Ordinary differential equation approximation of gamma distributed delay model

AbstractIn many models of pharmacodynamic systems with delays, a delay of an input is introduced by means of the convolution with the gamma distribution. An approximation of the convolution integral of bound functions based on a system of ordinary differential equations that utilizes properties of the binomial series has been introduced. The approximation converges uniformly on every compact time interval and an estimate of the approximation error has been found\(O\left( {\frac{1}{{N^{\nu } }}} \right)\) where\(N\) is the number of differential equations and\(\nu\) is the shape parameter of the gamma distribution. The accuracy of approximation has been tested on a set of input functions for which the convolution is known explicitly. For tested functions,\(N \ge 20\) has resulted in an  accurate approximation, if\(\nu \ge 1\). However, if\(\nu 100\) might be necessary to achieve acceptable accuracy. Finally, the approximation was applied to estimate parameters for the distributed delay model of chemotherapy-induced myelosuppression from previously published WBC count data in rats treated with 5-fluorouracil.
Source: Journal of Pharmacokinetics and Pharmacodynamics - Category: Drugs & Pharmacology Source Type: research

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