling (SRSS) which combines the advantages of stratification with RSS. In the present paper, we consider the information content of SRSS in terms of extropy measure. Some results using stochastic orders properties are obtained. The effect of imperfect ranking on discrimination information is analytically investigated. It is proved that discrimination information between the perfect SRSS and simple random sampling (SRS) data sets performs better than that of between the imperfect SRSS and SRS data sets.

The severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) is highly contagious, and the coronavirus disease 2019 (COVID-19) pandemic caused by it has forced many countries to adopt ‘lockdown’ measures to prevent the spread of the epidemic through social isolation of citizens. Some countries proposed universal mask wearing as a protection measure of public health to strengthen national prevention efforts and to limit the wider spread of the epidemic. In order to reveal the epidemic prevention efficacy of masks, this paper systematically evaluates the experimental studies of various masks and filter materials, summarises the general characteristics of the filtration efficiency of isolation masks with particle size, and reveals the actual efficacy of masks by combining the volume distribution characteristics of human exhaled droplets with different particle sizes and the SARS-CoV-2 virus load of nasopharynx and throat swabs from patients. The existing measured data show that the filtration efficiency of all kinds of masks for large particles and extra-large droplets is close to 100%. From the perspective of filtering the total number of pathogens discharged in the environment and protecting vulnerable individuals from breathing live viruses, the mask has a higher protective effect. If considering the weighted average filtration efficiency with different particle sizes, the filtration efficiencies of the N95 mask and the ordinary mask are 99.4% and 98.5%, respectively. The mask can avoid releasing active viruses to the environment from the source of infection, thus maximising the protection of vulnerable individuals by reducing the probability of inhaling a virus. Therefore, if the whole society strictly implements the policy of publicly wearing masks, the risk of large-scale spread of the epidemic can be greatly reduced. Compared with the overall cost of social isolation, limited personal freedoms and forced suspension of economic activities, the inconvenience for citizens caused by wearing masks is perfectly acceptable.

The aim of this study was to explore the impact of polymorphism of PD-1 gene and its interaction with tea drinking on susceptibility to tuberculosis (TB). A total of 503 patients with TB and 494 controls were enrolled in this case–control study. Three single-nucleotide polymorphisms of PD-1 (rs7568402, rs2227982 and rs36084323) were genotyped and unconditional logistic regression analysis was used to identify the association between PD-1 polymorphism and TB, while marginal structural linear odds models were used to estimate the interactions. Genotypes GA (OR 1.434), AA (OR 1.891) and GA + AA (OR 1.493) at rs7568402 were more prevalent in the TB patients than in the controls (P < 0.05). The relative excess risk of interaction (RERI) between rs7568402 of PD-1 genes and tea drinking was −0.3856 (95% confidence interval −0.7920 to −0.0209, P < 0.05), which showed a negative interaction. However, the RERIs between tea drinking and both rs2227982 and rs36084323 of PD-1 genes were not statistically significant. Our data demonstrate that rs7568402 of PD-1 genes was associated with susceptibility to TB, and there was a significant negative interaction between rs7568402 and tea drinking. Therefore, preventive measures through promoting the consumption of tea should be emphasised in the high-risk populations.

This note re-investigates the smooth tests for the equality of distributions introduced by Bera et al. (2013, Econometric Theory 29, 419–446) and provides a modified smooth test which works for the general case with two sample sizes m and n. Asymptotic properties of the proposed test statistic under both the null and the alternative hypothesis are studied.

This paper considers the estimation of dynamic causal effects using a proxy structural vector-autoregressive model with possibly nonstationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither knowledge of the presistence properties of the variables nor pretests for nonstationarity. The proposed consistent covariance matrix estimator is robust and is easy to implement in practice. When all regressors are indeed stationary, the method becomes the same as the standard procedure.

This paper develops an asymptotic theory of nonlinear least squares estimation by establishing a new framework that can be easily applied to various nonlinear regression models with heteroscedasticity. As an illustration, we explore an application of the framework to nonlinear regression models with nonstationarity and heteroscedasticity. In addition to these main results, this paper provides a maximum inequality for a class of martingales, which is of interest in its own right.

Severe COVID-19 cases place immediate pressure on hospital resources. To assess this, we analysed survival duration in the first 39 fatal cases in Wuhan, China. Time from onset and hospitalization to death declined rapidly, from ~40 to 7 days, and ~25 to 4 days, respectively, in the outbreak’s first month.

It is important to understand the temporal trend of the paediatric severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral load to estimate the transmission potential of children in schools and communities. We determined the differences in SARS-CoV-2 viral load dynamics between nasopharyngeal samples of infected asymptomatic and symptomatic children. Serial cycle threshold values of SARS-CoV-2 from the nasopharynx of a cohort of infected children were collected for analysis. Among 17 infected children, 10 (58.8%) were symptomatic. Symptomatic children, when compared to asymptomatic children, had higher viral loads (mean cycle threshold on day 7 of illness 28.6 vs. 36.7, P = 0.02). Peak SARS-CoV-2 viral loads occurred around day 2 of illness in infected children. Although we were unable to directly demonstrate infectivity, the detection of significant amount of virus in the upper airway of asymptomatic children suggest that they have the potential to shed and transmit SARS-CoV-2. Our study highlights the importance of contact tracing and screening for SARS-CoV-2 in children with epidemiological risk factors regardless of their symptom status, in order to improve containment of the virus in the community, including educational settings.

This paper considers the customers’ equilibrium and socially optimal joining–balking behavior in a single-server Markovian queue with a single working vacation and Bernoulli interruptions. The model is motivated by practical service systems where the service rate can be adjusted according to whether or not the system is empty. Specifically, we focus on a single-server queue in which the server's service rate is reduced from a regular to a lower one when the system becomes empty. This lower rate period is called a working vacation for the server which may represent that part of the service facility is under a maintenance process or works on other non-queueing job, or simply for saving the energy (for a machine server case). In this paper, we assume that the working vacation period is terminated after a random period or with probability p after serving a customer in a non-empty system. Such a system is called a queue with single working vacation and Bernoulli interruptions. Customers are strategic and can make choice of joining or balking based on different levels of system information. We consider four scenarios: fully observable, almost observable, almost unobservable, and fully unobservable queue cases. Under a reward-cost structure, we analyze the customer's equilibrium and social-optimal strategies. In addition, the effects of system parameters on optimal strategies are illustrated by numerical examples.

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

This study applied causal criteria in directed acyclic graphs for handling covariates in associations for prognosis of severe coronavirus disease 2019 (COVID-19) cases. To identify non-specific blood tests and risk factors as predictors of hospitalisation due to COVID-19, one has to exclude noisy predictors by comparing the concordance statistics (area under the curve − AUC) for positive and negative cases of severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2). Predictors with significant AUC at negative stratum should be either controlled for their confounders or eliminated (when confounders are unavailable). Models were classified according to the difference of AUC between strata. The framework was applied to an open database with 5644 patients from Hospital Israelita Albert Einstein in Brazil with SARS-CoV-2 reverse transcription – polymerase chain reaction (RT-PCR) exam. C-reactive protein (CRP) was a noisy predictor: hospitalisation could have happened due to causes other than COVID-19 even when SARS-CoV-2 RT-PCR is positive and CRP is reactive, as most cases are asymptomatic to mild. Candidates of characteristic response from moderate-to-severe inflammation of COVID-19 were: combinations of eosinophils, monocytes and neutrophils, with age as risk factor; and creatinine, as risk factor, sharpens the odds ratio of the model with monocytes, neutrophils and age.