Let $\gamma(G)$ and $${\gamma _ \circ }(G)$$ denote the sizes of a smallest dominating set and smallest independent dominating set in a graph G, respectively. One of the first results in probabilistic combinatorics is that if G is an n-vertex graph of minimum degree at least d, then

$$\begin{equation}\gamma(G) \leq \frac{n}{d}(\log d + 1).\end{equation}$$

In this paper the main result is that if G is any n-vertex d-regular graph of girth at least five, then

$$\begin{equation}\gamma_(G) \leq \frac{n}{d}(\log d + c)\end{equation}$$

$d \rightarrow \infty$

$$\begin{equation}\gamma_(G) \sim \frac{n}{d}\log d.\end{equation}$$

Furthermore, if G is a disjoint union of ${n}/{(2d)}$ complete bipartite graphs $K_{d,d}$, then ${\gamma_\circ}(G) = \frac{n}{2}$. We also prove that there are n-vertex graphs G of minimum degree d and whose maximum degree grows not much faster than d log d such that ${\gamma_\circ}(G) \sim {n}/{2}$ as $d \rightarrow \infty$. Therefore both the girth and regularity conditions are required for the main result.

Past studies using the positive deviance (PD) approach in the field of infection prevention and control (IPC) have primarily focused on impacts on healthcare-associated infection rates. This research aimed to determine if health professionals who exhibit PD behaviours have distinctive socio-cognitive profiles compared to non-PD professionals, and to examine the impact of a PD intervention on healthcare professionals’ (HPs) behavioural changes in maintaining IPC guidelines. In a cross-sectional study among 135 HPs, respondents first filled out a socio-cognitive characteristics questionnaire, and after 5 months were requested to complete a self-reported behavioural change questionnaire. The main findings indicate that socio-cognitive variables such as external locus of control, perceived threat and social learning were significant predictors of a person exhibiting PD behaviours. Almost 70% of HPs reported behavioural change and creating social networks as a result of the PD intervention in maintaining IPC guidelines, 16.9% of them are a ‘PD boosters’ (a new group of HPs who have adopted the positive practices of PDs that were originally identified, and also added additional practices of their own). Social networks can contribute to internalizing and raising personal accountability even among non-PD professionals, by creating a mind map that makes each person believe they are an important node in the network, regardless of their status and role. Health intervention programmes should purposely make visible and prominent social network connections in the hospital system.

Dromedary camels remain the currently identified reservoir for the Middle East respiratory syndrome coronavirus (MERS-CoV). The virus is released in the secretions of the infected camels, especially the nasal tract. The virus shedding curve through the nasal secretions was studied. Although human transmission of the virus through the respiratory tract of close contact people with dromedary reported previously, the exact mechanism of transmission is still largely unknown. The main goal of this study was to check the possibility of MERS-CoV shedding in the exhaled air of the infected camels. To achieve this goal, we conducted a follow-up study in one of the dromedary camel herds, December 2018–April 2019. We tested nasal swabs, breath samples from animals within this herd by the real-time PCR. Our results showed that some of the tested nasal swabs and breath were positive from 24 March 2019 until 7 April 2019. The phylogenetic analysis of the obtained S and N gene sequences revealed the detected viruses are clustering together with some human and camel samples from the eastern region, especially from Al-Hufuf city, as well as some samples from Qatar and Jordon. These results are clearly showing the possibility of shedding of the virus in the breath of the infected camels. This could explain, at least in part, the mechanism of transmission of MERS-CoV from animals to humans. This study is confirming the shedding of MERS-CoV in the exhaled air of the infected camels. Further studies are needed for a better understanding of the MERS-CoV.

To determine what exacerbate severity of the COVID-19 among patients without comorbidities and advanced age and investigate potential clinical indicators for early surveillance, we adopted a nested case−control study, design in which severe cases (case group, n = 67) and moderate cases (control group, n = 67) of patients diagnosed with COVID-19 without comorbidities, with ages ranging from 18 to 50 years who admitted to Wuhan Tongji Hospital were matched based on age, sex and BMI. Demographic and clinical characteristics, and risk factors associated with severe symptoms were analysed. Percutaneous oxygen saturation (SpO2), lymphocyte counts, C-reactive protein (CRP) and IL-10 were found closely associated with severe COVID-19. The adjusted multivariable logistic regression analyses revealed that the independent risk factors associated with severe COVID-19 were CRP (OR 2.037, 95% CI 1.078–3.847, P = 0.028), SpO2 (OR 1.639, 95% CI 0.943–2.850, P = 0.080) and lymphocyte (OR 1.530, 95% CI 0.850–2.723, P = 0.148), whereas the changes exhibited by indicators influenced incidence of disease severity. Males exhibited higher levels of indicators associated with inflammation, myocardial injury and kidney injury than the females. This study reveals that increased CRP levels and decreased SpO2 and lymphocyte counts could serve as potential indicators of severe COVID-19, independent of comorbidities, advanced age and sex. Males could at higher risk of developing severe symptoms of COVID-19 than females.

In Germany, sheep are the main source of human Q fever epidemics, but data on Coxiella burnetii (C. burnetii) infections and related risk factors in the German sheep population remain scarce. In this cross-sectional study, a standardised interview was conducted across 71 exclusively sheep as well as mixed (sheep and goat) farms to identify animal and herd level risk factors associated with the detection of C. burnetii antibodies or pathogen-specific gene fragments via univariable and multivariable logistic regression analysis. Serum samples and genital swabs from adult males and females of 3367 small ruminants from 71 farms were collected and analysed using ELISA and qPCR, respectively. On animal level, univariable analysis identified young animals (<2 years of age; odds ratio (OR) 0.33; 95% confidence interval (CI) 0.13–0.83) to reduce the risk for seropositivity significantly (p < 0.05). The final multivariable logistic models identified lambing all year-round (OR 3.46/3.65; 95% CI 0.80–15.06/0.41–32.06) and purchases of sheep and goats (OR 13.61/22.99; 95% CI 2.86–64.64/2.21–239.42) as risk factors on herd level for C. burnetii infection detected via ELISA and qPCR, respectively.

We analysed associations between exposure to nightlife businesses and severe acute respiratory syndrome coronavirus 2 PCR test results at a tertiary hospital in Tokyo between March and April 2020. A nightlife group was defined as those who had worked at or visited the businesses. We included 1517 individuals; 196 (12.9%) were categorised as the nightlife group. After propensity score matching, the proportion of positive PCR tests in the nightlife group was significantly higher than that in the non-nightlife group (nightlife, 63.8%; non-nightlife, 23.0%; P < 0.001). An inclusive approach to mitigate risks related to the businesses needs to be identified.

The coronavirus 2019 (COVID-19) outbreak in China rapidly spread throughout the world, becoming a threatening pandemic with unprecedented consequences. Mobile technologies have led to a revolution in health and their applicability in the context of COVID-19 is promising. In this commentary, we provide an overview of the role that mobile technologies play in the COVID-19 pandemic context and discuss the main issues associated. Four main domains stood out: health communication, prevention, support and research. Strengthening local surveillance systems, geographic contact tracing, support for clinical practice and data collection of real-time longitudinal data at the population level are some of the main advantages of the applications reported so far. The potential conflict to data privacy urges for discussion on their use in a responsible manner. Along with fair regulation and close monitoring of data collection and process, data anonymisation must be a standard and personal data must be deleted after its usage. Preparation is key for effective containment of a public health crisis and learning lessons on the role of mobile technologies is useful for future challenges in global health. It is noteworthy that their use must be driven by an equitable and inclusive orientation, and mostly integrated into an articulated policy to respond to the crisis.

COVID-19 has caused a major global pandemic and necessitated unprecedented public health restrictions in almost every country. Understanding risk factors for severe disease in hospitalised patients is critical as the pandemic progresses. This observational cohort study aimed to characterise the independent associations between the clinical outcomes of hospitalised patients and their demographics, comorbidities, blood tests and bedside observations. All patients admitted to Northwick Park Hospital, London, UK between 12 March and 15 April 2020 with COVID-19 were retrospectively identified. The primary outcome was death. Associations were explored using Cox proportional hazards modelling. The study included 981 patients. The mortality rate was 36.0%. Age (adjusted hazard ratio (aHR) 1.53), respiratory disease (aHR 1.37), immunosuppression (aHR 2.23), respiratory rate (aHR 1.28), hypoxia (aHR 1.36), Glasgow Coma Scale <15 (aHR 1.92), urea (aHR 2.67), alkaline phosphatase (aHR 2.53), C-reactive protein (aHR 1.15), lactate (aHR 2.67), platelet count (aHR 0.77) and infiltrates on chest radiograph (aHR 1.89) were all associated with mortality. These important data will aid clinical risk stratification and provide direction for further research.