Algorithms for Reconstructing DDoS Attack Graphs using Probabilistic Packet Marking

DoS and DDoS attacks are widely used and pose a constant threat. Here we explore Probability Packet Marking (PPM), one of the important methods for reconstructing the attack-graph and detect the attackers. We present two algorithms. Differently from others, their stopping time is not fixed a priori. It rather depends on the actual distance of the attacker from the victim. Our first algorithm returns the graph at the earliest feasible time, and turns out to guarantee high success probability. The second algorithm enables attaining any predetermined success probability at the expense of a longer runtime. We study the performance of the two algorithms theoretically, and compare them to other algorithms by simulation. Finally, we consider the order in which the marks corresponding to the various edges of the attack graph are obtained by the victim. We show that, although edges closer to the victim tend to be discovered earlier in the process than farther edges, the differences are much smaller than previously thought.Comment: 30 pages, 4 figures, 4 table

Global, regional, and national incidence, prevalence, and years lived with disability for 328 diseases and injuries for 195 countries, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016

As mortality rates decline, life expectancy increases, and populations age, non-fatal outcomes of diseases and injuries are becoming a larger component of the global burden of disease. The Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) provides a comprehensive assessment of prevalence, incidence, and years lived with disability (YLDs) for 328 causes in 195 countries and territories from 1990 to 2016

Global, regional, and national under-5 mortality, adult mortality, age-specific mortality, and life expectancy, 1970–2016: a systematic analysis for the Global Burden of Disease Study 2016

BACKGROUND: Detailed assessments of mortality patterns, particularly age-specific mortality, represent a crucial input that enables health systems to target interventions to specific populations. Understanding how all-cause mortality has changed with respect to development status can identify exemplars for best practice. To accomplish this, the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) estimated age-specific and sex-specific all-cause mortality between 1970 and 2016 for 195 countries and territories and at the subnational level for the five countries with a population greater than 200 million in 2016. METHODS: We have evaluated how well civil registration systems captured deaths using a set of demographic methods called death distribution methods for adults and from consideration of survey and census data for children younger than 5 years. We generated an overall assessment of completeness of registration of deaths by dividing registered deaths in each location-year by our estimate of all-age deaths generated from our overall estimation process. For 163 locations, including subnational units in countries with a population greater than 200 million with complete vital registration (VR) systems, our estimates were largely driven by the observed data, with corrections for small fluctuations in numbers and estimation for recent years where there were lags in data reporting (lags were variable by location, generally between 1 year and 6 years). For other locations, we took advantage of different data sources available to measure under-5 mortality rates (U5MR) using complete birth histories, summary birth histories, and incomplete VR with adjustments; we measured adult mortality rate (the probability of death in individuals aged 15-60 years) using adjusted incomplete VR, sibling histories, and household death recall. We used the U5MR and adult mortality rate, together with crude death rate due to HIV in the GBD model life table system, to estimate age-specific and sex-specific death rates for each location-year. Using various international databases, we identified fatal discontinuities, which we defined as increases in the death rate of more than one death per million, resulting from conflict and terrorism, natural disasters, major transport or technological accidents, and a subset of epidemic infectious diseases; these were added to estimates in the relevant years. In 47 countries with an identified peak adult prevalence for HIV/AIDS of more than 0·5% and where VR systems were less than 65% complete, we informed our estimates of age-sex-specific mortality using the Estimation and Projection Package (EPP)-Spectrum model fitted to national HIV/AIDS prevalence surveys and antenatal clinic serosurveillance systems. We estimated stillbirths, early neonatal, late neonatal, and childhood mortality using both survey and VR data in spatiotemporal Gaussian process regression models. We estimated abridged life tables for all location-years using age-specific death rates. We grouped locations into development quintiles based on the Socio-demographic Index (SDI) and analysed mortality trends by quintile. Using spline regression, we estimated the expected mortality rate for each age-sex group as a function of SDI. We identified countries with higher life expectancy than expected by comparing observed life expectancy to anticipated life expectancy on the basis of development status alone. FINDINGS: Completeness in the registration of deaths increased from 28% in 1970 to a peak of 45% in 2013; completeness was lower after 2013 because of lags in reporting. Total deaths in children younger than 5 years decreased from 1970 to 2016, and slower decreases occurred at ages 5-24 years. By contrast, numbers of adult deaths increased in each 5-year age bracket above the age of 25 years. The distribution of annualised rates of change in age-specific mortality rate differed over the period 2000 to 2016 compared with earlier decades: increasing annualised rates of change were less frequent, although rising annualised rates of change still occurred in some locations, particularly for adolescent and younger adult age groups. Rates of stillbirths and under-5 mortality both decreased globally from 1970. Evidence for global convergence of death rates was mixed; although the absolute difference between age-standardised death rates narrowed between countries at the lowest and highest levels of SDI, the ratio of these death rates-a measure of relative inequality-increased slightly. There was a strong shift between 1970 and 2016 toward higher life expectancy, most noticeably at higher levels of SDI. Among countries with populations greater than 1 million in 2016, life expectancy at birth was highest for women in Japan, at 86·9 years (95% UI 86·7-87·2), and for men in Singapore, at 81·3 years (78·8-83·7) in 2016. Male life expectancy was generally lower than female life expectancy between 1970 and 2016, an

Global, regional, and national disability-adjusted life-years (DALYs) for 333 diseases and injuries and healthy life expectancy (HALE) for 195 countries and territories, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016

BACKGROUND: Measurement of changes in health across locations is useful to compare and contrast changing epidemiological patterns against health system performance and identify specific needs for resource allocation in research, policy development, and programme decision making. Using the Global Burden of Diseases, Injuries, and Risk Factors Study 2016, we drew from two widely used summary measures to monitor such changes in population health: disability-adjusted life-years (DALYs) and healthy life expectancy (HALE). We used these measures to track trends and benchmark progress compared with expected trends on the basis of the Socio-demographic Index (SDI). METHODS: We used results from the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 for all-cause mortality, cause-specific mortality, and non-fatal disease burden to derive HALE and DALYs by sex for 195 countries and territories from 1990 to 2016. We calculated DALYs by summing years of life lost and years of life lived with disability for each location, age group, sex, and year. We estimated HALE using age-specific death rates and years of life lived with disability per capita. We explored how DALYs and HALE differed from expected trends when compared with the SDI: the geometric mean of income per person, educational attainment in the population older than age 15 years, and total fertility rate. FINDINGS: The highest globally observed HALE at birth for both women and men was in Singapore, at 75·2 years (95% uncertainty interval 71·9-78·6) for females and 72·0 years (68·8-75·1) for males. The lowest for females was in the Central African Republic (45·6 years [42·0-49·5]) and for males was in Lesotho (41·5 years [39·0-44·0]). From 1990 to 2016, global HALE increased by an average of 6·24 years (5·97-6·48) for both sexes combined. Global HALE increased by 6·04 years (5·74-6·27) for males and 6·49 years (6·08-6·77) for females, whereas HALE at age 65 years increased by 1·78 years (1·61-1·93) for males and 1·96 years (1·69-2·13) for females. Total global DALYs remained largely unchanged from 1990 to 2016 (-2·3% [-5·9 to 0·9]), with decreases in communicable, maternal, neonatal, and nutritional (CMNN) disease DALYs offset by increased DALYs due to non-communicable diseases (NCDs). The exemplars, calculated as the five lowest ratios of observed to expected age-standardised DALY rates in 2016, were Nicaragua, Costa Rica, the Maldives, Peru, and Israel. The leading three causes of DALYs globally were ischaemic heart disease, cerebrovascular disease, and lower respiratory infections, comprising 16·1% of all DALYs. Total DALYs and age-standardised DALY rates due to most CMNN causes decreased from 1990 to 2016. Conversely, the total DALY burden rose for most NCDs; however, age-standardised DALY rates due to NCDs declined globally. INTERPRETATION: At a global level, DALYs and HALE continue to show improvements. At the same time, we observe that many populations are facing growing functional health loss. Rising SDI was associated with increases in cumulative years of life lived with disability and decreases in CMNN DALYs offset by increased NCD DALYs. Relative compression of morbidity highlights the importance of continued health interventions, which has changed in most locations in pace with the gross domestic product per person, education, and family planning. The analysis of DALYs and HALE and their relationship to SDI represents a robust framework with which to benchmark location-specific health performance. Country-specific drivers of disease burden, particularly for causes with higher-than-expected DALYs, should inform health policies, health system improvement initiatives, targeted prevention efforts, and development assistance for health, including financial and research investments for all countries, regardless of their level of sociodemographic development. The presence of countries that substantially outperform others suggests the need for increased scrutiny for proven examples of best practices, which can help to extend gains, whereas the presence of underperforming countries suggests the need for devotion of extra attention to health systems that need more robust support. FUNDING: Bill & Melinda Gates Foundation

Population and fertility by age and sex for 195 countries and territories, 1950–2017: a systematic analysis for the Global Burden of Disease Study 2017

Background: Population estimates underpin demographic and epidemiological research and are used to track progress on numerous international indicators of health and development. To date, internationally available estimates of population and fertility, although useful, have not been produced with transparent and replicable methods and do not use standardised estimates of mortality. We present single-calendar year and single-year of age estimates of fertility and population by sex with standardised and replicable methods. Methods: We estimated population in 195 locations by single year of age and single calendar year from 1950 to 2017 with standardised and replicable methods. We based the estimates on the demographic balancing equation, with inputs of fertility, mortality, population, and migration data. Fertility data came from 7817 location-years of vital registration data, 429 surveys reporting complete birth histories, and 977 surveys and censuses reporting summary birth histories. We estimated age-specific fertility rates (ASFRs; the annual number of livebirths to women of a specified age group per 1000 women in that age group) by use of spatiotemporal Gaussian process regression and used the ASFRs to estimate total fertility rates (TFRs; the average number of children a woman would bear if she survived through the end of the reproductive age span [age 10–54 years] and experienced at each age a particular set of ASFRs observed in the year of interest). Because of sparse data, fertility at ages 10–14 years and 50–54 years was estimated from data on fertility in women aged 15–19 years and 45–49 years, through use of linear regression. Age-specific mortality data came from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 estimates. Data on population came from 1257 censuses and 761 population registry location-years and were adjusted for underenumeration and age misreporting with standard demographic methods. Migration was estimated with the GBD Bayesian demographic balancing model, after incorporating information about refugee migration into the model prior. Final population estimates used the cohort-component method of population projection, with inputs of fertility, mortality, and migration data. Population uncertainty was estimated by use of out-of-sample predictive validity testing. With these data, we estimated the trends in population by age and sex and in fertility by age between 1950 and 2017 in 195 countries and territories. Findings: From 1950 to 2017, TFRs decreased by 49\ub74% (95% uncertainty interval [UI] 46\ub74–52\ub70). The TFR decreased from 4\ub77 livebirths (4\ub75–4\ub79) to 2\ub74 livebirths (2\ub72–2\ub75), and the ASFR of mothers aged 10–19 years decreased from 37 livebirths (34–40) to 22 livebirths (19–24) per 1000 women. Despite reductions in the TFR, the global population has been increasing by an average of 83\ub78 million people per year since 1985. The global population increased by 197\ub72% (193\ub73–200\ub78) since 1950, from 2\ub76 billion (2\ub75–2\ub76) to 7\ub76 billion (7\ub74–7\ub79) people in 2017; much of this increase was in the proportion of the global population in south Asia and sub-Saharan Africa. The global annual rate of population growth increased between 1950 and 1964, when it peaked at 2\ub70%; this rate then remained nearly constant until 1970 and then decreased to 1\ub71% in 2017. Population growth rates in the southeast Asia, east Asia, and Oceania GBD super-region decreased from 2\ub75% in 1963 to 0\ub77% in 2017, whereas in sub-Saharan Africa, population growth rates were almost at the highest reported levels ever in 2017, when they were at 2\ub77%. The global average age increased from 26\ub76 years in 1950 to 32\ub71 years in 2017, and the proportion of the population that is of working age (age 15–64 years) increased from 59\ub79% to 65\ub73%. At the national level, the TFR decreased in all countries and territories between 1950 and 2017; in 2017, TFRs ranged from a low of 1\ub70 livebirths (95% UI 0\ub79–1\ub72) in Cyprus to a high of 7\ub71 livebirths (6\ub78–7\ub74) in Niger. The TFR under age 25 years (TFU25; number of livebirths expected by age 25 years for a hypothetical woman who survived the age group and was exposed to current ASFRs) in 2017 ranged from 0\ub708 livebirths (0\ub707–0\ub709) in South Korea to 2\ub74 livebirths (2\ub72–2\ub76) in Niger, and the TFR over age 30 years (TFO30; number of livebirths expected for a hypothetical woman ageing from 30 to 54 years who survived the age group and was exposed to current ASFRs) ranged from a low of 0\ub73 livebirths (0\ub73–0\ub74) in Puerto Rico to a high of 3\ub71 livebirths (3\ub70–3\ub72) in Niger. TFO30 was higher than TFU25 in 145 countries and territories in 2017. 33 countries had a negative population growth rate from 2010 to 2017, most of which were located in central, eastern, and western Europe, whereas population growth rates of more than 2\ub70% were seen in 33 of 46 countries in sub-Saharan Africa. In 2017, less than 65% of the national population was of working age in 12 of 34 high-income countries, and less than 50% of the national population was of working age in Mali, Chad, and Niger. Interpretation: Population trends create demographic dividends and headwinds (ie, economic benefits and detriments) that affect national economies and determine national planning needs. Although TFRs are decreasing, the global population continues to grow as mortality declines, with diverse patterns at the national level and across age groups. To our knowledge, this is the first study to provide transparent and replicable estimates of population and fertility, which can be used to inform decision making and to monitor progress. Funding: Bill & Melinda Gates Foundation

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4% (62.3 (55.1–70.8) million) to 6.4% (58.3 (47.6–70.7) million), but is predicted to remain above the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025. Prevalence of overweight increased from 5.2% (30 (22.8–38.5) million) in 2000 to 6.0% (55.5 (44.8–67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic

Population and fertility by age and sex for 195 countries and territories, 1950–2017: a systematic analysis for the Global Burden of Disease Study 2017

Background: Population estimates underpin demographic and epidemiological research and are used to track progress on numerous international indicators of health and development. To date, internationally available estimates of population and fertility, although useful, have not been produced with transparent and replicable methods and do not use standardised estimates of mortality. We present single-calendar year and single-year of age estimates of fertility and population by sex with standardised and replicable methods. Methods: We estimated population in 195 locations by single year of age and single calendar year from 1950 to 2017 with standardised and replicable methods. We based the estimates on the demographic balancing equation, with inputs of fertility, mortality, population, and migration data. Fertility data came from 7817 location-years of vital registration data, 429 surveys reporting complete birth histories, and 977 surveys and censuses reporting summary birth histories. We estimated age-specific fertility rates (ASFRs; the annual number of livebirths to women of a specified age group per 1000 women in that age group) by use of spatiotemporal Gaussian process regression and used the ASFRs to estimate total fertility rates (TFRs; the average number of children a woman would bear if she survived through the end of the reproductive age span [age 10–54 years] and experienced at each age a particular set of ASFRs observed in the year of interest). Because of sparse data, fertility at ages 10–14 years and 50–54 years was estimated from data on fertility in women aged 15–19 years and 45–49 years, through use of linear regression. Age-specific mortality data came from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 estimates. Data on population came from 1257 censuses and 761 population registry location-years and were adjusted for underenumeration and age misreporting with standard demographic methods. Migration was estimated with the GBD Bayesian demographic balancing model, after incorporating information about refugee migration into the model prior. Final population estimates used the cohort-component method of population projection, with inputs of fertility, mortality, and migration data. Population uncertainty was estimated by use of out-of-sample predictive validity testing. With these data, we estimated the trends in population by age and sex and in fertility by age between 1950 and 2017 in 195 countries and territories. Findings: From 1950 to 2017, TFRs decreased by 49·4% (95% uncertainty interval [UI] 46·4–52·0). The TFR decreased from 4·7 livebirths (4·5–4·9) to 2·4 livebirths (2·2–2·5), and the ASFR of mothers aged 10–19 years decreased from 37 livebirths (34–40) to 22 livebirths (19–24) per 1000 women. Despite reductions in the TFR, the global population has been increasing by an average of 83·8 million people per year since 1985. The global population increased by 197·2% (193·3–200·8) since 1950, from 2·6 billion (2·5–2·6) to 7·6 billion (7·4–7·9) people in 2017; much of this increase was in the proportion of the global population in south Asia and sub-Saharan Africa. The global annual rate of population growth increased between 1950 and 1964, when it peaked at 2·0%; this rate then remained nearly constant until 1970 and then decreased to 1·1% in 2017. Population growth rates in the southeast Asia, east Asia, and Oceania GBD super-region decreased from 2·5% in 1963 to 0·7% in 2017, whereas in sub-Saharan Africa, population growth rates were almost at the highest reported levels ever in 2017, when they were at 2·7%. The global average age increased from 26·6 years in 1950 to 32·1 years in 2017, and the proportion of the population that is of working age (age 15–64 years) increased from 59·9% to 65·3%. At the national level, the TFR decreased in all countries and territories between 1950 and 2017; in 2017, TFRs ranged from a low of 1·0 livebirths (95% UI 0·9–1·2) in Cyprus to a high of 7·1 livebirths (6·8–7·4) in Niger. The TFR under age 25 years (TFU25; number of livebirths expected by age 25 years for a hypothetical woman who survived the age group and was exposed to current ASFRs) in 2017 ranged from 0·08 livebirths (0·07–0·09) in South Korea to 2·4 livebirths (2·2–2·6) in Niger, and the TFR over age 30 years (TFO30; number of livebirths expected for a hypothetical woman ageing from 30 to 54 years who survived the age group and was exposed to current ASFRs) ranged from a low of 0·3 livebirths (0·3–0·4) in Puerto Rico to a high of 3·1 livebirths (3·0–3·2) in Niger. TFO30 was higher than TFU25 in 145 countries and territories in 2017. 33 countries had a negative population growth rate from 2010 to 2017, most of which were located in central, eastern, and western Europe, whereas population growth rates of more than 2·0% were seen in 33 of 46 countries in sub-Saharan Africa. In 2017, less than 65% of the national population was of working age in 12 of 34 high-income countries, and less than 50% of the national population was of working age in Mali, Chad, and Niger. Interpretation: Population trends create demographic dividends and headwinds (ie, economic benefits and detriments) that affect national economies and determine national planning needs. Although TFRs are decreasing, the global population continues to grow as mortality declines, with diverse patterns at the national level and across age groups. To our knowledge, this is the first study to provide transparent and replicable estimates of population and fertility, which can be used to inform decision making and to monitor progress

Population and fertility by age and sex for 195 countries and territories, 1950-2017: a systematic analysis for the Global Burden of Disease Study 2017

BACKGROUND: Population estimates underpin demographic and epidemiological research and are used to track progress on numerous international indicators of health and development. To date, internationally available estimates of population and fertility, although useful, have not been produced with transparent and replicable methods and do not use standardised estimates of mortality. We present single-calendar year and single-year of age estimates of fertility and population by sex with standardised and replicable methods. METHODS: We estimated population in 195 locations by single year of age and single calendar year from 1950 to 2017 with standardised and replicable methods. We based the estimates on the demographic balancing equation, with inputs of fertility, mortality, population, and migration data. Fertility data came from 7817 location-years of vital registration data, 429 surveys reporting complete birth histories, and 977 surveys and censuses reporting summary birth histories. We estimated age-specific fertility rates (ASFRs; the annual number of livebirths to women of a specified age group per 1000 women in that age group) by use of spatiotemporal Gaussian process regression and used the ASFRs to estimate total fertility rates (TFRs; the average number of children a woman would bear if she survived through the end of the reproductive age span [age 10-54 years] and experienced at each age a particular set of ASFRs observed in the year of interest). Because of sparse data, fertility at ages 10-14 years and 50-54 years was estimated from data on fertility in women aged 15-19 years and 45-49 years, through use of linear regression. Age-specific mortality data came from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 estimates. Data on population came from 1257 censuses and 761 population registry location-years and were adjusted for underenumeration and age misreporting with standard demographic methods. Migration was estimated with the GBD Bayesian demographic balancing model, after incorporating information about refugee migration into the model prior. Final population estimates used the cohort-component method of population projection, with inputs of fertility, mortality, and migration data. Population uncertainty was estimated by use of out-of-sample predictive validity testing. With these data, we estimated the trends in population by age and sex and in fertility by age between 1950 and 2017 in 195 countries and territories

Magnesium sulphate and the development of the common bean cultivated in an Ultisol of Northeast Australia Sulfato de magnésio e o desenvolvimento do feijoeiro comum cultivado em um Ultissolo do Nordeste da Australia

Magnesium applications (MgS0(4).7H(2)0) to achieve 8 and 16 mmol c/cm3 of Mg (324 and 1284 kg of MgS0(4) ha-1) were made on one Ultisol from Australia Northeast to correct Mg deficiency in plants and to verify the optimum level of Mg to grow common bean (Phaseolus vulgaris L). Magnesium was applied together with lime, N, K, Cu, Zn, B, and Mo as calcium carbonate, ammonium nitrate, potassium phosphate, cupric and zinc sulphate, boric acid and sodium molybdate respectively a month before planting and P as phosphoric acid at the planting. The pH reached the equilibrium after six weeks of incubation. Higher electrical conductivity (EC) was observed in soil where Mg was applied to reach 8 mmol c/cm3 in the absence of common bean and 16 mmol c/cm3 when the plant was present. Higher plant height, leaf area, dry matter weight:leaf area ratio and nutrient concentrations were observed in plants cultivated in soils treated with Mg to reach 8 mmol c/cm3 and 16 mmol c/cm3 when the plant was present. The plant top P content was very low but N, Ca and Mg contents can be considered normal for the common bean.<br>Aplicações de sulfato de magnésio (MgS0(4).7H(2)0) para atigir 8 e 16 mmol c/cm3 de Mg (324 e 1284 kg de MgS0(4) ha-1) foram realizadas em um solo Ultissolo com a finalidade de corrigir deficiências de Mg no feijoeiro e verificar o nível de Mg suficiente para cultivar o feijão comum (Phaseolus vugaris L). O magnésio foi aplicado junto com calcário, N, K, Cu, Zn, B e Mo, como carbonato de cálcio, nitrato de amônio, fosfato de potássio, sulfato de cobre, sulfato de zinco, ácido bórico e molibidato de sódio respectivamente, um mês antes do plantio e o P como ácido fosfórico no plantio. O pH alcançou o equilíbrio após seis semanas de incubação. A condutividade elétrica mais alta (CE) foi observada em solo onde o Mg foi aplicado para atingir 8 mmol c/cm3 na ausência e 16 mmol c/cm3 na presença do feijoeiro A altura das plantas , área foliar, relação matéria seca/área foliar e concentrações de nutrientes no tecido foram maiores nas plantas cultivadas em solos tratados com Mg para atigir 8 mmol c/cm3 . O teor de P foi muito baixo mas os de N, Ca e Mg podem ser considerados normais para o feijoeiro comum

Global, regional, and national incidence, prevalence, and years lived with disability for 328 diseases and injuries for 195 countries, 1990-2016 : a systematic analysis for the Global Burden of Disease Study 2016

Background As mortality rates decline, life expectancy increases, and populations age, non-fatal outcomes of diseases and injuries are becoming a larger component of the global burden of disease. The Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016) provides a comprehensive assessment of prevalence, incidence, and years lived with disability (YLDs) for 328 causes in 195 countries and territories from 1990 to 2016. Methods We estimated prevalence and incidence for 328 diseases and injuries and 2982 sequelae, their non-fatal consequences. We used DisMod-MR 2.1, a Bayesian meta-regression tool, as the main method of estimation, ensuring consistency between incidence, prevalence, remission, and cause of death rates for each condition. For some causes, we used alternative modelling strategies if incidence or prevalence needed to be derived from other data. YLDs were estimated as the product of prevalence and a disability weight for all mutually exclusive sequelae, corrected for comorbidity and aggregated to cause level. We updated the Socio-demographic Index (SDI), a summary indicator of income per capita, years of schooling, and total fertility rate. GBD 2016 complies with the Guidelines for Accurate and Transparent Health Estimates Reporting (GATHER). Findings Globally, low back pain, migraine, age-related and other hearing loss, iron-deficiency anaemia, and major depressive disorder were the five leading causes of YLDs in 2016, contributing 57.6 million (95% uncertainty interval [UI] 40.8-75.9 million [7.2%, 6.0-8.3]), 45.1 million (29.0-62.8 million [5.6%, 4.0-7.2]), 36.3 million (25.3-50.9 million [4.5%, 3.8-5.3]), 34.7 million (23.0-49.6 million [4.3%, 3.5-5.2]), and 34.1 million (23.5-46.0 million [4.2%, 3.2-5.3]) of total YLDs, respectively. Age-standardised rates of YLDs for all causes combined decreased between 1990 and 2016 by 2.7% (95% UI 2.3-3.1). Despite mostly stagnant age-standardised rates, the absolute number of YLDs from non-communicable diseases has been growing rapidly across all SDI quintiles, partly because of population growth, but also the ageing of populations. The largest absolute increases in total numbers of YLDs globally were between the ages of 40 and 69 years. Age-standardised YLD rates for all conditions combined were 10.4% (95% UI 9.0-11.8) higher in women than in men. Iron-deficiency anaemia, migraine, Alzheimer's disease and other dementias, major depressive disorder, anxiety, and all musculoskeletal disorders apart from gout were the main conditions contributing to higher YLD rates in women. Men had higher age-standardised rates of substance use disorders, diabetes, cardiovascular diseases, cancers, and all injuries apart from sexual violence. Globally, we noted much less geographical variation in disability than has been documented for premature mortality. In 2016, there was a less than two times difference in age-standardised YLD rates for all causes between the location with the lowest rate (China, 9201 YLDs per 100 000, 95% UI 6862-11943) and highest rate (Yemen, 14 774 YLDs per 100 000, 11 018-19 228). Interpretation The decrease in death rates since 1990 for most causes has not been matched by a similar decline in age-standardised YLD rates. For many large causes, YLD rates have either been stagnant or have increased for some causes, such as diabetes. As populations are ageing, and the prevalence of disabling disease generally increases steeply with age, health systems will face increasing demand for services that are generally costlier than the interventions that have led to declines in mortality in childhood or for the major causes of mortality in adults. Up-todate information about the trends of disease and how this varies between countries is essential to plan for an adequate health-system response. Copyright (C) The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license.Peer reviewe