Mathematical modeling and qualitative analysis of insulin therapies.
Several insulin therapies are widely in clinical use with the basic strategy that mimics insulin secretion in a normal glucose-insulin endocrine metabolic regulatory system. In this paper, we model the insulin therapies using a delay differential equation model. We study the dynamics of the model both qualitatively and quantitatively. The analytical results show the existence and uniqueness of a stable periodic solution that corresponds to ultradian insulin secretion oscillations. Numerically we simulate the insulin administration based on our model. The numerical simulation results are in agreement with findings of clinical studies.
Wang
Haiyan
H
Department of Mathematical Sciences and Applied Computing, Arizona State University, Phoenix, AZ 85069-7100, USA. wangh@asu.edu
Li
Jiaxu
J
Kuang
Yang
Y
D000204:Activity Cycles; D001786:Blood Glucose / Q000378:metabolism; D003922:Diabetes Mellitus, Type 1 / Q000097:blood / Q000188:drug therapy / Q000503:physiopathology; D006801:Humans; D007328:Insulin / Q000008:administration & dosage* / Q000378:metabolism; D007332:Insulin Infusion Systems / Q000706:statistics & numerical data*; D000078790:Insulin Secretion; D008433:Mathematics; D008954:Models, Biological
D001786:Blood Glucose; D007328:Insulin