A blow-up mechanism for a chemotaxis model
A mathematical model of combined drug therapy of HIV infection.
A note on the OD-QSSA and Bohl-Marek methods applied to a class of mathematical models
The complex (bio)chemical reaction systems, frequently possess fast/slow phenomena, represent both difficulties and challenges for numerical simulation. We develop and test an enhancement of the classical QSSA (quasi-steady-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 Vejchodský (2014) and further developed by Papáček (2021) and Matonoha (2022), is...
A periodic model for the dynamics of cell volume
We prove the existence and uniqueness of a positive periodic solution for a model describing the dynamics of cell volume flux, introduced by Julio A. Hernández [Bull. Math. Biol. 69 (2007), 1631-1648]. We also show that the periodic solution is a global attractor. Our results confirm the conjectures made in an interesting recent book of P. J. Torres [Atlantis Press, 2015].
A semilinear parabolic boundary-value problem in bioreactors theory.
A study of the temperature dependence of bienzyme systems and enzymatic chains.
A Time-dependent Biochemical System
Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions
Quasi-steady state assumptions are often used to simplify complex systems of ordinary differential equations in the modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original system and to have a small number of variables. This enables to use the stability and bifurcation analysis to reveal a deeper structure in the dynamics of the original system. This contribution shows that introducing delays to quasi-steady state assumptions...
Atherosclerosis Initiation Modeled as an Inflammatory Process
In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL concentrations...