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This paper is concerned with the stability of a SEIR (susceptible-exposed-infectious-recovered) model with the age of infection and vaccination. Firstly, we prove the positivity, boundedness, and asymptotic smoothness of the solutions. Next, the existence and local stability of disease-free and endemic steady states are shown. The basic reproduction number R0 is introduced. Furthermore, the global stability of the disease-free and endemic steady states is derived. Numerical simulations are shown to illustrate our theoretical results.

Substantial progress has been made in identification of type 2 diabetes (T2D) risk loci in the past few years, but our understanding of the genetic basis of T2D in ethnically diverse populations remains limited. We performed a genome-wide association study and a replication study in Chinese Hans comprising 8,569 T2D case subjects and 8,923 control subjects in total, from which 10 single nucleotide polymorphisms were selected for further follow-up in a de novo replication sample of 3,410 T2D case and 3,412 control subjects and an in silico replication sample of 6,952 T2D case and 11,865 control subjects. Besides confirming seven established T2D loci (CDKAL1, CDKN2A/B, KCNQ1, CDC123, GLIS3, HNF1B, and DUSP9) at genome-wide significance, we identified two novel T2D loci, including G-protein–coupled receptor kinase 5 (GRK5) (rs10886471: P = 7.1 × 10−9) and RASGRP1 (rs7403531: P = 3.9 × 10−9), of which the association signal at GRK5 seems to be specific to East Asians. In nondiabetic individuals, the T2D risk-increasing allele of RASGRP1-rs7403531 was also associated with higher HbA1c and lower homeostasis model assessment of β-cell function (P = 0.03 and 0.0209, respectively), whereas the T2D risk-increasing allele of GRK5-rs10886471 was also associated with higher fasting insulin (P = 0.0169) but not with fasting glucose. Our findings not only provide new insights into the pathophysiology of T2D, but may also shed light on the ethnic differences in T2D susceptibility.

Common Variants in CDKAL1 , CDKN2A/B , IGF2BP2 , SLC30A8 , and HHEX/IDE Genes Are Associated With Type 2 Diabetes and Impaired Fasting Glucose in a Chinese Han Population Ying Wu 1 , Huaixing Li 1 , Ruth J.F. Loos 2 , Zhijie Yu 1 , Xingwang Ye 1 , Lihua Chen 1 , An Pan 1 , Frank B. Hu 3 and Xu Lin 1 1 Key Laboratory of Nutrition and Metabolism, Institute for Nutritional Sciences, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences and Graduate School of the Chinese Academy of Sciences, Shanghai, China 2 Medical Research Council Epidemiology Unit, Institute of Metabolic Science, Addenbrooke's Hospital, Cambridge, U.K 3 Department of Nutrition, Harvard School of Public Health, Harvard University, Boston, Massachusetts Corresponding author: Dr. Xu Lin, xlin{at}sibs.ac.cn Abstract OBJECTIVE— Genome-wide association studies have identified common variants in CDKAL1 , CDKN2A/B , IGF2BP2 , SLC30A8 , HHEX/IDE , EXT2 , and LOC387761 loci that significantly increase the risk of type 2 diabetes. We aimed to replicate these observations in a population-based cohort of Chinese Hans and examine the associations of these variants with type 2 diabetes and diabetes-related phenotypes. RESEARCH DESIGN AND METHODS— We genotyped 17 single nucleotide polymorhisms (SNPs) in 3,210 unrelated Chinese Hans, including 424 participants with type 2 diabetes, 878 with impaired fasting glucose (IFG), and 1,908 with normal fasting glucose. RESULTS— We confirmed the associations between type 2 diabetes and variants near CDKAL1 (odds ratio 1.49 [95% CI 1.27–1.75]; P = 8.91 × 10 −7 ) and CDKN2A/B (1.31 [1.12–1.54]; P = 1.0 × 10 −3 ). We observed significant association of SNPs in IGF2BP2 (1.17 [1.03–1.32]; P = 0.014) and SLC30A8 (1.12 [1.01–1.25]; P = 0.033) with combined IFG/type 2 diabetes. The SNPs in CDKAL1 , IGF2BP2 , and SLC30A8 were also associated with impaired β-cell function estimated by homeostasis model assessment of β-cell function. When combined, each additional risk allele from CDKAL1 -rs9465871, CDKN2A/B -rs10811661, IGF2BP2 -rs4402960, and SLC30A8 -rs13266634 increased the risk for type 2 diabetes by 1.24-fold ( P = 2.85 × 10 −7 ) or for combined IFG/type 2 diabetes by 1.21-fold ( P = 6.31 × 10 −11 ). None of the SNPs in EXT2 or LOC387761 exhibited significant association with type 2 diabetes or IFG. Significant association was observed between the HHEX/IDE SNPs and type 2 diabetes in individuals from Shanghai only ( P < 0.013) but not in those from Beijing ( P > 0.33). CONCLUSIONS— Our results indicate that in Chinese Hans, common variants in CDKAL1 , CDKN2A/B , IGF2BP2 , and SLC30A8 loci independently or additively contribute to type 2 diabetes risk, likely mediated through β-cell dysfunction. Footnotes Published ahead of print at http://diabetes.diabetesjournals.org on 15 July 2008. Y.W. and H.L. contributed equally to this article. Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered. See http://creativecommons.org/licenses/by-nc-nd/3.0/ for details. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. Accepted July 3, 2008. Received January 14, 2008. DIABETES

Aims/hypothesis Although microbiota-derived endotoxaemia has previously been shown to induce metabolic disorders, data from population-based longitudinal studies are scarce. This study therefore investigated the associations between lipopolysaccharide binding protein (LBP) levels and 6 year incident metabolic syndrome (MetS), as well as the potentially modifying effects of obesity status in middle-aged and older Chinese men and women. Methods A total of 2,529 men and women aged 50–70 years from Beijing and Shanghai, China, were followed for 6 years. Those free of MetS at baseline (1,312) were included in the analyses for the risk of developing MetS. Baseline plasma LBP was measured using an ELISA kit. Results During the 6 year follow-up, 449 (34.2%) participants developed MetS. Baseline LBP was significantly associated with BMI, waist circumference, blood lipid profile and C-reactive protein (CRP) both at baseline and during follow-up (all p  < 0.05). The RR for incident MetS comparing extreme quartiles of LBP was 1.28 (95% CI 1.04, 1.58), after multivariate adjustment including BMI and CRP. In stratified analysis, LBP was positively associated with incident MetS only in normal-weight participants (RR, comparing extreme tertiles, 1.59; 95% CI 1.18, 2.15; p trend  = 0.002), but not in their overweight/obese counterparts (RR, comparing extreme tertiles, 0.99; 95% CI 0.80, 1.22; p trend  = 0.880). A significant interaction was observed between LBP and obesity status ( p interaction  = 0.013). Conclusions/interpretation Our study suggested that elevated plasma LBP was associated with an increased risk of developing MetS among middle-aged and older Chinese, especially in normal-weight individuals.

Few studies assessed effects of individual and multiple ions simultaneously on metabolic outcomes, due to methodological limitation. By combining advanced ionomics and mutual information, a quantifying measurement for mutual dependence between two random variables, we investigated associations of ion modules/networks with overweight/obesity, metabolic syndrome (MetS) and type 2 diabetes (T2DM) in 976 middle-aged Chinese men and women. Fasting plasma ions were measured by inductively coupled plasma mass spectroscopy. Significant ion modules were selected by mutual information to construct disease related ion networks. Plasma copper and phosphorus always ranked the first two among three specific ion networks associated with overweight/obesity, MetS and T2DM. Comparing the ranking of ion individually and in networks, three patterns were observed (1) \"Individual ion,\" such as potassium and chrome, which tends to work alone; (2) \"Module ion,\" such as iron in T2DM, which tends to act in modules/network; and (3) \"Module-individual ion,\" such as copper in overweight/obesity, which seems to work equivalently in either way. In conclusion, by using the novel approach of the ionomics strategy and the information theory, we observed potential associations of ions individually or as modules/networks with metabolic disorders. Certainly, these findings need to be confirmed in future biological studies.

Variants in the Fat Mass–and Obesity-Associated ( FTO ) Gene Are Not Associated With Obesity in a Chinese Han Population Huaixing Li 1 , Ying Wu 1 , Ruth J.F. Loos 2 , Frank B. Hu 3 , Yong Liu 1 , Jing Wang 1 , Zhijie Yu 1 and Xu Lin 1 1 Key Laboratory of Systems Biology, Institute for Nutritional Sciences, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences and Graduate School of the Chinese Academy of Sciences, Shanghai, China 2 MRC Epidemiology Unit, Institute of Metabolic Science, Addenbrooke's Hospital, Cambridge, U.K 3 Department of Nutrition, Harvard School of Public Health, Boston, Massachusetts Address correspondence and reprint requests to Dr. Xu Lin, Institute for Nutritional Sciences, Shanghai, 200031, China. E-mail: xlin{at}sibs.ac.cn Abstract OBJECTIVE— Recently, genome-wide association studies have provided evidence that several common variants within the fat mass–and obesity-associated ( FTO ) gene were significantly associated with obesity in populations of European origin. However, their effects in other ethnic populations remain to be elucidated. RESEARCH DESIGN AND METHODS— In this study, we examined the association between three FTO variants (rs8050136, rs9939609, and rs9930506) and obesity and related traits in a population-based study of 3,210 unrelated Chinese Han subjects from Shanghai and Beijing. In secondary analyses, we also tested for association with type 2 diabetes and related traits. Logistics regression and generalized linear models were used to test for additive and dominant effects of the risk alleles. RESULTS— The minor allele frequencies of rs8050136, rs9939609, and rs9930506 in our population (0.12, 0.12, and 0.20, respectively) were substantially lower than those observed for populations of European descent (e.g., for CEU population of HapMap: 0.45, 0.48, and 0.45, respectively). Despite our study being sufficiently powered to detect effects similar to those previously reported, none of the FTO SNPs were found to be associated with obesity, overweight, BMI, waist circumference, or body fat percentage. In addition, none of the SNPs exhibited significant associations with fasting levels of plasma glucose, A1C, insulin, or β-cell function (estimated via homeostasis model assessment) under either an additive or a dominant model in the quantitative trait analyses. Analyses stratified by sex or geographical region did not change these observations. CONCLUSIONS— Our data do not support that the FTO common variants are major contributors of obesity or type 2 diabetes in the Chinese Han population. HOMA-B, homeostasis model assessment of β-cell function HOMA-S, homeostasis model assessment of insulin sensitivity LD, linkage disequilibrium MAF, minor allele frequency SNP, single nucleotide polymorphism Footnotes Published ahead of print at http://diabetes.diabetesjournals.org on 22 October 2007. DOI: 10.2337/db07-1130. H.L. and Y.W. contributed equally to this work. Additional information for this article can be found in an online appendix at http://dx.doi.org/10.2337/db07-1130 . The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. Accepted October 16, 2007. Received August 18, 2007. DIABETES