Geodesic
A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation
Applications of Mathematics, Tome 51 (2006) no. 6, pp. 549-564 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability and bifurcation behavior. Clinical treatment of periodic catatonic schizophrenia is discussed in presence of transportation delays. Numerical simulations are presented to support analytic results.
In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability and bifurcation behavior. Clinical treatment of periodic catatonic schizophrenia is discussed in presence of transportation delays. Numerical simulations are presented to support analytic results.
DOI : 10.1007/s10492-006-0020-z
Classification : 34K18, 34K20, 34K60, 92C30, 92C50
Keywords: feedback mechanism; distributed time delay; discrete time delay; asymptotic stability; catatonic schizophrenia; hormone therapy 
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     year = {2006},
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Mukhopadhyay, Banibrata; Bhattacharyya, Rakhi. A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation. Applications of Mathematics, Tome 51 (2006) no. 6, pp. 549-564. doi: 10.1007/s10492-006-0020-z

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