Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Authors : Mehmet Kocabiyik, Mevlüde Yakit Ongun

Pages : 1675-1691

Doi:10.35378/gujs.1027381

View : 175 | Download : 267

Publication Date : 2023-12-01

Article Type : Research Paper

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