SENSITIVITY ANALYSIS AND GLOBAL ATTRACTIVITY OF THE HPA AXIS IN A DEPRESSION MODEL
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.
L. R. Melinda Smith, M.A. and P. Jeanne Segal, â€œDepression symptoms and warning signs.â€ https://www.helpguide.org/ articles/
accessed on 2019-11-14, 2019)
C. E. GalvÃ¡n-Tejada, L. A. Zanella-Calzada,H. Gamboa-Rosales, J. I. GalvÃ¡n-Tejada, N. M. ChÃ¡vez-Lamas, M. Gracia-CortÃ©s, R. Magallanes-Quintanar, J. M. Celaya-Padilla, et al., â€œDepression episodes detection in unipolar and bipolar patients: Amethodology with feature extraction and feature selection with genetic algorithms using activity motion signal as information source,â€ Mobile Information Systems, vol. 2019, 2019.
L. R. Melinda Smith, M.A. andP. Jeanne Segal, â€œDepression symptoms and warning signs.â€ https://www.helpguide.org/articles/
accessed on 2019-11-14, 2019).
M. Andersen, F. Vinther, and J. T. Ottesen, â€œMathematical modeling of the hypothalamicâ€“pituitaryâ€“adrenalgland (hpa) axis, including hippocampal mechanisms,â€Mathematical biosciences, vol. 246, no. 1, pp. 122â€“138,2013.
J. Gudmand-Hoeyer, S. Timmermann, and J. T. Ottesen,â€œPatient-specific modeling of the neuroendocrine hpa axis and its relation to depression: Ultradian and circadianoscillations,â€ Mathematical biosciences, vol. 257,pp. 23â€“32, 2014.
E. O. Bangsgaard and J. T. Ottesen, â€œPatient specific modeling of the hpa axis related to clinical diagnosis of depression,â€ Mathematical biosciences, vol. 287,pp. 24â€“35, 2017.
Wikimedia, â€œNewtonâ€™s method.â€ https://en.wikipedia.org/wiki/
Newtonâ€™s_method, (Last accessed on 2019-05-13, 2019)
P. Holme and N. Masuda, â€œThe basic reproduction number as a predictor for epidemic outbreaks in temporal networks,â€ PloS one, vol. 10, no. 3, p. e0120567, 2015.
P. Van den Driessche and J. Watmough, â€œReproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,â€ Mathematical biosciences, vol. 180, no. 1-2, pp. 29â€“48, 2002.
L. F. Shampine, Numerical solution of ordinary differential equations. Routledge, 2018.
F. Blanchini and S. Miani, Set-theoretic methods in control. Springer, 2008.
X. Niu, T. Zhang, and Z. Teng, â€œThe asymptotic behavior of a non autonomous eco-epidemic model with disease in the prey,â€ Applied Mathematical Modelling, vol. 35, no. 1, pp. 457â€“470, 2011.
Z. Zhang and L. Wang, â€œGlobal attractivity of a positive periodic solution for a non autonomous stage structured population dynamics with time delay and diffusion,â€Journal of mathematical analysis and applications, vol. 319, no. 1, pp. 17â€“33, 2006.
C. C. A.-S. License., â€œUniform continuity.â€ http://mathonline.wikidot
.com/uniform-continuity, (Last accessed on 2019-8-16, 2018).
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