An Approximate Solution for Glucose Model via Parameterization Method in Optimal Control Problems

Journal of Chemical Health Risks

دوره 11، شماره 3، آذر 2021، صفحه 291-298   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.22034/jchr.2021.1914210.1218

نویسندگان

Mohammad Gholami baladezaei¹؛ Morteza Gachpazan^{* 1}؛ Saedeh Foadian²؛ Hosein Mohammad-Pour Kargar³

¹Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

²Department of Applied Mathematics, Islamic Azad University, Damghan Branch, Damghan, Iran

³Department of Biology, Islamic Azad University, Damghan Branch, Damghan, Iran

چکیده

Glucose tolerance test is advised to detection of pre-diabetics and mild diabetics in the medical practice. Several mathematical models such as glucose model, were proposed for mimicking the blood glucose-insulin interaction. To predict accurate insulin requirement for each glucose concentration, we need to solve optimal control problems. In this model, constraints are linear and nonlinear forms of cost function. Although ordinary methods can be used in glucose model, but non-negative natures of medical variables made them difficult to use. To finding a new approximate solution of glucose model, parameterization method with non-negative coefficients in polynomial was used. In this state parameterization method, we use polynomials that ensure that the control variable is non-negative in this model. And increases the time for the model solution to be non-negative compared to conventional methods. The simplicity, lower requirement for mathematical calculations and more compatibility with variables are positive aspects of our parameterization method.

کلیدواژه‌ها

Glucose model؛ State parameterization؛ Optimal control problems (OCP)؛ Approximation 2010 MSC: 49J15؛ 49J20

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