Displaying similar documents to “Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions”

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

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2006)

Applications of Mathematics

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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...

On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks

Ctirad Matonoha, Štěpán Papáček, Volodymyr Lynnyk (2022)

Applications of Mathematics

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We develop and test a relatively simple enhancement of the classical model reduction method applied to a class of chemical networks with mass conservation properties. Both the methods, being (i) the standard quasi-steady-state approximation method, and (ii) the novel so-called delayed quasi-steady-state approximation method, firstly proposed by Vejchodský (2014), are extensively presented. Both theoretical and numerical issues related to the setting of delays are discussed. Namely, for...

An epidemic model with a time delay in transmission

Q. J. A. Khan, E. V. Krishnan (2003)

Applications of Mathematics

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We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.