Differential and Integral Equations

Monotonicity of time to peak response with respect to drug dose for turnover models

Hoai-Minh Nguyen and Lambertus A. Peletier

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In this paper we analyze the monotonicity of the time to peak response $T_{\rm max}$ with respect to the drug dose $D$ for the four different turnover models I - IV, as introduced by Dayneka et al. [2]. We do this for the situation when the drug is supplied through an initial bolus, and eliminated according to a single exponential function and stimulation or inhibition takes place through a Hill function. We show that in Models I and III, in which the drug impacts the production term, the function $T_{\rm max}(D)$ is increasing for all values of the system- and the drug parameters. For Model II (inhibition of the loss term) the situation is more delicate. Here we prove monotonicity of $T_{\rm max}(D)$ for a substantial range of values of the rate- and drug constants, but leave the question of monotonicity open for some values. Finally, in Model IV (stimulation of the loss term) the function $T_{\rm max}(D)$ is known not to be monotone for some values of the rate constants and $I_{\rm max}$ [12].

Article information

Differential Integral Equations Volume 22, Number 1/2 (2009), 1-26.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34C60: Qualitative investigation and simulation of models 392C45


Nguyen, Hoai-Minh; Peletier, Lambertus A. Monotonicity of time to peak response with respect to drug dose for turnover models. Differential Integral Equations 22 (2009), no. 1/2, 1--26. https://projecteuclid.org/euclid.die/1356038551.

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