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      A critical review of mathematical models and data used in diabetology

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      Author(s): 1 , , 1
      Publication date (Electronic):
      Journal: BioMedical Engineering OnLine
      Publisher: BioMed Central

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          Abstract

          The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present paper we propose a global overview of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms.

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          The effect of irbesartan on the development of diabetic nephropathy in patients with type 2 diabetes.

          H H Parving, H Lehnert, J Bröchner-Mortensen … (2001)
          Microalbuminuria and hypertension are risk factors for diabetic nephropathy. Blockade of the renin-angiotensin system slows the progression to diabetic nephropathy in patients with type 1 diabetes, but similar data are lacking for hypertensive patients with type 2 diabetes. We evaluated the renoprotective effect of the angiotensin-II-receptor antagonist irbesartan in hypertensive patients with type 2 diabetes and microalbuminuria. A total of 590 hypertensive patients with type 2 diabetes and microalbuminuria were enrolled in this multinational, randomized, double-blind, placebo-controlled study of irbesartan, at a dose of either 150 mg daily or 300 mg daily, and were followed for two years. The primary outcome was the time to the onset of diabetic nephropathy, defined by persistent albuminuria in overnight specimens, with a urinary albumin excretion rate that was greater than 200 microg per minute and at least 30 percent higher than the base-line level. The base-line characteristics in the three groups were similar. Ten of the 194 patients in the 300-mg group (5.2 percent) and 19 of the 195 patients in the 150-mg group (9.7 percent) reached the primary end point, as compared with 30 of the 201 patients in the placebo group (14.9 percent) (hazard ratios, 0.30 [95 percent confidence interval, 0.14 to 0.61; P< 0.001] and 0.61 [95 percent confidence interval, 0.34 to 1.08; P=0.081 for the two irbesartan groups, respectively). The average blood pressure during the course of the study was 144/83 mm Hg in the placebo group, 143/83 mm Hg in the 150-mg group, and 141/83 mm Hg in the 300-mg group (P=0.004 for the comparison of systolic blood pressure between the placebo group and the combined irbesartan groups). Serious adverse events were less frequent among the patients treated with irbesartan (P=0.02). Irbesartan is renoprotective independently of its blood-pressure-lowering effect in patients with type 2 diabetes and microalbuminuria.
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            The burden of non communicable diseases in developing countries

            Abdesslam Boutayeb, Saber Boutayeb (2005)
            Background By the dawn of the third millennium, non communicable diseases are sweeping the entire globe, with an increasing trend in developing countries where, the transition imposes more constraints to deal with the double burden of infective and non-infective diseases in a poor environment characterised by ill-health systems. By 2020, it is predicted that these diseases will be causing seven out of every 10 deaths in developing countries. Many of the non communicable diseases can be prevented by tackling associated risk factors. Methods Data from national registries and international organisms are collected, compared and analyzed. The focus is made on the growing burden of non communicable diseases in developing countries. Results Among non communicable diseases, special attention is devoted to cardiovascular diseases, diabetes, cancer and chronic pulmonary diseases. Their burden is affecting countries worldwide but with a growing trend in developing countries. Preventive strategies must take into account the growing trend of risk factors correlated to these diseases. Conclusion Non communicable diseases are more and more prevalent in developing countries where they double the burden of infective diseases. If the present trend is maintained, the health systems in low-and middle-income countries will be unable to support the burden of disease. Prominent causes for heart disease, diabetes, cancer and pulmonary diseases can be prevented but urgent (preventive) actions are needed and efficient strategies should deal seriously with risk factors like smoking, alcohol, physical inactivity and western diet.
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              The UKPDS risk engine: a model for the risk of coronary heart disease in Type II diabetes (UKPDS 56).

              R. Stevens, V. Kothari, A. I. Adler … (2001)
              A definitive model for predicting absolute risk of coronary heart disease (CHD) in male and female people with Type II diabetes is not yet available. This paper provides an equation for estimating the risk of new CHD events in people with Type II diabetes, based on data from 4540 U.K. Prospective Diabetes Study male and female patients. Unlike previously published risk equations, the model is diabetes-specific and incorporates glycaemia, systolic blood pressure and lipid levels as risk factors, in addition to age, sex, ethnic group, smoking status and time since diagnosis of diabetes. All variables included in the final model were statistically significant (P<0.001, except smoking for which P=0.0013) in likelihood ratio testing. This model provides the estimates of CHD risk required by current guidelines for the primary prevention of CHD in Type II diabetes.
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                Author and article information

                Journal
                Journal ID (nlm-ta): Biomed Eng Online
                Title: BioMedical Engineering OnLine
                Publisher: BioMed Central (London )
                ISSN (Electronic): 1475-925X
                Publication date Collection: 2006
                Publication date (Electronic): 29 June 2006
                Volume: 5
                Page: 43
                Affiliations
                [1 ]Department of Mathematics Faculty of Sciences, Oujda, Morocco
                Article
                Publisher ID: 1475-925X-5-43
                DOI: 10.1186/1475-925X-5-43
                PMC ID: 1553453
                PubMed ID: 16808835
                SO-VID: 3dafa27c-9736-437d-b197-5226b5d52537
                Copyright © Copyright © 2006 Boutayeb and Chetouani; licensee BioMed Central Ltd.
                License:

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                Date received : 8 May 2006
                Date accepted : 29 June 2006
                Categories
                Subject: Review

                ScienceOpen disciplines: Biomedical engineering
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                ScienceOpen disciplines: Biomedical engineering

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