Bifurcation analysis of glucose model with obesity effect

Abstract

Due to the importance of studying the change in glucose which affected by obesity and results in a negative effect on the health of the body, In this paper, glucose metabolism model was developed to study the effect of obesity. The bifurcations and related dynamical behaviors of our model were studied completely . For the non-delay model, it is shown that the model undergoes co-dimension 1 bifurcation such as transcritical, Hopf and saddle bifurcations, and co-dimension 2 bifurcation such as generated hopf, zero-hopf and cusp bifurcations. On the other hand, we consider there is a lag for responding of Insulin sensitivity under obesity effect. Therefore, the time delay τ is deemed as an additional factor in the glucose metabolism model. We set the condition for the existence of the delay parameter value for which the model displays a Hopf bifurcation. Finally, numerical simulations are given to support theoretical analysis and also to show the complex dynamical behaviors including families of periodic curves. The described dynamics of this model can obviously illustrate several clinical observations for obesity effect on glucose level, oscillation and disorder, supporting its potential role in control of blood glucose.

Keywords

• Glucose metabolism model
• Obesity
• Time delay