16 citations · 42 across the 5 of their papers we have counts for
5 papers
Evolution of populations with strategy-dependent time delays
Jacek Miȩkisz, Marek Bodnar
We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we rep…
Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein
Agnieszka Bartłomiejczyk, Marek Bodnar
We analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer fo…
A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications
Magdalena U. Bogdańska, Marek Bodnar, Juan Belmonte-Beitia +4
Low grade gliomas (LGGs) are infiltrative and incurable primary brain tumours with typically slow evolution. These tumours usually occur in young and otherwise healthy patients, br…
Analysis of the family of angiogenesis models with distributed time delays
Marek Bodnar, Monika J. Piotrowska
In the presented paper a family of angiogenesis models, that is a generalisation of Hahnfeldt et al. model is proposed. Considered family of models is a system of two differential…
General model of a cascade of reactions with time delays: global stability analysis
Marek Bodnar
The problem considered in this paper consists of a cascade of reactions with discrete as well as distributed delays, which arose in the context of Hes1 gene expression. For the abs…