A note on the OD-QSSA and Bohl-Marek methods applied to a class of mathematical models

Authors: Štěpán Papáček, Ctirad Matonoha
Publication year: 2025
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Programs and Algorithms of Numerical Mathematics 22 : Proceedings of Seminar
Bibliographic citation: PAPÁČEK, Štěpán, MATONOHA, Ctirad. A note on the OD-QSSA and Bohl-Marek methods applied to a class of mathematical models. In: CHLEBOUN, J., PAPEŽ, J., SEGETH, K., ŠÍSTEK, J., VEJCHODSKÝ, T., eds. Programs and Algorithms of Numerical Mathematics 22 : Proceedings of Seminar. Praha: Matematicky ustav AV CR, v. v. i., 2025, S. 127-136. ISBN 978-80-85823-74-5
Dostupné z: doi:10.21136/panm.2024.12.
DOI: 10.21136/panm.2024.12
ID: 635707

Abstract

The complex (bio)chemical reaction systems, frequently possess fast/slow phenomena, represent both diffculties and challenges for numerical simulation. We develop and test an enhancement of the classical QSSA (quasisteady-state approximation) model reduction method applied to a system of chemical reactions. The novel model reduction method, the so-called delayed quasi-steady-state approximation method, proposed by Vejchodsky (2014) and further developed by Papacek (2021) and Matonoha (2022), is extensively presented on a case study based on Michaelis-Menten enzymatic reaction completed with the substrate transport. Eventually, an innovative approach called the Bohl-Marek method is shown on the same numerical example.