Calculation of nonlinear vibrations of piecewise-linear systems using the shooting method

In this paper, an explicit formulation of the shooting scheme for computation of multiple periodic attractors of a harmonically excited oscillator which is asymmetric with both stiffness and viscous damping piecewise linearities is derived. The numerical simulation by the shooting method is compared with that by the incremental harmonic balance method (IHB method), which shows that the shooting method is in many respects distinctively advantageous over the incremental harmonic balance method

Abnormal features of oceanographic characteristics in upwelling Vietnam waters under impact of El Niño events

The summer upwelling that occurs in coastal waters of South Central Vietnam is one of the major hydrographic features in the South China Sea. A weakening of the upwelling after major El Niño events was observed in the literature for previous El Nino events and was verified here from the analysis of new satellite image data sets of sea surface temperature (SST) and surface wind. The analysis of empirical orthogonal function (EOF) from of monthly SST as well as of temporal and spatial variations of SST and wind force allow us to identify abnormal characteristics in ocean surface water that happened after El Niño episode, in agreement with previous studies. Those abnormal characteristics in Vietnam upwelling waters appeared mainly during the summers of 1998, 2003, 2010 and 2016 years for the El Niño decline phase. The upwelling weakening during El Niño decline episodes is associated with the following signals: (1) Wind force and Ekman pump are very weak; (2) the cold  and high chlorophyll-a  tongue is shifted northward but not extended eastward; (3) for years when El Nino occurs, SST strongly increases and reaches a peak in May or early June of next year, during the declining phase of El Niño episode; (4) upwelling phenomenon typically occurs during August and not July. Using a reanalysis dataset derived from the HYCOM/NCODA system coupled with a local Finite Element Model (FEM) allow us to complete our knowledge about the abnormal oceanographic characteristics of deeper water layers after El Niño episodes. The analysis of spatial variations of oceanography fields derived from HYCOM/NCODA/FEM system along zonal and meridional sections and vertical profiles as well as the results obtained from water mass analysis allow us to identify in details the abnormal oceanic characteristics of deeper water layers during the declining  El Niño phase. Those are; (5) Sea water in both surface and deeper water layers were transported dominantly northward  but not eastward; (6) The thermo-halocline layer in South Vietnam upwelling center was deeper (about 90 -100m), compared with previous El Nino and normal years (50-60 m and 35-40 m, respectively); (7) Extreme global warming in recent years (2012-2016) pressed the thermo-halocline layer in upwelling center deeper (90-100 m) during summer. Under the influence of the ocean global warming, this process should progress continuously, the depth of thermo-halocline layer should become therefore deeper and deeper in next years.References Barthel, K., R. Rosland, and N. C. Thai, 2009. Modelling the circulation on the continental shelf of the province Khanh Hoa in Vietnam, J. Mar. Syst., 77(1-2), 89-113. Bui Hong Long, Tran Van Chung, 2009. Calculations of currents in the upwelling region along south-central Vietnamese coast, using three dimensions (3-D) nonlinear model”, Journal of Marine Science and Technology - VAST, 9(2), 01-25 (in Vietnamese). Bui Hong Long, Tran Van Chung, 2017. Preliminary studies on the impact of climate change on the upwelling region south Central Vietnam in summer.  Journal of Marine Science and Technology - VAST , 17(1), 01-19 (in Vietnamese). Colling, A., 2001. Ocean Circulation, Open University Course Team. Second Edition. ISBN 978-0-7506-5278-0. Dippner, J. W., and N. Loick-Wilde, 2011. A redefinition of water masses in the Vietnamese upwelling area, J. Mar. Syst., 84(1-2), 42-47. Hale, W.G, Margham, J.P,  and Sauder, V.A, 2005. Collins Dictionary of  Biology 3rd . London: Collin. Huang, Q.-Z.,W.-Z. Wang, Y. S. Li, and C. W. Li, 1994. Current characteristics of the South China Sea, in Oceanology of China Sea, edited by D. Zhou, Y.-B. Liang, and C. K. Tsebgm, 39-47, Kluwer Acad., Norwell, Mass. H.E. Hurlburt, E.P. Chassignet, J.A. Cummings, A.B. Kara, E.J. Metzger, J.F. Shriver, O.M. Smedstad, A.J. Wallcraft, and C.N. Barron, 2008. Eddy-resolving Global Ocean Prediction, in M. Hecht and H. Hasumi, eds., Ocean Modeling in an Eddying Regime, Geophysical Monograph 177 (American Geophysical Union, Washington, DC ). Knauss, J.A., 2005. Introduction to Physical Oceanography, Waveland Press. Second Edition. ISBN 978-1-57766-429-1. Kuo. N. J, Zheng. Q, Ho C. R, 2004.  Response of Vietnam coastal upwelling to the 1997-1998 ENSO event observed by multisensor data, Remote sensing of Environment, 15 January, 89(1), 106-115. Le Phuoc Trinh, Nguyen Tien Dung, Nguyen Van Minh, Le Minh Tan, Nguyen Kim Vinh, 1981. A proposal of studies on the upwelling of Southeastern coast of Vietnam, Collection of Marine Research Works, 2(2), 13-31 (in Vietnamese). Nguyen Van Long and Vo. Si  Tuan, 2010. Status of coral reefs in Vietnam following the 2010 coral bleaching event. In: Kimura T, Tun K (eds) Status of Coral Reefs in East Asian Seas Region: Ministry of the Environment, Japan, 29-49. NOAA National Centers for Environmental Information, State of the Climate: Global Analysis for Annual 2010, published online January 2011, retrieved on March 25, 2017 from http://www.ncdc.noaa.gov/sotc/global/201013. Ose, T., Y. Song, and A. Kitoh, 1997. Sea surface temperature in the South China Sea: An index for the Asian monsoon and ENSO system, J. Meteorol. Soc. Japan., 75, 1091-1107. Pohlmann, T., 1987. A three dimensional circulation model of the South China Sea., 245-268. In Three-Dimensional Models of Marine and Estuarine Dynamics, ed. by J. J. Nihoul and B. M. Jamart, Elsevier, New York. Qu, T,  Kim, Y.Y, Yaremchuk, M., Tozuka. T, Ishida, A, Yamagata, T., 2004. Can Luzon strait transport play a role in conveying the impact of ENSO to the South China Sea J. Clim. 17, 3644-3657 Shaw, P. T., and S. Y. Chao, 1994.  Surface Circulation in the South China Sea, Deep-Sea Res., I(41), 1663-1683. Siswanto, E., H. Ye, D. Yamazaki, and D.L. Tang 2017. Detailed spatiotemporal impacts of El Niño on phytoplankton biomass in the South China Sea, J. Geophys. Res. Oceans, 122, doi:10.1002/2016JC012276. Sverdrup, H.U., M.W. Johnson and Fleming, R.H., 1942. The Oceans: their physics, chemistry and general biology. Prentice Hall, New York, 1087p. Tang D. L., H. Kawamura, H. Doan Nhu, and W. Takahashi, 2004. Remote sensing oceanography of a harmful algal bloom off the coast of southeastern Vietnam, J. Geophys. Res., 109, C03014, doi:10.1029/ 2003JC002045. Thai Minh Quang, 2016. Studies on influence of  2016.  El Niño event to coral bleaching phenomena in coastal waters in Ninh Hai - Ninh Thuan province. Technical report of  basic research pro­ject funded by Institute of Oceanography - the Vietnam Academy of Science and Technology (in Vietnamese). Tong Phuoc Hoang Son, Vo Van Lanh and Lau Va Khin, 2005. Application of empirical orthogonal function (EOF) for studying thermal structure in sea surface water in South China Sea. The 26th Asian Remote sensing Conference, 7-11 November 2005 in Hanoi. Tran Van Chung, Bui Hong Long, 2016. Effect of temperature field and anomalies of sea water level in East Vietnam Sea in relationship to global climate change - Journal of Marine Science and Technology - VAST, 16(3), 255-266 (in Vietnamese). Vo Van Lanh, 1995. The environmental characteristics of strongly upwelling waters in south of Vietnam and its ecological impacts. Technical report of National project KT03.05. Institute of Oceanography, 480p (in Vietnamese). Vo Si Tuan, 2000. The corals at Con Dao archipelago (South Vietnam): before, during and after the bleaching event in 1998. In: Proceeding of 9th International Coral Reef Symposium, Bali, Indonesia, 23rd-27th October, 895-899. Wang B., An S., 2005. A method for detecting season-dependent modes of climate variability: S-EOF analysis. Geophys. Res. Lett., 32, L15710. Wyrtki K., 1961. Physical oceanography of the Southeast Asian waters, Naga Rep. 2, 195p, Scripps Inst. of Oceanogr., La Jolla, Calif. Xie S.-P., Q. Xie, D. Wang and W. T. Liu, 2003. Summer upwelling in the South China Sea and its role in regional climate variations, J. Geophys. Res., 108(C8), 3261, doi:10.1029/2003JC001867. Xie S.-P., C.-H. Chang, Q. Xie and D. Wang, 2007. Intraseasonal variability in the summer South China Sea: Wind jet, cold filament, and recirculations, J. Geophys. Res., 112, C10008, doi:10.1029/2007JC004238

Contributions of mean and shape of blood pressure distribution to worldwide trends and variations in raised blood pressure: A pooled analysis of 1018 population-based measurement studies with 88.6 million participants

© The Author(s) 2018. Background: Change in the prevalence of raised blood pressure could be due to both shifts in the entire distribution of blood pressure (representing the combined effects of public health interventions and secular trends) and changes in its high-blood-pressure tail (representing successful clinical interventions to control blood pressure in the hypertensive population). Our aim was to quantify the contributions of these two phenomena to the worldwide trends in the prevalence of raised blood pressure. Methods: We pooled 1018 population-based studies with blood pressure measurements on 88.6 million participants from 1985 to 2016. We first calculated mean systolic blood pressure (SBP), mean diastolic blood pressure (DBP) and prevalence of raised blood pressure by sex and 10-year age group from 20-29 years to 70-79 years in each study, taking into account complex survey design and survey sample weights, where relevant. We used a linear mixed effect model to quantify the association between (probittransformed) prevalence of raised blood pressure and age-group- and sex-specific mean blood pressure. We calculated the contributions of change in mean SBP and DBP, and of change in the prevalence-mean association, to the change in prevalence of raised blood pressure. Results: In 2005-16, at the same level of population mean SBP and DBP, men and women in South Asia and in Central Asia, the Middle East and North Africa would have the highest prevalence of raised blood pressure, and men and women in the highincome Asia Pacific and high-income Western regions would have the lowest. In most region-sex-age groups where the prevalence of raised blood pressure declined, one half or more of the decline was due to the decline in mean blood pressure. Where prevalence of raised blood pressure has increased, the change was entirely driven by increasing mean blood pressure, offset partly by the change in the prevalence-mean association. Conclusions: Change in mean blood pressure is the main driver of the worldwide change in the prevalence of raised blood pressure, but change in the high-blood-pressure tail of the distribution has also contributed to the change in prevalence, especially in older age groups

Rising rural body-mass index is the main driver of the global obesity epidemic in adults

Body-mass index (BMI) has increased steadily in most countries in parallel with a rise in the proportion of the population who live in cities(.)(1,2) This has led to a widely reported view that urbanization is one of the most important drivers of the global rise in obesity(3-6). Here we use 2,009 population-based studies, with measurements of height and weight in more than 112 million adults, to report national, regional and global trends in mean BMI segregated by place of residence (a rural or urban area) from 1985 to 2017. We show that, contrary to the dominant paradigm, more than 55% of the global rise in mean BMI from 1985 to 2017-and more than 80% in some low- and middle-income regions-was due to increases in BMI in rural areas. This large contribution stems from the fact that, with the exception of women in sub-Saharan Africa, BMI is increasing at the same rate or faster in rural areas than in cities in low- and middle-income regions. These trends have in turn resulted in a closing-and in some countries reversal-of the gap in BMI between urban and rural areas in low- and middle-income countries, especially for women. In high-income and industrialized countries, we noted a persistently higher rural BMI, especially for women. There is an urgent need for an integrated approach to rural nutrition that enhances financial and physical access to healthy foods, to avoid replacing the rural undernutrition disadvantage in poor countries with a more general malnutrition disadvantage that entails excessive consumption of low-quality calories.Peer reviewe

Height and body-mass index trajectories of school-aged children and adolescents from 1985 to 2019 in 200 countries and territories: a pooled analysis of 2181 population-based studies with 65 million participants

Summary Background Comparable global data on health and nutrition of school-aged children and adolescents are scarce. We aimed to estimate age trajectories and time trends in mean height and mean body-mass index (BMI), which measures weight gain beyond what is expected from height gain, for school-aged children and adolescents. Methods For this pooled analysis, we used a database of cardiometabolic risk factors collated by the Non-Communicable Disease Risk Factor Collaboration. We applied a Bayesian hierarchical model to estimate trends from 1985 to 2019 in mean height and mean BMI in 1-year age groups for ages 5–19 years. The model allowed for non-linear changes over time in mean height and mean BMI and for non-linear changes with age of children and adolescents, including periods of rapid growth during adolescence. Findings We pooled data from 2181 population-based studies, with measurements of height and weight in 65 million participants in 200 countries and territories. In 2019, we estimated a difference of 20 cm or higher in mean height of 19-year-old adolescents between countries with the tallest populations (the Netherlands, Montenegro, Estonia, and Bosnia and Herzegovina for boys; and the Netherlands, Montenegro, Denmark, and Iceland for girls) and those with the shortest populations (Timor-Leste, Laos, Solomon Islands, and Papua New Guinea for boys; and Guatemala, Bangladesh, Nepal, and Timor-Leste for girls). In the same year, the difference between the highest mean BMI (in Pacific island countries, Kuwait, Bahrain, The Bahamas, Chile, the USA, and New Zealand for both boys and girls and in South Africa for girls) and lowest mean BMI (in India, Bangladesh, Timor-Leste, Ethiopia, and Chad for boys and girls; and in Japan and Romania for girls) was approximately 9–10 kg/m2. In some countries, children aged 5 years started with healthier height or BMI than the global median and, in some cases, as healthy as the best performing countries, but they became progressively less healthy compared with their comparators as they grew older by not growing as tall (eg, boys in Austria and Barbados, and girls in Belgium and Puerto Rico) or gaining too much weight for their height (eg, girls and boys in Kuwait, Bahrain, Fiji, Jamaica, and Mexico; and girls in South Africa and New Zealand). In other countries, growing children overtook the height of their comparators (eg, Latvia, Czech Republic, Morocco, and Iran) or curbed their weight gain (eg, Italy, France, and Croatia) in late childhood and adolescence. When changes in both height and BMI were considered, girls in South Korea, Vietnam, Saudi Arabia, Turkey, and some central Asian countries (eg, Armenia and Azerbaijan), and boys in central and western Europe (eg, Portugal, Denmark, Poland, and Montenegro) had the healthiest changes in anthropometric status over the past 3·5 decades because, compared with children and adolescents in other countries, they had a much larger gain in height than they did in BMI. The unhealthiest changes—gaining too little height, too much weight for their height compared with children in other countries, or both—occurred in many countries in sub-Saharan Africa, New Zealand, and the USA for boys and girls; in Malaysia and some Pacific island nations for boys; and in Mexico for girls. Interpretation The height and BMI trajectories over age and time of school-aged children and adolescents are highly variable across countries, which indicates heterogeneous nutritional quality and lifelong health advantages and risks

Repositioning of the global epicentre of non-optimal cholesterol

High blood cholesterol is typically considered a feature of wealthy western countries(1,2). However, dietary and behavioural determinants of blood cholesterol are changing rapidly throughout the world(3) and countries are using lipid-lowering medications at varying rates. These changes can have distinct effects on the levels of high-density lipoprotein (HDL) cholesterol and non-HDL cholesterol, which have different effects on human health(4,5). However, the trends of HDL and non-HDL cholesterol levels over time have not been previously reported in a global analysis. Here we pooled 1,127 population-based studies that measured blood lipids in 102.6 million individuals aged 18 years and older to estimate trends from 1980 to 2018 in mean total, non-HDL and HDL cholesterol levels for 200 countries. Globally, there was little change in total or non-HDL cholesterol from 1980 to 2018. This was a net effect of increases in low- and middle-income countries, especially in east and southeast Asia, and decreases in high-income western countries, especially those in northwestern Europe, and in central and eastern Europe. As a result, countries with the highest level of non-HDL cholesterol-which is a marker of cardiovascular riskchanged from those in western Europe such as Belgium, Finland, Greenland, Iceland, Norway, Sweden, Switzerland and Malta in 1980 to those in Asia and the Pacific, such as Tokelau, Malaysia, The Philippines and Thailand. In 2017, high non-HDL cholesterol was responsible for an estimated 3.9 million (95% credible interval 3.7 million-4.2 million) worldwide deaths, half of which occurred in east, southeast and south Asia. The global repositioning of lipid-related risk, with non-optimal cholesterol shifting from a distinct feature of high-income countries in northwestern Europe, north America and Australasia to one that affects countries in east and southeast Asia and Oceania should motivate the use of population-based policies and personal interventions to improve nutrition and enhance access to treatment throughout the world.Peer reviewe

Worldwide trends in hypertension prevalence and progress in treatment and control from 1990 to 2019: a pooled analysis of 1201 population-representative studies with 104 million participants.

BACKGROUND: Hypertension can be detected at the primary health-care level and low-cost treatments can effectively control hypertension. We aimed to measure the prevalence of hypertension and progress in its detection, treatment, and control from 1990 to 2019 for 200 countries and territories. METHODS: We used data from 1990 to 2019 on people aged 30-79 years from population-representative studies with measurement of blood pressure and data on blood pressure treatment. We defined hypertension as having systolic blood pressure 140 mm Hg or greater, diastolic blood pressure 90 mm Hg or greater, or taking medication for hypertension. We applied a Bayesian hierarchical model to estimate the prevalence of hypertension and the proportion of people with hypertension who had a previous diagnosis (detection), who were taking medication for hypertension (treatment), and whose hypertension was controlled to below 140/90 mm Hg (control). The model allowed for trends over time to be non-linear and to vary by age. FINDINGS: The number of people aged 30-79 years with hypertension doubled from 1990 to 2019, from 331 (95% credible interval 306-359) million women and 317 (292-344) million men in 1990 to 626 (584-668) million women and 652 (604-698) million men in 2019, despite stable global age-standardised prevalence. In 2019, age-standardised hypertension prevalence was lowest in Canada and Peru for both men and women; in Taiwan, South Korea, Japan, and some countries in western Europe including Switzerland, Spain, and the UK for women; and in several low-income and middle-income countries such as Eritrea, Bangladesh, Ethiopia, and Solomon Islands for men. Hypertension prevalence surpassed 50% for women in two countries and men in nine countries, in central and eastern Europe, central Asia, Oceania, and Latin America. Globally, 59% (55-62) of women and 49% (46-52) of men with hypertension reported a previous diagnosis of hypertension in 2019, and 47% (43-51) of women and 38% (35-41) of men were treated. Control rates among people with hypertension in 2019 were 23% (20-27) for women and 18% (16-21) for men. In 2019, treatment and control rates were highest in South Korea, Canada, and Iceland (treatment >70%; control >50%), followed by the USA, Costa Rica, Germany, Portugal, and Taiwan. Treatment rates were less than 25% for women and less than 20% for men in Nepal, Indonesia, and some countries in sub-Saharan Africa and Oceania. Control rates were below 10% for women and men in these countries and for men in some countries in north Africa, central and south Asia, and eastern Europe. Treatment and control rates have improved in most countries since 1990, but we found little change in most countries in sub-Saharan Africa and Oceania. Improvements were largest in high-income countries, central Europe, and some upper-middle-income and recently high-income countries including Costa Rica, Taiwan, Kazakhstan, South Africa, Brazil, Chile, Turkey, and Iran. INTERPRETATION: Improvements in the detection, treatment, and control of hypertension have varied substantially across countries, with some middle-income countries now outperforming most high-income nations. The dual approach of reducing hypertension prevalence through primary prevention and enhancing its treatment and control is achievable not only in high-income countries but also in low-income and middle-income settings. FUNDING: WHO

Worldwide trends in hypertension prevalence and progress in treatment and control from 1990 to 2019: a pooled analysis of 1201 population-representative studies with 104 million participants

Background Hypertension can be detected at the primary health-care level and low-cost treatments can effectively control hypertension. We aimed to measure the prevalence of hypertension and progress in its detection, treatment, and control from 1990 to 2019 for 200 countries and territories. Methods We used data from 1990 to 2019 on people aged 30–79 years from population-representative studies with measurement of blood pressure and data on blood pressure treatment. We defined hypertension as having systolic blood pressure 140 mm Hg or greater, diastolic blood pressure 90 mm Hg or greater, or taking medication for hypertension. We applied a Bayesian hierarchical model to estimate the prevalence of hypertension and the proportion of people with hypertension who had a previous diagnosis (detection), who were taking medication for hypertension (treatment), and whose hypertension was controlled to below 140/90 mm Hg (control). The model allowed for trends over time to be non-linear and to vary by age. Findings The number of people aged 30–79 years with hypertension doubled from 1990 to 2019, from 331 (95% credible interval 306–359) million women and 317 (292–344) million men in 1990 to 626 (584–668) million women and 652 (604–698) million men in 2019, despite stable global age-standardised prevalence. In 2019, age-standardised hypertension prevalence was lowest in Canada and Peru for both men and women; in Taiwan, South Korea, Japan, and some countries in western Europe including Switzerland, Spain, and the UK for women; and in several low-income and middle-income countries such as Eritrea, Bangladesh, Ethiopia, and Solomon Islands for men. Hypertension prevalence surpassed 50% for women in two countries and men in nine countries, in central and eastern Europe, central Asia, Oceania, and Latin America. Globally, 59% (55–62) of women and 49% (46–52) of men with hypertension reported a previous diagnosis of hypertension in 2019, and 47% (43–51) of women and 38% (35–41) of men were treated. Control rates among people with hypertension in 2019 were 23% (20–27) for women and 18% (16–21) for men. In 2019, treatment and control rates were highest in South Korea, Canada, and Iceland (treatment >70%; control >50%), followed by the USA, Costa Rica, Germany, Portugal, and Taiwan. Treatment rates were less than 25% for women and less than 20% for men in Nepal, Indonesia, and some countries in sub-Saharan Africa and Oceania. Control rates were below 10% for women and men in these countries and for men in some countries in north Africa, central and south Asia, and eastern Europe. Treatment and control rates have improved in most countries since 1990, but we found little change in most countries in sub-Saharan Africa and Oceania. Improvements were largest in high-income countries, central Europe, and some upper-middle-income and recently high-income countries including Costa Rica, Taiwan, Kazakhstan, South Africa, Brazil, Chile, Turkey, and Iran. Interpretation Improvements in the detection, treatment, and control of hypertension have varied substantially across countries, with some middle-income countries now outperforming most high-income nations. The dual approach of reducing hypertension prevalence through primary prevention and enhancing its treatment and control is achievable not only in high-income countries but also in low-income and middle-income settings

Global variations in diabetes mellitus based on fasting glucose and haemogloblin A1c

Fasting plasma glucose (FPG) and haemoglobin A1c (HbA1c) are both used to diagnose diabetes, but may identify different people as having diabetes. We used data from 117 population-based studies and quantified, in different world regions, the prevalence of diagnosed diabetes, and whether those who were previously undiagnosed and detected as having diabetes in survey screening had elevated FPG, HbA1c, or both. We developed prediction equations for estimating the probability that a person without previously diagnosed diabetes, and at a specific level of FPG, had elevated HbA1c, and vice versa. The age-standardised proportion of diabetes that was previously undiagnosed, and detected in survey screening, ranged from 30% in the high-income western region to 66% in south Asia. Among those with screen-detected diabetes with either test, the agestandardised proportion who had elevated levels of both FPG and HbA1c was 29-39% across regions; the remainder had discordant elevation of FPG or HbA1c. In most low- and middle-income regions, isolated elevated HbA1c more common than isolated elevated FPG. In these regions, the use of FPG alone may delay diabetes diagnosis and underestimate diabetes prevalence. Our prediction equations help allocate finite resources for measuring HbA1c to reduce the global gap in diabetes diagnosis and surveillance.peer-reviewe

Worldwide trends in hypertension prevalence and progress in treatment and control from 1990 to 2019: a pooled analysis of 1201 population-representative studies with 104 million participants

Background Hypertension can be detected at the primary health-care level and low-cost treatments can effectively control hypertension. We aimed to measure the prevalence of hypertension and progress in its detection, treatment, and control from 1990 to 2019 for 200 countries and territories. Methods We used data from 1990 to 2019 on people aged 30-79 years from population-representative studies with measurement of blood pressure and data on blood pressure treatment. We defined hypertension as having systolic blood pressure 140 mm Hg or greater, diastolic blood pressure 90 mm Hg or greater, or taking medication for hypertension. We applied a Bayesian hierarchical model to estimate the prevalence of hypertension and the proportion of people with hypertension who had a previous diagnosis (detection), who were taking medication for hypertension (treatment), and whose hypertension was controlled to below 140/90 mm Hg (control). The model allowed for trends over time to be non-linear and to vary by age. Findings The number of people aged 30-79 years with hypertension doubled from 1990 to 2019, from 331 (95% credible interval 306-359) million women and 317 (292-344) million men in 1990 to 626 (584-668) million women and 652 (604-698) million men in 2019, despite stable global age-standardised prevalence. In 2019, age-standardised hypertension prevalence was lowest in Canada and Peru for both men and women; in Taiwan, South Korea, Japan, and some countries in western Europe including Switzerland, Spain, and the UK for women; and in several low-income and middle-income countries such as Eritrea, Bangladesh, Ethiopia, and Solomon Islands for men. Hypertension prevalence surpassed 50% for women in two countries and men in nine countries, in central and eastern Europe, central Asia, Oceania, and Latin America. Globally, 59% (55-62) of women and 49% (46-52) of men with hypertension reported a previous diagnosis of hypertension in 2019, and 47% (43-51) of women and 38% (35-41) of men were treated. Control rates among people with hypertension in 2019 were 23% (20-27) for women and 18% (16-21) for men. In 2019, treatment and control rates were highest in South Korea, Canada, and Iceland (treatment >70%; control >50%), followed by the USA, Costa Rica, Germany, Portugal, and Taiwan. Treatment rates were less than 25% for women and less than 20% for men in Nepal, Indonesia, and some countries in sub-Saharan Africa and Oceania. Control rates were below 10% for women and men in these countries and for men in some countries in north Africa, central and south Asia, and eastern Europe. Treatment and control rates have improved in most countries since 1990, but we found little change in most countries in sub-Saharan Africa and Oceania. Improvements were largest in high-income countries, central Europe, and some upper-middle-income and recently high-income countries including Costa Rica, Taiwan, Kazakhstan, South Africa, Brazil, Chile, Turkey, and Iran. Interpretation Improvements in the detection, treatment, and control of hypertension have varied substantially across countries, with some middle-income countries now outperforming most high-income nations. The dual approach of reducing hypertension prevalence through primary prevention and enhancing its treatment and control is achievable not only in high-income countries but also in low-income and middle-income settings. Copyright (C) 2021 World Health Organization; licensee Elsevier