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Stochastic model of drug concentration level during IV-administration

Dzhalladova Irada, Růžičková Miroslava

Opuscula Mathematica

2022

Vol. 42, no. 6

833--847

A stochastic model describing the concentration of the drug in the body during its IV-administration is discussed. The paper compares a deterministic model created with certain simplifications with the stochastic model. Fluctuating and irregular patterns of plasma concentrations of some drugs observed during intravenous infusion are explained. An illustrative example is given with certain values of drug infusion rate and drug elimination rate.

Dynamic system with random structure for modeling security and risk management in cyberspace

Dzhalladova Irada, Ruzickova Miroslava

Opuscula Mathematica

2019

Vol. 39, no. 1

23--37

We deal with the investigation of L2-stability of the trivial solution to the system of difference equations with coefficients depending on a semi-Markov chain. In our considerations, random transformations of solutions are assumed. Necessary and sufficient conditions for L2-stability of the trivial solution to such systems are obtained. A method is proposed for constructing Lyapunov functions and the conditions for its existence are justified. The dynamic system and methods discussed in the paper are very well suited for use as models for protecting information in cyberspace.