Monotonicity of time to peak response with respect to drug dose for turnover models. (English) Zbl 1240.34244

Nguyen, Hoai-Minh; Peletier, Lambertus A.

Differ. Integral Equ. 22, No. 1-2, 1-25 (2009).

The authors analyze four different turnover models for the physiological effect of drugs published by N. L. Dayneka, V. Garg and W. J. Jusko [“Comparison of four basic models of indirect pharmacodynamic responses”, Journal of Pharmacokinetics and Pharmacodynamics 21, No. 4, 457–478, (1993, doi:10.1007/BF01061691)]. The monotonicity of the time to peak response \(T_{\max }\) with respect to the drug dose \(D\) is analysed. The authors consider 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. Monotonicity of \(T_{\max }(D)\) for various ranges of model parameters is proved.

Reviewer: Robert Mařík (Brno)

MSC:

34C60	Qualitative investigation and simulation of ordinary differential equation models
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
92C50	Medical applications (general)

Keywords:

turnover model; peak response; differential equation