A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation

Banibrata Mukhopadhyay; Rakhi Bhattacharyya

Applications of Mathematics (2006)

  • Volume: 51, Issue: 6, page 549-564
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Mukhopadhyay, Banibrata, and Bhattacharyya, Rakhi. "A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation." Applications of Mathematics 51.6 (2006): 549-564. <http://eudml.org/doc/33266>.

@article{Mukhopadhyay2006,
abstract = {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.},
author = {Mukhopadhyay, Banibrata, Bhattacharyya, Rakhi},
journal = {Applications of Mathematics},
keywords = {feedback mechanism; distributed time delay; discrete time delay; asymptotic stability; catatonic schizophrenia; hormone therapy; feedback mechanism; distributed time delay; discrete time delay; asymptotic stability; catatonic schizophrenia},
language = {eng},
number = {6},
pages = {549-564},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation},
url = {http://eudml.org/doc/33266},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Mukhopadhyay, Banibrata
AU - Bhattacharyya, Rakhi
TI - A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 6
SP - 549
EP - 564
AB - 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.
LA - eng
KW - feedback mechanism; distributed time delay; discrete time delay; asymptotic stability; catatonic schizophrenia; hormone therapy; feedback mechanism; distributed time delay; discrete time delay; asymptotic stability; catatonic schizophrenia
UR - http://eudml.org/doc/33266
ER -

References

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