Monotonicity of time to peak response with respect to drug dose for turnover models (Q636969)

The authors analyze four different turnover models for the physiological effect of drugs published by \textit{N. L. Dayneka, V. Garg} and \textit{W. J. Jusko} [``Comparison of four basic models of indirect pharmacodynamic responses'', Journal of Pharmacokinetics and Pharmacodynamics 21, No. 4, 457--478, (1993, \url{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.