Lyapunov functions and strict stability of Caputo fractional differential equations

One of the main properties studied in the qualitative theory of differential equations is the stability of solutions. The stability of fractional order systems is quite recent. There are several approaches in the literature to study stability, one of which is the Lyapunov approach. However, the Lyapunov approach to fractional differential equations causes many difficulties. In this paper a new definition (based on the Caputo fractional Dini derivative) for the derivative of Lyapunov functions to study a nonlinear Caputo fractional differential equation is introduced. Comparison results using this definition and scalar fractional differential equations are presented, and sufficient conditions for strict stability and uniform strict stability are given. Examples are presented to illustrate the theory

Prevalence of diabetic retinopathy in Tehran province: a population-based study

<p>Abstract</p> <p>Background</p> <p>To determine the prevalence and characteristics of diabetic retinopathy (DR) among Iranian patients with diabetes.</p> <p>Methods</p> <p>Design: population-based cross-sectional study.</p> <p>Participants: patients with diabetes aged 25 to 64 years in Tehran province, Iran. This survey was conducted from April to October 2007. The study sample was derived from the first national survey of risk factors for non-communicable disease. Diabetes mellitus was defined as a fasting plasma glucose of ≥ 7.0 mmol/l (126 mg/dl) or more, use of diabetic medications, or a physician's diagnosis of diabetes. All patients known to have diabetes underwent an eye examination by bio-microscope and indirect ophthalmoscope to check for any signs of DR through dilated pupils by + 78 lens. Participants were also interviewed and examined to determine their demographic characteristics, medical conditions and the regularity of their eye visits.</p> <p>Results</p> <p>Among 7989 screened patients, 759 (9.5%) had diabetes. Of them, 639 patients (84.2%) underwent eye examination. Five patients (0.7%) with media opacity were excluded. Of 634 examined patients with diabetes, 240 had some degree of diabetic retinopathy, and the overall standardized prevalence of any retinopathy was 37.0% (95% CI: 33.2-40.8), including 27.3% (95% CI: 23.7-30.8) (n = 175) with non-proliferative and 9.6% (95% CI: 7.3-11.9) (n = 65) with proliferative diabetic retinopathy. Clinically significant macular edema and vision-threatening retinopathy were detected in 5.8% (95% CI: 4.0-7.7) (n = 38) and 14.0% (95% CI: 11.3-16.7) (n = 95) of patients, respectively. Only 143 patients (22.6%) with diabetes had a history of regular eye examination.</p> <p>Conclusion</p> <p>This study demonstrated a high prevalence and poor control of DR in Tehran province. This suggests the need for adequate prevention and treatment in patients with diabetes.</p

Comprehensive assessment of metabolic syndrome among rural Bangladeshi women

Background: Metabolic syndrome (MS), defined as a constellation of cardiovascular disease (CVD) risk factors, is one of the fastest growing public health burdens in the Asia-Pacific region. This trend is despite the fact that people in this region are no more overweight than Europeans and Americans. Unfortunately, in South Asia, MS screening has only been performed in a few countries other than Bangladesh. Therefore the present study is designed to conduct a comprehensive screening of MS in Bangladeshi rural women, which includes estimation of prevalence and assessment of risk factor. Methods: A total of 1535 rural Bangladesh women aged ≥ 15 years were studied using a population based crosssectional survey. The prevalence of MS was estimated using NCEP ATP III, modified NCEP ATP III and IDF criteria. Results: The prevalence rates of MS were 25.60 % (NCEP ATP III), 36.68 % (modified NCEP ATP III), and 19.80 % (IDF), as revealed by the present study. Furthermore, based on the NCEP ATP III criteria, 11.60 % of the subjects were found to have excess waist circumference; 29.12 % had elevated blood pressure, 30.42 % had elevated fasting plasma glucose level, 85.47 % had low HDL values and 26.91 % had increased triglyceride values. Low plasma HDL level was found to be the most common abnormality in the target population and elevated waist circumference was the least frequent component. Conclusions: The present study reveals a high prevalence of MS and its associated risk factors in rural Bangladeshi women. These findings are important in that they provide insights that will be helpful in formulating effective public health policy, notably the development of future health prevention strategies in Bangladesh

Consensus Middle East and North Africa Registry on Inborn Errors of Immunity

Background: Inborn errors of immunity (IEIs) are a heterogeneous group of genetic defects of immunity, which cause high rates of morbidity and mortality mainly among children due to infectious and non-infectious complications. The IEI burden has been critically underestimated in countries from middle- and low-income regions and the majority of patients with IEI in these regions lack a molecular diagnosis. Methods: We analyzed the clinical, immunologic, and genetic data of IEI patients from 22 countries in the Middle East and North Africa (MENA) region. The data was collected from national registries and diverse databases such as the Asian Pacific Society for Immunodeficiencies (APSID) registry, African Society for Immunodeficiencies (ASID) registry, Jeffrey Modell Foundation (JMF) registry, J Project centers, and International Consortium on Immune Deficiency (ICID) centers. Results: We identified 17,120 patients with IEI, among which females represented 39.4%. Parental consanguinity was present in 60.5% of cases and 27.3% of the patients were from families with a confirmed previous family history of IEI. The median age of patients at the onset of disease was 36 months and the median delay in diagnosis was 41 months. The rate of registered IEI patients ranges between 0.02 and 7.58 per 100,000 population, and the lowest rates were in countries with the highest rates of disability-adjusted life years (DALY) and death rates for children. Predominantly antibody deficiencies were the most frequent IEI entities diagnosed in 41.2% of the cohort. Among 5871 patients genetically evaluated, the diagnostic yield was 83% with the majority (65.2%) having autosomal recessive defects. The mortality rate was the highest in patients with non-syndromic combined immunodeficiency (51.7%, median age: 3.5 years) and particularly in patients with mutations in specific genes associated with this phenotype (RFXANK, RAG1, and IL2RG). Conclusions: This comprehensive registry highlights the importance of a detailed investigation of IEI patients in the MENA region. The high yield of genetic diagnosis of IEI in this region has important implications for prevention, prognosis, treatment, and resource allocation

Global fertility in 204 countries and territories, 1950–2021, with forecasts to 2100: a comprehensive demographic analysis for the Global Burden of Disease Study 2021

Background Accurate assessments of current and future fertility—including overall trends and changing population age structures across countries and regions—are essential to help plan for the profound social, economic, environmental, and geopolitical challenges that these changes will bring. Estimates and projections of fertility are necessary to inform policies involving resource and health-care needs, labour supply, education, gender equality, and family planning and support. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 produced up-to-date and comprehensive demographic assessments of key fertility indicators at global, regional, and national levels from 1950 to 2021 and forecast fertility metrics to 2100 based on a reference scenario and key policy-dependent alternative scenarios. Methods To estimate fertility indicators from 1950 to 2021, mixed-effects regression models and spatiotemporal Gaussian process regression were used to synthesise data from 8709 country-years of vital and sample registrations, 1455 surveys and censuses, and 150 other sources, and to generate age-specific fertility rates (ASFRs) for 5-year age groups from age 10 years to 54 years. ASFRs were summed across age groups to produce estimates of total fertility rate (TFR). Livebirths were calculated by multiplying ASFR and age-specific female population, then summing across ages 10–54 years. To forecast future fertility up to 2100, our Institute for Health Metrics and Evaluation (IHME) forecasting model was based on projections of completed cohort fertility at age 50 years (CCF50; the average number of children born over time to females from a specified birth cohort), which yields more stable and accurate measures of fertility than directly modelling TFR. CCF50 was modelled using an ensemble approach in which three sub-models (with two, three, and four covariates variously consisting of female educational attainment, contraceptive met need, population density in habitable areas, and under-5 mortality) were given equal weights, and analyses were conducted utilising the MR-BRT (meta-regression—Bayesian, regularised, trimmed) tool. To capture time-series trends in CCF50 not explained by these covariates, we used a first-order autoregressive model on the residual term. CCF50 as a proportion of each 5-year ASFR was predicted using a linear mixed-effects model with fixed-effects covariates (female educational attainment and contraceptive met need) and random intercepts for geographical regions. Projected TFRs were then computed for each calendar year as the sum of single-year ASFRs across age groups. The reference forecast is our estimate of the most likely fertility future given the model, past fertility, forecasts of covariates, and historical relationships between covariates and fertility. We additionally produced forecasts for multiple alternative scenarios in each location: the UN Sustainable Development Goal (SDG) for education is achieved by 2030; the contraceptive met need SDG is achieved by 2030; pro-natal policies are enacted to create supportive environments for those who give birth; and the previous three scenarios combined. Uncertainty from past data inputs and model estimation was propagated throughout analyses by taking 1000 draws for past and present fertility estimates and 500 draws for future forecasts from the estimated distribution for each metric, with 95% uncertainty intervals (UIs) given as the 2·5 and 97·5 percentiles of the draws. To evaluate the forecasting performance of our model and others, we computed skill values—a metric assessing gain in forecasting accuracy—by comparing predicted versus observed ASFRs from the past 15 years (2007–21). A positive skill metric indicates that the model being evaluated performs better than the baseline model (here, a simplified model holding 2007 values constant in the future), and a negative metric indicates that the evaluated model performs worse than baseline. Findings During the period from 1950 to 2021, global TFR more than halved, from 4·84 (95% UI 4·63–5·06) to 2·23 (2·09–2·38). Global annual livebirths peaked in 2016 at 142 million (95% UI 137–147), declining to 129 million (121–138) in 2021. Fertility rates declined in all countries and territories since 1950, with TFR remaining above 2·1—canonically considered replacement-level fertility—in 94 (46·1%) countries and territories in 2021. This included 44 of 46 countries in sub-Saharan Africa, which was the super-region with the largest share of livebirths in 2021 (29·2% [28·7–29·6]). 47 countries and territories in which lowest estimated fertility between 1950 and 2021 was below replacement experienced one or more subsequent years with higher fertility; only three of these locations rebounded above replacement levels. Future fertility rates were projected to continue to decline worldwide, reaching a global TFR of 1·83 (1·59–2·08) in 2050 and 1·59 (1·25–1·96) in 2100 under the reference scenario. The number of countries and territories with fertility rates remaining above replacement was forecast to be 49 (24·0%) in 2050 and only six (2·9%) in 2100, with three of these six countries included in the 2021 World Bank-defined low-income group, all located in the GBD super-region of sub-Saharan Africa. The proportion of livebirths occurring in sub-Saharan Africa was forecast to increase to more than half of the world's livebirths in 2100, to 41·3% (39·6–43·1) in 2050 and 54·3% (47·1–59·5) in 2100. The share of livebirths was projected to decline between 2021 and 2100 in most of the six other super-regions—decreasing, for example, in south Asia from 24·8% (23·7–25·8) in 2021 to 16·7% (14·3–19·1) in 2050 and 7·1% (4·4–10·1) in 2100—but was forecast to increase modestly in the north Africa and Middle East and high-income super-regions. Forecast estimates for the alternative combined scenario suggest that meeting SDG targets for education and contraceptive met need, as well as implementing pro-natal policies, would result in global TFRs of 1·65 (1·40–1·92) in 2050 and 1·62 (1·35–1·95) in 2100. The forecasting skill metric values for the IHME model were positive across all age groups, indicating that the model is better than the constant prediction. Interpretation Fertility is declining globally, with rates in more than half of all countries and territories in 2021 below replacement level. Trends since 2000 show considerable heterogeneity in the steepness of declines, and only a small number of countries experienced even a slight fertility rebound after their lowest observed rate, with none reaching replacement level. Additionally, the distribution of livebirths across the globe is shifting, with a greater proportion occurring in the lowest-income countries. Future fertility rates will continue to decline worldwide and will remain low even under successful implementation of pro-natal policies. These changes will have far-reaching economic and societal consequences due to ageing populations and declining workforces in higher-income countries, combined with an increasing share of livebirths among the already poorest regions of the world

Hispanic health in the USA: a scoping review of the literature

Hispanics are the largest minority group in the USA. They contribute to the economy, cultural diversity, and health of the nation. Assessing their health status and health needs is key to inform health policy formulation and program implementation. To this end, we conducted a scoping review of the literature and national statistics on Hispanic health in the USA using a modified social-ecological framework that includes social determinants of health, health disparities, risk factors, and health services, as they shape the leading causes of morbidity and mortality. These social, environmental, and biological forces have modified the epidemiologic profile of Hispanics in the USA, with cancer being the leading cause of mortality, followed by cardiovascular diseases and unintentional injuries. Implementation of the Affordable Care Act has resulted in improved access to health services for Hispanics, but challenges remain due to limited cultural sensitivity, health literacy, and a shortage of Hispanic health care providers. Acculturation barriers and underinsured or uninsured status remain as major obstacles to health care access. Advantageous health outcomes from the “Hispanic Mortality Paradox” and the “Latina Birth Outcomes Paradox” persist, but health gains may be offset in the future by increasing rates of obesity and diabetes. Recommendations focus on the adoption of the Health in All Policies framework, expanding access to health care, developing cultural sensitivity in the health care workforce, and generating and disseminating research findings on Hispanic health