Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Year 2023, Volume: 36 Issue: 4, 1675 - 1691, 01.12.2023

Mehmet Kocabıyık , Mevlüde Yakıt Ongun

https://doi.org/10.35378/gujs.1027381

Cited By: 2

Abstract

Estimating the effects of drugs at different stages is directly proportional to the duration of recovery and the duration of pulling through with the disease. It is very important to estimate the effects of drugs at different stages. For this reason, solving Pharmacokinetic models which investigate these effects are very important. In this study, numerical solutions of one, two, and three-compartment nonlinear Pharmacokinetic models have been studied. Distributed order differential equations have been used for the solution. Numerical solutions have been found with the density function contained in distributed order differential equations and different values of this function. A nonstandard finite difference scheme has been used for numerical solutions. Finally, stability analyses of equilibrium points of the obtained discretized system have also been researched with the help of the Matignon criterion.

Keywords

Pharmacokinetic models, Distributed order differential equations, Stability Analysis, Schur-Cohn criteria, Nonstandard finite difference scheme

Supporting Institution

Scientific and Technological Research Council of Turkey (TUBITAK)

Project Number

2211-E Program

Thanks

One of the authors, Mehmet KOCABIYIK, thanks the Scientific and Technological Research Council of Turkey (TUBITAK) for providing financial and moral support with the 2211-E Program.

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