A mathematical model for the burden of diabetes and its complications

Abstract

BackgroundThe incidence and prevalence of diabetes are increasing all over the world. Complications of diabetes constitute a burden for the individuals and the whole society.MethodsIn the present paper, ordinary differential equations and numerical approximations are used to monitor the size of populations of diabetes with and without complications.ResultsDifferent scenarios are discussed according to a set of parameters and the dynamical evolution of the population from the stage of diabetes to the stage of diabetes with complications is clearly illustrated.ConclusionsThe model shows how efficient and cost-effective strategies can be obtained by acting on diabetes incidence and/or controlling the evolution to the stage of complications.

Therapeutic Modelling of Type 1 Diabetes

“…The main objective here is to prescribe a more accurate, but less simple, method of arranging the palatable composition of a diabetic diet. The modified coupled differential equations for the plasma glucose and insulin concentration [1][2][3][4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22], when the normal fasting level of plasma glucose is 70 -120 mg/dl, are given as follows…”

“…Previous models describing the mechanism of glucose metabolism have mostly focused on type 2 diabetes, most notably the classical minimal model for explaining the profile of glucose concentration over time. [4,5] Here we summarize the conclusions of these studies for management of diabetes, and attempt to lay out a framework for further development of these models to include pump therapy. These models are often formulated as a system of differential equations that describes the profile of insulin release and the dynamics of glucose concentration over specified period of time.…”

Burden of Diabetes Type 2 Through Modelling and Simulation

“…The literature dealing with different aspects of diabetes has become enormous and very heterogeneous even in the case when searching is limited to mathematical modelling and simulation processes of this disease. Some of them are describing glucose-insulin dynamics Makroglou et al, 2006;Shianga & Kandeelc 2010), some represent epidemiological descriptions of this non communicable disease (Boutayeb et al, 2004;Atanasijević-Kunc et al, 2008b), while others describe disease development (Eddy & Schlessinger, 2003a;2003b;Kristöfel, et al, 2007) or the relations to risk factors which are in correlation with diabetes development (Brock et al, 2009;MMWR 2004;Atanasijević-Kunc et al, 2008c). Diabetes can represent by itself or even more intense in combination with other possible chronic diseases (dislipidemia, hypertension) or life style (smoking, alcohol consumption, inactivity) the risk for developing different cardiovascular diseases (Levenson et al, 2002;Atanasijević-Kunc et al, 2008c;.…”

“…Diabetes can represent by itself or even more intense in combination with other possible chronic diseases (dislipidemia, hypertension) or life style (smoking, alcohol consumption, inactivity) the risk for developing different cardiovascular diseases (Levenson et al, 2002;Atanasijević-Kunc et al, 2008c;. Additional aspect, important for modelling structure, can represent social and economical burden of the discussed disease and/or treatment efficacy, which is often interpreted through different pharmacoeconomical studies (Boutayeb et al, 2004;Tarride et al, 2010;Arnold, 2010;Atanasijević-Kunc et al, 2011), where cost-effectiveness analysis and cost -utility analysis provide a basic comparison of different treatment policies or drug efficacy. All mentioned situations can be interpreted as open or closed -loop problems (Atanasijević- Kunc et al, 2008c;Bellazzi, 2001;Lam, 2002;Makroglou, 2006), where especially in the second case the analysis should take into account stability and sensitivity of system behaviour.…”

“…1 (Boutayeb et al, 2004). Input signal u(t) represents the incidence of D2, while C(t) and D(t) are the numbers of D2 patients with and without complications, respectively.…”