Stochastic model of drug concentration level during IV-administration

• Autorzy: Dzhalladova Irada , Růžičková Miroslava

Identyfikatory

DOI

10.7494/OpMath.2022.42.6.833

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

IV-administration; deterministic model; stochastic differential equation; mean value; delay differential equation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 6
• Strony: 833--847
• Opis fizyczny: Bibliogr. 13 poz., wykr.

Twórcy

autor

Dzhalladova Irada

• University of Białystok, Faculty of Mathematics, Department of Analysis, K. Ciołkowskiego 1M, 15-245 Białystok, Poland

• https://orcid.org/0000-0003-3158-6844

autor

Růžičková Miroslava

• University of Białystok, Faculty of Mathematics, Department of Analysis, K. Ciołkowskiego 1M, 15-245 Białystok, Poland

• https://orcid.org/0000-0002-7724-763X

Bibliografia

• [1] T.A. Ahmed, Basic Pharmacokinetic Concepts and Some Clinical Applications, Technology & Medicine, 2015.
• [2] T. Buclin, M. Nicod, S. Kellenberger, Pharmacokinetics. UNIL, University of Lausanne, 2009.
• [3] V. Claassen, Neglected factors in pharmacology and neuroscience research, Techniques in the Behavioral and Neural Sciences, vol. 12, Elsevier Science B.V., Amsterdam, 1994.
• [4] J. Diblík, M. Růžičková, Asymptotic behavior of solutions and positive solutions of differential delayed equations, Funct. Differ. Equ. 14 (2007), no. 1, 83–105.
• [5] J. Diblík, I. Dzhalladova, M. Michalková, M. Růžičková, Modeling of applied problems by stochastic systems and their analysis using the moment equations, Adv. Difference Equ. 2013 (2013), Article no. 152.
• [6] J. Diblík, I. Dzhalladova, M. Michalková, M. Růžičková, Moment equations in modeling a stable foreign currency exchange market in conditions of uncertainty, Abstr. Appl. Anal. 2013 (2013), Art. ID 172847.
• [7] I. Dzhalladova, M. Růžičková, Dynamic system with random structure for modeling security and risk management in cyberspace, Opuscula Math. 39 (2019), no. 1, 23–37.
• [8] I. Dzhalladova, M. Růžičková, V. Štoudková Růžičková, Stability of the zero solution of nonlinear differential equations under the influence of white noise, Adv. Difference Equ. 2015 (2015), Article no. 143.
• [9] I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations, Clarendon Press, 1991.
• [10] M.A. Khanday, A. Rafiq, K. Nazir, Mathematical models for drug diffusion through the compartments of blood and tissue medium, Alexandria Journal of Medicine 53 (2017), 245–249.
• [11] M. Růžičková, J. Diblík, G. Vážanová, Mathematical Modeling of the IV-administered Drug Concentration Level, AIP Conference Proceedings 1978, 430011 (2018).
• [12] M. Růžičková, I. Dzhalladova, J. Laitochová, J. Diblík, Solution to a stochastic pursuit model using moment equations, Discrete Contin. Dyn. Syst. Ser. B 23 (2018), 473–485.
• [13] G. Scutt, D. Waxman, Improved estimates of mean pharmacokinetic parameters for increased accuracy in dosing and reduced risk to patients, British Journal of Clinical Pharmacology 87 (2021), no. 9, 3518–3530.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).