SummaryBackgroundUnderstanding potential trajectories in health and drivers of health is crucial to guiding long-term investments and policy implementation. Past work on forecasting has provided an incomplete landscape of future health scenarios, highlighting a need for a more robust modelling platform from which policy options and potential health trajectories can be assessed. This study provides a novel approach to modelling life expectancy, all-cause mortality and cause of death forecasts —and alternative future scenarios—for 250 causes of death from 2016 to 2040 in 195 countries and territories.MethodsWe modelled 250 causes and cause groups organised by the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) hierarchical cause structure, using GBD 2016 estimates from 1990–2016, to generate predictions for 2017–40. Our modelling framework used data from the GBD 2016 study to systematically account for the relationships between risk factors and health outcomes for 79 independent drivers of health. We developed a three-component model of cause-specific mortality: a component due to changes in risk factors and select interventions; the underlying mortality rate for each cause that is a function of income per capita, educational attainment, and total fertility rate under 25 years and time; and an autoregressive integrated moving average model for unexplained changes correlated with time. We assessed the performance by fitting models with data from 1990–2006 and using these to forecast for 2007–16. Our final model used for generating forecasts and alternative scenarios was fitted to data from 1990–2016. We used this model for 195 countries and territories to generate a reference scenario or forecast through 2040 for each measure by location. Additionally, we generated better health and worse health scenarios based on the 85th and 15th percentiles, respectively, of annualised rates of change across location-years for all the GBD risk factors, income per person, educational attainment, select intervention coverage, and total fertility rate under 25 years in the past. We used the model to generate all-cause age-sex specific mortality, life expectancy, and years of life lost (YLLs) for 250 causes. Scenarios for fertility were also generated and used in a cohort component model to generate population scenarios. For each reference forecast, better health, and worse health scenarios, we generated estimates of mortality and YLLs attributable to each risk factor in the future.FindingsGlobally, most independent drivers of health were forecast to improve by 2040, but 36 were forecast to worsen. As shown by the better health scenarios, greater progress might be possible, yet for some drivers such as high body-mass index (BMI), their toll will rise in the absence of intervention. We forecasted global life expectancy to increase by 4·4 years (95% UI 2·2 to 6·4) for men and 4·4 years (2·1 to 6·4) for women by 2040, but based on better and worse health scenarios, trajectories could range from a gain of 7·8 years (5·9...

Summary Background Understanding potential patterns in future population levels is crucial for anticipating and planning for changing age structures, resource and health-care needs, and environmental and economic landscapes. Future fertility patterns are a key input to estimation of future population size, but they are surrounded by substantial uncertainty and diverging methodologies of estimation and forecasting, leading to important differences in global population projections. Changing population size and age structure might have profound economic, social, and geopolitical impacts in many countries. In this study, we developed novel methods for forecasting mortality, fertility, migration, and population. We also assessed potential economic and geopolitical effects of future demographic shifts. Methods We modelled future population in reference and alternative scenarios as a function of fertility, migration, and mortality rates. We developed statistical models for completed cohort fertility at age 50 years (CCF50). Completed cohort fertility is much more stable over time than the period measure of the total fertility rate (TFR). We modelled CCF50 as a time-series random walk function of educational attainment and contraceptive met need. Age-specific fertility rates were modelled as a function of CCF50 and covariates. We modelled age-specific mortality to 2100 using underlying mortality, a risk factor scalar, and an autoregressive integrated moving average (ARIMA) model. Net migration was modelled as a function of the Socio-demographic Index, crude population growth rate, and deaths from war and natural disasters; and use of an ARIMA model. The model framework was used to develop a reference scenario and alternative scenarios based on the pace of change in educational attainment and contraceptive met need. We estimated the size of gross domestic product for each country and territory in the reference scenario. Forecast uncertainty intervals (UIs) incorporated uncertainty propagated from past data inputs, model estimation, and forecast data distributions. Findings The global TFR in the reference scenario was forecasted to be 1·66 (95% UI 1·33–2·08) in 2100. In the reference scenario, the global population was projected to peak in 2064 at 9·73 billion (8·84–10·9) people and decline to 8·79 billion (6·83–11·8) in 2100. The reference projections for the five largest countries in 2100 were India (1·09 billion [0·72–1·71], Nigeria (791 million [594–1056]), China (732 million [456–1499]), the USA (336 million [248–456]), and Pakistan (248 million [151–427]). Findings also suggest a shifting age structure in many parts of the world, with 2·37 billion (1·91–2·87) individuals older than 65 years and 1·70 billion (1·11–2·81) individuals younger than 20 years, forecasted globally in 2100. By 2050, 151 countries were forecasted to have a TFR lower than the replacement level (TFR <2·1), and 183 were forecasted to have a TFR lower than repl...

The superheated Meissner state in type-I superconductors is studied both analytically and numerically within the framework of Ginzburg-Landau theory. Using the method of matched asymptotic expansions we have developed a systematic expansion for the solutions of the Ginzburg-Landau equations in the limit of small κ, and have determined the maximum superheating field H sh for the existence of the metastable, superheated Meissner state as an expansion in powers of κ 1/2 . Our numerical solutions of these equations agree quite well with the asymptotic solutions for κ < 0.5. The same asymptotic methods are also used to study the stability of the solutions, as well as a modified version of the Ginzburg-Landau equations which incorporates nonlocal electrodynamics. Finally, we compare our numerical results for the superheating field for large-κ against recent asymptotic results for large-κ, and again find a close agreement. Our results demonstrate the efficacy of the method of matched asymptotic expansions for dealing with problems in inhomogeneous superconductivity involving boundary layers.