The purpose of this paper is twofold. The first part is to introduce relative-$\chi_{\alpha}^{2}$, Jensen-$\chi_{\alpha}^{2}$ and (p, w)-Jensen-$\chi_{\alpha}^2$ divergence measures and then examine their properties. In addition, we also explore possible connections between these divergence measures and Jensen–Shannon entropy measure. In the second part, we introduce $(p,\eta)$-mixture model and then show it to be an optimal solution to three different optimization problems based on $\chi_{\alpha}^{2}$ divergence measure. We further study the relative-$\chi_{\alpha}^{2}$ divergence measure for escort and arithmetic mixture densities. We also provide some results associated with relative-$\chi_{\alpha}^{2}$ divergence measure of mixed reliability systems. Finally, to demonstrate the usefulness of the Jensen-$\chi_{\alpha}^{2}$ divergence measure, we apply it to a real example in image processing and present some numerical results. Our findings in this regard show that the Jensen-$\chi_{\alpha}^{2}$ is an effective criteria for quantifying the similarity between two images.

To inform coverage by potential vaccines, we aimed to systematically review evidence on the prevalence and distribution of non-typhoidal Salmonella enterica serogroups and serovars. We searched four databases from inception through 4 June 2021. Articles were included that reported at least one non-typhoidal S. enterica strain by serogroup or serovar isolated from a normally sterile site. Of serogrouped isolates, we pooled the prevalence of serogroup O:4, serogroup O:9, and other serogroups using random-effects meta-analyses. Of serotyped isolates, we pooled the prevalence of Salmonella Typhimurium (member of serogroup O:4), Salmonella Enteritidis (member of serogroup O:9), and other serovars. Of 82 studies yielding 24,253 serogrouped isolates, the pooled prevalence (95% CI) was 44.6% (36.2%–48.2%) for serogroup O:4, 45.5% (37.0%–49.1%) for serogroup O:9, and 9.9% (6.1%–13.3%) for other serogroups. Of serotyped isolates, the pooled prevalence (95%CI) was 36.8% (29.9%–44.0%) for Salmonella Typhimurium, 37.8% (33.2%–42.4%) for Salmonella Enteritidis, and 18.4% (11.4%–22.9%) for other serovars. Of global serogrouped non-typhoidal Salmonella isolates from normally sterile sites, serogroup O:4 and O:9 together accounted for 90%, and among serotyped isolates, serovars Typhimurium and Enteritidis together accounted for 75%. Vaccine development strategies covering serogroups O:4 and O:9, or serovars Typhimurium and Enteritidis, have the potential to prevent the majority of non-typhoidal Salmonella invasive disease.

In this paper, we study the optimal VIX-linked target benefit (TB) pension design. By applying the dynamic programming approach, we show the optimal risk-sharing structure for the benefit payment exhibits a linear form that consists of three components: (1) a model-robust performance adjustment, (2) a counter-cyclical volatility adjustment that depends on the VIX index, and (3) a TB level that is partially indexed to the cost-of-living adjustment. Differences between our results and the previous literature are highlighted via both theoretical derivations and numerical illustrations.

We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.

This study estimated the treatment cost of pediatric abdominal tuberculosis that potentially needs surgical treatment in India. Data were collected from 38 in-patient children at Christian Medical Hospital, Ludhiana as part of a clinical study conducted to establish the patterns of presentation and outcomes of abdominal tuberculosis in an Indian setting. A bottom-up approach was used to estimate the costs from a healthcare provider perspective, and a generalized linear model (GLM) was run to find variables that had an impact on the costs. Costs were reported in international dollars ($) and India Rupees (INR). The results show that the average direct cost was $3095.00 (standard deviation [SD]: 3480.82) or 68,065.13 INR (SD: 76,539.69). The GLM results established that duration of treatment and surgical treatment were significantly associated with higher costs. Efforts of eliminating the condition should be strengthened.

There are some connections between aging notions, stochastic orders, and expected utilities. It is known that the DRHR (decreasing reversed hazard rate) aging notion can be characterized via the comparative statics result of risk aversion, and that the location-independent riskier order preserves monotonicity between risk premium and the Arrow–Pratt measure of risk aversion, and that the dispersive order preserves this monotonicity for the larger class of increasing utilities. Here, the aging notions ILR (increasing likelihood ratio), IFR (increasing failure rate), IGLR (increasing generalized likelihood ratio), and IGFR (increasing generalized failure rate) are characterized in terms of expected utilities. Based on these observations, we recover the closure properties of ILR, IFR, and DRHR under convolution, and of IGLR and IGFR under product, and investigate the closure properties of the dispersive order, location-independent riskier order, excess wealth order, the total time on test transform order under convolution, and the star order under product. We have some new findings.

Aspergillosis is a rising concern worldwide; however, its prevalence is not well documented in China. This retrospective study determined Aspergillus’s epidemiology and antifungal susceptibilities at Meizhou People’s Hospital, South China. From 2017 to 2022, the demographic, clinical, and laboratory data about aspergillosis were collected from the hospital’s records and analysed using descriptive statistics, chi-square test, and ANOVA. Of 474 aspergillosis cases, A. fumigatus (75.32%) was the most common, followed by A. niger (9.92%), A. flavus (8.86%), and A. terreus (5.91%). A 5.94-fold increase in aspergillosis occurred during the study duration, with the highest cases reported from the intensive care unit (52.74%) – chronic pulmonary aspergillosis (79.1%) and isolated from sputum (62.93%). Only 38 (8.02%) patients used immunosuppressant drugs, while gastroenteritis (5.7%), haematologic malignancy (4.22%), and cardiovascular disease (4.22%) were the most prevalent underlying illnesses. In A. fumigatus, the wild-type (WT) isolates against amphotericin B (99.1%) were higher than triazoles (97–98%), whereas, in non-fumigatus Aspergillus species, the triazole (95–100%) WT proportion was greater than amphotericin B (91–95%). Additionally, there were significantly fewer WT A. fumigatus isolates for itraconazole and posaconazole in outpatients than inpatients. These findings may aid in better understanding and management of aspergillosis in the region.

In this study, we investigate the creation and persistence of interfirm ties in a large-scale business transaction network. Business transaction relations (firms buying or selling products or services to each other) are driven by economic motives, but because trust is essential to business relationships, the social connections of owners or the geographical proximity of firms can also influence their development. However, studying the formation of interfirm business transaction ties on a large scale is rare, because of the significant data demand. The business transaction and the ownership networks of Hungarian firms are constructed from two administrative datasets for 2016 and 2017. We show that direct or indirect connections in this two-layered network, including open triads in the business network, contribute to both the creation and persistence of business transaction ties. For our estimations, we utilize log-linear models and emphasize their efficiency in predicting links in such large networks. We contribute to the literature by presenting different patterns of business connections in a nationwide multilayer interfirm network.

More than half a century ago, it was proved that the increasing failure rate (IFR) property is preserved under the formation of k-out-of-n systems (order statistics) when the lifetimes of the components are independent and have a common absolutely continuous distribution function. However, this property has not yet been proved in the discrete case. Here we give a proof based on the log-concavity property of the function $f({{\mathrm{e}}}^x)$. Furthermore, we extend this property to general distribution functions and general coherent systems under some conditions.

Within the last decade, online sustainability knowledge-action platforms have proliferated. We surveyed 198 sustainability-oriented sites and conducted a review of 41 knowledge-action platforms, which we define as digital tools that advance sustainability through organized activities and knowledge dissemination. We analyzed platform structure and functionality through a systematic coding process based on key issues identified in three bodies of literature: (a) the emergence of digital platforms, (b) the localization of the sustainable development goals (SDGs), and (c) the importance of multi-level governance to sustainability action. While online collaborative tools offer an array of resources, our analysis indicates that they struggle to provide context-sensitivity and higher-level analysis of the trade-offs and synergies between sustainability actions. SDG localization adds another layer of complexity where multi-level governance, actor, and institutional priorities may generate tensions as well as opportunities for intra- and cross-sectoral alignment. On the basis of our analysis, we advocate for the development of integrative open-source and dynamic global online data management tools that would enable the monitoring of progress and facilitate peer-to-peer exchange of ideas and experience among local government, community, and business stakeholders. We argue that by showcasing and exemplifying local actions, an integrative platform that leverages existing content from multiple extant platforms through effective data interoperability can provide additional functionality and significantly empower local actors to accelerate local to global actions, while also complex system change.

Consider a well-shuffled deck of cards of n different types where each type occurs m times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is removed from the deck. The total number of correct guesses in a complete feedback game has attracted significant interest in the past few decades. Under different regimes of m, n, the expected number of correct guesses, under the greedy (optimal) strategy, has been obtained by various authors, while there are not many results available about the fluctuations. In this paper we establish a central limit theorem with Berry–Esseen bounds when m is fixed and n is large. Our results extend to the case of decks where different types may have different multiplicity, under suitable assumptions.

Dengue, chikungunya, and Zika are arboviruses that cause 390 million infections annually. Risk factors for hospitalization are poorly understood. Communities affected by these diseases have an escalating prevalence of allergies and obesity, which are linked to immune dysfunction. We assessed the association of allergies or body mass with hospitalization for an arbovirus infection. From 2014 to 2017, we recruited participants with a clinical diagnosis of arbovirus infection. Arbovirus infections were laboratory-confirmed and allergies were self-reported. Mid-upper arm circumference (MUAC), weight, and height were measured. We used two logistic regression models to assess the relationships between hospitalization and allergies and between hospitalization and body mass (MUAC for participants <20 years old and body mass index (BMI) for adults ≥20 years old). Models were stratified by age group and adjusted for confounders. For allergies, 41 of 265 were hospitalized. There was no association between allergies and hospitalization. For body mass, 34 of 251 were hospitalized. There was a 43% decrease in hospitalization odds for each additional centimetre MUAC among children (aOR 0.566, 95% CI 0.252–1.019) and a 12% decrease in hospitalization odds for each additional BMI unit among adults (aOR 0.877, 95% CI 0.752–0.998). Our work encourages the exploration of the underlying mechanisms.

Wild rabbits in Australia developed genetic resistance to the myxoma virus, which was introduced as a biological control agent. However, little is known about the rate at which this evolutionary change occurred. We collated data from challenge trials that estimated rabbit resistance to myxomatosis in Australia and expressed resistance on a continuous scale, enabling trends in its development to be assessed over 45 years up to 1995. Resistance initially increased rapidly, followed by a plateau lasting ten years, before a second rapid increase occurred associated with the introduction of European rabbit fleas as myxoma virus vectors. By contrast, in the United Kingdom, where rabbit flea vectors were already present when the myxoma virus initially spread, resistance developed more slowly. No estimates of rabbit resistance to myxomatosis have been made for almost 30 years, despite other highly lethal rabbit pathogens becoming established worldwide. Continued testing of wild-caught rabbits in Australia to determine current levels of resistance to myxomatosis is recommended to assess its current effectiveness for managing pest rabbits. Given the economic and environmental significance of invasive rabbits, it would be remiss to manage such biological resources and ecosystem services poorly.

The aim of this study was to evaluate the impact of coronavirus disease 2019 (COVID-19) on treatment outcomes in critically ill patients with carbapenem-resistant Acinetobacter baumannii (CRAB) bloodstream infection (BSI). This single-centre, retrospective cohort study was conducted in a 1,048-bed university-affiliated tertiary hospital in the Republic of Korea from January 2021 to March 2022. The study participants included consecutive hospitalised adult patients (aged ≥18 years) in the intensive care unit with CRAB monomicrobial BSI. During the study period, a total of 70 patients were included in our study, and 24 (34.3%) were diagnosed with COVID-19. The 28-day mortality rate was 64.3%. In the multivariate Cox proportional hazard regression analysis, diagnosis of COVID-19 (hazard ratio (HR), 2.91; 95% confidence interval (CI): 1.45–5.87), neutropenia (HR, 2.76; 95% CI: 1.04–7.29), Pitt bacteraemia score (per point; HR, 1.30; 95% CI: 1.19–1.41), and appropriate definite antibiotic therapy (HR, 0.31; 95% CI: 0.15–0.62) were independent predictors of 28-day mortality in patients with CRAB BSI. In conclusion, our findings suggested that COVID-19 has a negative prognostic impact on patients with CRAB BSI. Further study is needed to investigate the specific mechanisms of how COVID-19 worsens the prognosis of CRAB infection.

In the classical gambler’s ruin problem, the gambler plays an adversary with initial capitals z and $a-z$, respectively, where $a>0$ and $0< z < a$ are integers. At each round, the gambler wins or loses a dollar with probabilities p and $1-p$. The game continues until one of the two players is ruined. For even a and $0<z\leq {a}/{2}$, the family of distributions of the duration (total number of rounds) of the game indexed by $p \in [0,{\frac{1}{2}}]$ is shown to have monotone (increasing) likelihood ratio, while for ${a}/{2} \leq z<a$, the family of distributions of the duration indexed by $p \in [{\frac{1}{2}}, 1]$ has monotone (decreasing) likelihood ratio. In particular, for $z={a}/{2}$, in terms of the likelihood ratio order, the distribution of the duration is maximized over $p \in [0,1]$ by $p={\frac{1}{2}}$. The case of odd a is also considered in terms of the usual stochastic order. Furthermore, as a limit, the first exit time of Brownian motion is briefly discussed.

This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we establish identities for stationary measures and QSDs, which we use to derive tail asymptotics. In particular, for continuous-time Markov chains with asymptotic power law transition rates, tail asymptotics for stationary distributions and QSDs are classified into three types using three easily computable parameters: (i) super-exponential distributions, (ii) exponential-tailed distributions, and (iii) sub-exponential distributions. Our approach to establish tail asymptotics of stationary distributions is different from the classical semimartingale approach, and we do not impose ergodicity or moment bound conditions. In particular, the results also hold for explosive Markov chains, for which multiple stationary distributions may exist. Furthermore, our results on tail asymptotics of QSDs seem new. We apply our results to biochemical reaction networks, a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth–death processes. Our approach, together with the identities, easily extends to discrete-time Markov chains.

Older adults and people of colour are vulnerable to the COVID-19 pandemic, and mitigation behaviours reduce COVID-19 infection. We examined racial and ethnic differences in COVID-19 diagnosis and adherence to COVID-19 mitigation behaviours among U.S. older adults. Data were retrieved from the National Health and Aging Trends Study, a nationally representative prospective cohort with 3257 U.S. Medicare beneficiaries aged 65+. COVID-19 variables were collected in 2020; all other data in 2019. Odds of COVID-19 diagnosis and adherence to mitigation behaviours (handwashing, masking, social distancing) were analysed using logistic regression. Compared to White older adults, only Hispanic respondents had 2.7 times significantly higher odds of COVID-19 after adjusting for sociodemographics, health, and mitigation behaviours (aOR = 2.71, 95% CI = 1.20-6.12). Black older adults had 7.9 times significantly higher odds of masking (aOR = 7.94, 95% CI = 2.33-27.04) and 2.3 times higher odds of social distancing (aOR = 2.33, 95% CI = 1.28-4.24), after adjusting for sociodemographics and health. Among all racial and ethnic groups, only Hispanic older adults had a significantly elevated COVID-19 diagnosis. Despite higher adherence to COVID-19 mitigation behaviours among racial and ethnic minorities, especially Black older adults, odds of COVID-19 remained elevated. Research is needed to explore potential mechanisms for higher odds of COVID-19 among minority older adults.