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The compounded Bell generalized class of distributions is proposed in this article as an alternative to the compounded Poisson generalized family of distributions. Some properties and actuarial measures are presented. The properties of a special model named Bell Weibull (BellW) are obtained such as the linear representation of density, rth moment, incomplete moment, moment generating function using Wright generalized hypergeometric function and Meijer’s G function, the pth moment of order statistics, reliability, stochastic ordering, and residual and reversed residual life. Moreover, some commonly used entropy measures, namely, Rényi, Havrda and Charvat, and Arimoto and Tsallis entropy are obtained for the special model. From the inferential side, parameters are estimated using maximum likelihood estimation. The simulation study is performed to highlight the behavior of estimates. Some actuarial measures including expected shortfall, value at risk, tail value at risk, tail variance, and tail variance premium for the BellW model are presented with the numerical illustration. The usefulness of the proposed family is evaluated using insurance claims and COVID-19 datasets. Convincing results are obtained.

This study sought to identify the most accurate forecasting models for COVID-19-confirmed cases, deaths, and recovered patients in Pakistan. For COVID-19, time series data are available from 16 April to 15 August 2021 from the Ministry of National Health Services Regulation and Coordination’s health advice portal. Descriptive as well as time series models, autoregressive integrated moving average, exponential smoothing models (Brown, Holt, and Winters), neural networks, and Error, Trend, Seasonal (ETS) models were applied. The analysis was carried out using the R coding language. The descriptive analysis shows that the average number of confirmed cases, COVID-19-related deaths, and recovered patients reported each day were 2,916, 69.43, and 2,772, respectively. The highest number of COVID-19 confirmed cases and fatalities per day, however, were recorded on April 17, 2021 and April 27, 2021, respectively. ETS (M, N, M), neural network, nonlinear autoregressive (NNAR) (3, 1, 2), and NNAR (8, 1, 4) forecasting models were found to be the best among all other competing models for the reported confirmed cases, deaths, and recovered patients, respectively. COVID-19-confirmed outbreaks, deaths, and recovered patients were predicted to rise on average by around 0.75, 5.08, and 19.11% daily. These statistical results will serve as a guide for disease management and control.

Background: A consistent referral system and patient patronage are the primary connections between the three tiers in the healthcare delivery system. Patients were scheduled to visit primary care clinics for the first time. Subsequently, patients are moved to more distinguished healthcare facilities to receive additional care. Objectives: This study aims to investigate the reasons behind patients' transfer from primary and secondary care to tertiary care, as well as the critical factors that influence these referrals. Methods: This study employs a mixed‐methods approach to explore factors determining referral service provision across primary, secondary, and tertiary healthcare levels. Along with conducting semi‐structured interviews with healthcare professionals, we systematically examined a wealth of retrospective data on 1331 referred patients from 130 health facilities, including patient records, demographics, referral status, and clinical presentation. All statistical analysis was processed in R, and Corel Draw 12 was also used for graphical illustration. Results: Healthcare facilities referred most emergencies to several departments, including the cardiac care unit, medical, urology, intensive care unit/emergency, obstetrics and gynaecology, children's, orthopaedic, and psychiatry. The percentage of all cases referred is displayed ward‐by‐ward; the intensive care unit/emergency wards have a high referral ratio of 65.51%, while the obstetrics and gynaecology wards have an 18.40% referral ratio. Conclusion: There is a need for increased government investments to strengthen the capacity, human resources, and availability of equipment in primary, secondary, and tertiary public health facilities to deliver quality services in order to reduce the patient referral ratio. Key Points: Formalizing and institutionalizing the referral system and retraining all health‐care professionals.Reduce the epidemic's negative effects on social services, health systems, and the economy.Physicians must diligently perform systematic treatment for referral cases. [ABSTRACT FROM AUTHOR]

Background: Previously, most researchers explored the association between chronic obstructive pulmonary disease (COPD) and cardiovascular disease (CVD). This study investigates the distinct influence of COVID‐19 vaccination status on patients with both conditions. Objective: We investigate the relationship between COPD and CVD in a cohort of 838 individuals who presented with both conditions. Our aim is to understand how these conditions interact and how COVID‐19 vaccination status affects patient outcomes. Methods: A retrospective analysis was conducted on 838 patients with COPD and CVD treated at DHQ Hospital in Muzaffargarh, Punjab, Pakistan, from November 2022 to April 2023. We employed multiple logistic regression and the Wilcoxon signed‐rank test to assess the odds ratio and relative risk of COPD in patients with‐CVD under various conditions. Additionally, we analyzed time‐to‐death and survival using Kaplan–Meier methods. Results: Findings reveal a 7.95 times higher risk of death in patients without COVID‐19 vaccination compared with those who were vaccinated (95% CI, 6.12–10.33). Conversely, COVID‐19‐vaccinated patients exhibited a 0.221 times lower risk of recovery than their nonvaccinated counterparts (95% CI, 0.08–0.60). We also observed significant differences in time‐to‐death and recovery based on the presence of COPD and CVD, with vaccinated patients generally experiencing milder disease. Conclusion: Our study assessed the impact of COVID‐19 vaccination status on patient outcomes in patients with overlapping COPD and CVD. Individuals diagnosed with COPD and CVD display significant differences in terms of their probability of survival, with those who have received vaccinations. [ABSTRACT FROM AUTHOR]