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On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy

Jurjen Duintjer Tebbens, Ctirad Matonoha, Andreas Matthios, Štěpán Papáček (2019)

Applications of Mathematics

A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter...

On solving systems of differential algebraic equations

Marian Kwapisz (1992)

Applications of Mathematics

In the paper the comparison method is used to prove the convergence of the Picard iterations, the Seidel iterations, as well as some modifications of these methods applied to approximate solution of systems of differential algebraic equations. The both linear and nonlinear comparison equations are emloyed.

On systems governed by two alternating vector fields

Alois Klíč, Jan Řeháček (1994)

Applications of Mathematics

We investigate the nonautonomous periodic system of ODE’s of the form x ˙ = v ( x ) + r p ( t ) ( w ( x ) - v ( x ) ) , where r p ( t ) is a 2 p -periodic function defined by r p ( t ) = 0 for t 0 , p , r p ( t ) = 1 for t ( p , 2 p ) and the vector fields v and w are related by an involutive diffeomorphism.

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