We study the so-called frog model on ${\mathbb{Z}}$ with two types of lazy frogs, with parameters $p_1,p_2\in (0,1]$ respectively, and a finite expected number of dormant frogs per site. We show that for any such $p_1$ and $p_2$ there is positive probability that the two types coexist (i.e. that both types activate infinitely many frogs). This answers a question of Deijfen, Hirscher, and Lopes in dimension one.

Since the advent of direct-acting antiviral therapy, the elimination of hepatitis c virus (HCV) as a public health concern is now possible. However, identification of those who remain undiagnosed, and re-engagement of those who are diagnosed but remain untreated, will be essential to achieve this. We examined the extent of HCV infection among individuals undergoing liver function tests (LFT) in primary care. Residual biochemistry samples for 6007 patients, who had venous blood collected in primary care for LFT between July 2016 and January 2017, were tested for HCV antibody. Through data linkage to national and sentinel HCV surveillance databases, we also examined the extent of diagnosed infection, attendance at specialist service and HCV treatment for those found to be HCV positive. Overall HCV antibody prevalence was 4.0% and highest for males (5.0%), those aged 37–50 years (6.2%), and with an ALT result of 70 or greater (7.1%). Of those testing positive, 68.9% had been diagnosed with HCV in the past, 84.9% before the study period. Most (92.5%) of those diagnosed with chronic infection had attended specialist liver services and while 67.7% had ever been treated only 38% had successfully cleared infection. More than half of HCV-positive people required assessment, and potentially treatment, for their HCV infection but were not engaged with services during the study period. LFT in primary care are a key opportunity to diagnose, re-diagnose and re-engage patients with HCV infection and highlight the importance of GPs in efforts to eliminate HCV as a public health concern.

We derive closed-form solutions to some discounted optimal stopping problems related to the perpetual American cancellable dividend-paying put and call option pricing problems in an extension of the Black–Merton–Scholes model. The cancellation times are assumed to occur when the underlying risky asset price process hits some unobservable random thresholds. The optimal stopping times are shown to be the first times at which the asset price reaches stochastic boundaries depending on the current values of its running maximum and minimum processes. The proof is based on the reduction of the original optimal stopping problems to the associated free-boundary problems and the solution of the latter problems by means of the smooth-fit and modified normal-reflection conditions. We show that the optimal stopping boundaries are characterised as the maximal and minimal solutions of certain first-order nonlinear ordinary differential equations.

This paper examines the value-at-risk (VaR) implications of mean-variance hedging. We derive an equivalence between the VaR-based hedge and the mean-variance hedging. This method transfers the investor's subjective risk-aversion coefficient into the estimated VaR measure. As a result, we characterize the collapse probability bounds under which the VaR-based hedge could be insignificantly different from the minimum-variance hedge in the presence of estimation risk. The results indicate that the squared information ratio of futures returns is the primary factor determining the difference between the minimum-variance and VaR-based hedges.

Mycoplasma genitalium (MG) and Chlamydia trachomatis (CT) are the most common sexually transmitted pathogens, which can cause cervicitis, pelvic inflammation and infertility in female. In the present study, we collected the basic information, clinical results of leucorrhoea and human papillomavirus (HPV) infection of patients, who were involved in both MG and CT RNA detection in West China Second Hospital of Sichuan University from January 2019 to April 2021, ranging from 18 to 50 years old. The results showed that the infection frequencies of MG and CT were 2.6% and 6.5%, respectively. The infection rate of CT in gynaecological patients was significantly higher than that of MG (P < 0.001). Moreover, patients with CT infection often had symptoms of gynaecological diseases, while patients with MG infection remain often asymptomatic. By exploring the connection between MG or CT infection and vaginal secretions, we found that the infection of MG or CT promoted to the increase of vaginal leukocytes, and CT infection exacerbated the decrease of the number of Lactobacillus in the vagina. Further analysis suggested that independent infection and co-infection of MG or CT resulted in abnormal vaginal secretion, affecting the stability of vaginal environment, which may induce vaginal diseases. Unexpectedly, our study found no association between MG or CT infection and high-risk HPV infection. In conclusion, our study explored the infection of MG and CT among women in Southwest China for the first time, and revealed that the infection of MG or CT would affect the homeostasis of vaginal environment, which laid a foundation for the clinical diagnosis and treatment of MG and CT infection.

In this work the $\ell_q$-norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry–Esseen bounds in the regime $1\leq q < \infty$ are derived and complemented by a non-central limit theorem together with moderate and large deviations in the case where $q=\infty$. An application to the intersection volume of a regular simplex with an $\ell_p^n$-ball is also carried out.

The study aimed to explore the relationship between eosinophils and the prognosis of varicella in adults. We retrospectively reviewed the medical records of patients who were hospitalised in The Fifth People's Hospital of Suzhou with a diagnosis of adult varicella during the period between 1 January 2012 and 31 December 2020. Of the 359 patients, 228 (63.51%) had eosinopenia. The proportion of patients with mild type disease was significantly lower in the eosinopenia group than that in the non-eosinopenia group (50.44% vs. 65.65%, P = 0.006). The proportion of the patients with common type disease was significantly higher in the eosinopenia group than that in the non-eosinopenia group (39.47% vs. 28.24%, P = 0.039). The proportion of the patients with severe type disease was higher in the eosinopenia group, although the difference did not reach statistical significance (10.09% vs. 6.11%, P = 0.243). The rates of high fever (47.81% vs. 32.82%, P = 0.008; relative risk (RR) 1.296, 95% confidence interval (CI) 1.091–1.540), headache (43.42% vs. 22.14%, P < 0.001; RR 1.415, 95% CI 1.233–1.623), anorexia (53.51% vs. 35.88%, P = 0.001; RR 1.367, 95% CI 1.129–1.655) and complications (82.89% vs. 64.12%, P < 0.001; RR 2.106, 95% CI 1.460–3.038) were also significantly higher in the eosinopenia group. Among the complications, the liver injury and skin infection were more serious in the eosinopenia group. The disease course was significantly longer in the eosinopenia group than that in the non-eosinopenia group (9.43 ± 1.89 days vs. 8.73 ± 1.25 days, P < 0.001). The improvement rate of liver injury in the recovery period was lower in the eosinopenia group than that in the non-eosinopenia group (35.38% vs. 50%, P = 0.012). The study found that adult varicella patients with eosinopenia had a more serious condition, a higher morbidity of complications and a slower recovery. Blood eosinophils can be used as a new predictor of the severity of adult varicella.

Severe fever with thrombocytopenia syndrome (SFTS) virus has caused a large number of human infections since discovered in 2009. This study elucidated epidemiological features and fatal risk factors of SFTS cases accumulated up to ten years in Taizhou, a coastal prefecture of Zhejiang Province in Eastern China. A total of 188 hospitalised SFTS cases (including 40 deaths) reported to Taizhou Center for Disease Control and Prevention (CDC) during 2011–2020 were enrolled in the study. In the past decade, the annual incidence of SFTS increased over the years (P < 0.001) along with an expanding epidemic area, and the case fatality of hospitalised cases has remained high (21.3%). Although most cases occurred in hilly areas, a coastal island had the highest incidence and case fatality. The majority of cases were over the age of 60 years (72.3%), and both incidence and case fatality of SFTS increased with age. Multivariate logistic regression analysis showed that age (OR 7.47, 95% CI 1.32–42.33; P = 0.023), and haemorrhagic manifestations including petechiae (OR 7.76, 95% CI 1.17–51.50; P = 0.034), gingival haemorrhage (OR 5.38, 95% CI 1.25–23.15; P = 0.024) and melena (OR 5.75, 95% CI 1.18–28.07; P = 0.031) were significantly associated with the death of SFTS cases. Five family clusters identified were farmers, among four of which the index patients were female with a history of hypertension. Based on the study, age is a critical risk factor for incidence and case fatality of SFTS. With an increased annual incidence over the last ten years, SFTS remains a public health threat that should not be ignored. Further study is needed to look at the natural foci in the coastal islands.

In this paper we define a family of preferential attachment models for random graphs with fitness in the following way: independently for each node, at each time step a random fitness is drawn according to the position of a moving average process with positive increments. We will define two regimes in which our graph reproduces some features of two well-known preferential attachment models: the Bianconi–Barabási and Barabási–Albert models. We will discuss a few conjectures on these models, including the convergence of the degree sequence and the appearance of Bose–Einstein condensation in the network when the drift of the fitness process has order comparable to the graph size.

Motivated by applications to wireless networks, cloud computing, data centers, etc., stochastic processing networks have been studied in the literature under various asymptotic regimes. In the heavy traffic regime, the steady-state mean queue length is proved to be $\Theta({1}/{\epsilon})$, where $\epsilon$ is the heavy traffic parameter (which goes to zero in the limit). The focus of this paper is on obtaining queue length bounds on pre-limit systems, thus establishing the rate of convergence to heavy traffic. For the generalized switch, operating under the MaxWeight algorithm, we show that the mean queue length is within $\textrm{O}({\log}({1}/{\epsilon}))$ of its heavy traffic limit. This result holds regardless of the complete resource pooling (CRP) condition being satisfied. Furthermore, when the CRP condition is satisfied, we show that the mean queue length under the MaxWeight algorithm is within $\textrm{O}({\log}({1}/{\epsilon}))$ of the optimal scheduling policy. Finally, we obtain similar results for the rate of convergence to heavy traffic of the total queue length in load balancing systems operating under the ‘join the shortest queue’ routeing algorithm.

During the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) intracellular life-cycle, two large polyproteins, pp1a and pp1ab, are produced. Processing of these by viral cysteine proteases, the papain-like protease (PLpro) and the chymotrypsin-like 3C-like protease (3CL-pro) release non-structural proteins necessary for the establishment of the viral replication and transcription complex (RTC), crucial for viral replication. Hence, these proteases are considered prime targets against which anti-coronavirus disease 2019 (COVID-19) drugs could be developed. Here, we describe the expression of a highly soluble and functionally active recombinant 3CL-pro using Escherichia coli BL21 cells. We show that the enzyme functions in a dimeric form and exhibits an unexpected inhibitory profile because its activity is potently blocked by serine rather than cysteine protease inhibitors. In addition, we assessed the ability of our 3CL-pro to function as a carrier for the receptor binding domain (RBD) of the Spike protein. The co-expressed chimeric protein, 3CLpro-RBD, did not exhibit 3CL-pro activity, but its enhanced solubility made purification easier and improved RBD antigenicity when tested against serum from vaccinated individuals in ELISAs. Chimeric proteins containing the 3CL-pro could represent an innovative approach to developing new COVID-19 vaccines.

In May of 2018, PulseNet, the national molecular subtyping network for enteric pathogens, detected a multistate cluster of illnesses caused by an uncommon molecular subtype of Salmonella serovar Mbandaka. A case was defined as an illness in a person infected with the outbreak strain of Salmonella Mbandaka with illness onset on or after 3 March 2018 and before 1 September 2018. One-hundred thirty-six cases from 36 states were identified; 35 hospitalisations and no deaths were reported. Ill people ranged in age from <1 year to 95 years (median: 57 years). When standardised questionnaires did not generate a strong hypothesis, opened-ended interviews were performed. Sixty-three of 84 (75%) ultimately reported consuming or possibly consuming a specific sweetened puffed wheat cereal in the week before illness onset. Environmental sampling performed at the cereal manufacturing facility yielded the outbreak strain. The outbreak strain was also isolated from open cereal samples from ill people's homes and from a sealed retail sample. Due to these findings, the brand owner of the product issued a voluntary recall of the cereal on 14 June 2018. Additional investigation of the manufacturing facility identified persistent environmental contamination with Salmonella Mbandaka that was closely genetically related to other isolates in the outbreak. This investigation highlights the ability of Salmonella to survive in low-moisture environments, and the potential for prolonged outbreaks linked to products with long shelf lives and large distribution areas.

This study assessed the infant feeding practices and their determinants among human immune deficiency virus (HIV)-positive mothers with infants (0–12 months).

A cross-sectional study design adopting qualitative and quantitative data collection procedures was used. This study was carried out from Awach Health Center IV in Gulu city, Uganda. We enrolled 108 adult participants who were HIV-positive mothers with an infant from October to December 2021. Semi-structured questionnaire and focused group discussion (FGD) guide were used in data collection. Data were collected, edited, coded and entered into Epi info. The data were analysed using SPSS version 22. Qualitative data were analysed using Atlas.ti software.

Of the 108 mothers, 83/108 (77%) practised exclusive breastfeeding (EBF) while 25/108 (23%) practised mixed feeding. Qualitative results also showed that EBF was the preferred choice. Majority of the respondents 104/108 (96.3%) believed HIV can be transmitted to their babies. Factors associated with infant feeding practices at multivariant level analysis at 5% significance were age of the child (OR 0.706, 95% CI 0.210–0.988), income level (OR 1.296, 95% CI 1.150–10.631).

Majority of mothers had good knowledge about the prevention of mother-to-child transmission. Mothers should deliver from hospitals, more sensitisations for these mothers to appreciate the benefits of EBF.

Globally, countries have used diverse methods to report data during the COVID-19 pandemic. Using international guidelines and principles of emergency management, we compare national data reporting systems in African countries in order to determine lessons for future pandemics. We analyse COVID-19 reporting practices across 54 African countries through 2020. Reporting systems were diverse and included summaries, press releases, situation reports and online dashboards. These systems were communicated via social media accounts and websites belonging to ministries of health and public health. Data variables from the reports included event detection (cases/deaths/recoveries), risk assessment (demographics/co-morbidities) and response (total tests/hospitalisations). Of countries with reporting systems, 36/53 (67.9%) had recurrent situation reports and/or online dashboards which provided more extensive data. All of these systems reported cases, deaths and recoveries. However, few systems contained risk assessment and response data, with only 5/36 (13.9%) reporting patient co-morbidities and 9/36 (25%) including total hospitalisations. Further evaluation of reporting practices in Cameroon, Egypt, Kenya, Senegal and South Africa as examples from different sub-regions revealed differences in reporting healthcare capacity and preparedness data. Improving the standardisation and accessibility of national data reporting systems could augment research and decision-making, as well as increase public awareness and transparency for national governments.

Even within well-studied organisms, many genes lack useful functional annotations. One way to generate such functional information is to infer biological relationships between genes or proteins, using a network of gene coexpression data that includes functional annotations. Signed distance correlation has proved useful for the construction of unweighted gene coexpression networks. However, transforming correlation values into unweighted networks may lead to a loss of important biological information related to the intensity of the correlation. Here, we introduce a principled method to construct weighted gene coexpression networks using signed distance correlation. These networks contain weighted edges only between those pairs of genes whose correlation value is higher than a given threshold. We analyze data from different organisms and find that networks generated with our method based on signed distance correlation are more stable and capture more biological information compared to networks obtained from Pearson correlation. Moreover, we show that signed distance correlation networks capture more biological information than unweighted networks based on the same metric. While we use biological data sets to illustrate the method, the approach is general and can be used to construct networks in other domains. Code and data are available on https://github.com/javier-pardodiaz/sdcorGCN.

Survivor funds are financial arrangements where participants agree to share the proceeds of a collective investment pool in a predescribed way depending on their survival. This offers investors a way to benefit from mortality credits, boosting financial returns. Following Denuit (2019, ASTIN Bulletin, 49, 591–617), participants are assumed to adopt the conditional mean risk sharing rule introduced in Denuit and Dhaene (2012, Insurance: Mathematics and Economics, 51, 265–270) to assess their respective shares in mortality credits. This paper looks at pools of individuals that are heterogeneous in terms of their survival probability and their contributions. Imposing mild conditions, we show that individual risk can be fully diversified if the size of the group tends to infinity. For large groups, we derive simple, hierarchical approximations of the conditional mean risk sharing rule.

In this article we consider a Monte-Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no time-discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee and Glynn (Operat. Res. 63, 2015) along with the multilevel particle filter (MLPF) approach of Jasra et al. (SIAM J. Numer. Anal. 55, 2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.

We consider the spectral analysis of several examples of bilateral birth–death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some probabilistic properties of the processes, such as recurrence, the invariant distribution (if it exists), and the probability current.