Sensitivity analysis and global attractivity of the hpa axis in a depression model
Keywords:
Depression, HPA axis, Mathematical modelling, Sensitivity analysis, Global attractivityAbstract
In this paper, we present mathematical model of depression that related hypothalamic-pituitary-adrenal (HPA) axis. HPA axis is an endocrine responsible for stress management that effects from changing level of hormones in HPA axis. Stress management affects the function of the HPA axis causing abnormal hormone secretion, which results in a tendency to depression. Dynamic of depression model is proposed by analysing positive and bounded solutions, existence of equilibria, local stability and sensitivity analysis of equilibrium point. Results of sensitivity analysis can determine which parameters have the most effect on the behaviour of the system. We also analyse global attractivity for impulsive behaviour of the HPA axis model. Moreover, some numerical results of these models may be more inspiring to treat patients more thoroughly and help to diagnose specific patients for low level of risk for depression.
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