Publications

Marek Bodnar

Number of publications: 105

2025

• Marek Bodnar , M. Vela-Pérez, A. Tryniecka-Maciążek, Analyzing the impact of proliferation and treatment parameters on low-grade glioma growth using mathematical models, Physica D: Nonlinear Phenomena, 472 2025, p. 134491. See in PBN
• Marek Bodnar , Monika Piotrowska , Mariusz Bodzioch, Juan Belmonte-Beitia, Urszula Foryś , Dual CAR-T cell therapy for glioblastoma: strategies to cure tumour diseases based on a mathematical model, Nonlinear Dynamics, 113 (2) 2025, p. 1637-1666. See in PBN

2023

• Agnieszka Bartłomiejczyk, Marek Bodnar , Hopf bifurcation in time‐delayed gene expression model with dimers, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 46 (11) 2023, p. 12087 - 12111. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Mariusz Bodzioch, Jose A. Romero-Rosales, Juan Belmonte Beitia, On the Analysis of a Mathematical Model of CAR–T Cell Therapy for Glioblastoma: Insights from a Mathematical Model, International Journal of Applied Mathematics and Computer Science, 33 (3) 2023, p. 379 - 394. See in PBN
• Agnieszka Bartłomiejczyk, Marek Bodnar , Magdalena U. Bogdańska, Monika Piotrowska , Travelling Waves for Low–Grade Glioma Growth and Response to A Chemotherapy Model, International Journal of Applied Mathematics and Computer Science, 33 (4) 2023, p. 569 - 581. See in PBN

2022

• Urszula Foryś , Marek Bodnar , Modeling of drug resistance: Comparison of two hypotheses for slowly proliferating tumors on the example of low‐grade gliomas, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 45 (8) 2022, p. 4161-4184. See in PBN
• Marek Bodnar , Joanna Krawczyk, Agnieszka Kowalewska, Some remarks on a mathematical model of COVID-19 pandemic with health care capacity, Mathematica Applicanda (Matematyka Stosowana). Annales Societatis Mathematicae Polonae Series III, 50 (1) 2022, p. 23-42. See in PBN

2021

• Jacek Miękisz , Marek Bodnar , Evolution of populations with strategy-dependent time delays, PHYSICAL REVIEW E, 103 (1) 2021, p. 12414:1-10. See in PBN

2020

• Agnieszka Bartłomiejczyk, Marek Bodnar , Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein, Communications in Nonlinear Science and Numerical Simulation, 84 2020, p. 105166. See in PBN
• Raffi Vardanyan, Marek Bodnar , Jacek Miękisz , Three-Player Games with Strategy-Dependent Time Delays, Dynamic Games and Applications, 10 2020, p. 664–675. See in PBN

2019

• Maja Szlenk , Marek Bodnar , Analysis of delay differential equations modelling tumor growth with angiogenesis, Mathematica Applicanda (Matematyka Stosowana). Annales Societatis Mathematicae Polonae Series III, 47 (2) 2019, p. 207-2017. See in PBN
• Marek Bodnar , Distributed delays in Hes1 gene expression model, Discrete and Continuous Dynamical Systems - Series B, 24 (5) 2019, p. 2125-2147. See in PBN
• Marek Bodnar , Magdalena Bogdańska, Monika Piotrowska , Mathematical Analysis of a Generalised Model of Chemotherapy for Low Grade Gliomas, Discrete and Continuous Dynamical Systems - Series B, 24 (5) 2019, p. 2149-2167. See in PBN
• Marek Bodnar , María Vela Pérez, Mathematical and numerical analysis of low-grade gliomas model and the effects of chemotherapy, Communications in Nonlinear Science and Numerical Simulation, 72 2019, p. 552--564. See in PBN
• Marek Bodnar , Urszula Foryś , Some remarks on modelling of drug resistance for low grade gliomas, Mathematica Applicanda (Matematyka Stosowana). Annales Societatis Mathematicae Polonae Series III, 47 (2) 2019, p. 151-164. See in PBN
• Marek Bodnar , Julia Grajek, The NF-κ B network as an example of a regulatory network with a positive and negative feedback loop, Mathematica Applicanda (Matematyka Stosowana). Annales Societatis Mathematicae Polonae Series III, 47 (2) 2019, p. 165-176. See in PBN

2018

• Monika Piotrowska , Marek Bodnar , Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model, Communications in Nonlinear Science and Numerical Simulation, 54 2018, p. 389-415. See in PBN
• Monika Piotrowska , Agnieszka Bartłomiejczyk, Marek Bodnar , Mathematical analysis of a generalised p53-Mdm2 protein gene expression model, Applied Mathematics and Computation, 328 2018, p. 26 - 44. See in PBN
• Marek Bodnar , Adam Korpusik, On the nonlocal discretization of the simplified Anderson-May model of viral infection, Mathematica Applicanda (Matematyka Stosowana). Annales Societatis Mathematicae Polonae Series III, 46 (1) 2018, p. 109-116. See in PBN

2017

• Magdalena Bogdańska, Marek Bodnar , Monika Piotrowska , Michael Murek, Philippe Schucht, Jürgen Beck, Alicia Martínez-González, Víctor M. Pérez-García, A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications, PLoS ONE, 2017, p. 1-24. See in PBN
• Magdalena Bogdańska, Marek Bodnar , Juan Belmonte-Beitia, Michael Murek, Philippe Schucht, Juergen Beck, Victor Manuel Pérez-García, A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications, Mathematical Biosciences, 288 2017, p. 1-13. See in PBN
• Agnieszka Bartłomiejczyk, Marek Bodnar , Analysis of a gene expression model, XXIII Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Jugowice, Poland, 11 September 2017 - 15 September 2017. See in PBN
• Emad Attia, Marek Bodnar , Urszula Foryś , Angiogenesis model with Erlang distributed delays, Mathematical Biosciences and Engineering, 14 (1) 2017, p. 1-15. See in PBN
• Magdalena Bogdańska, Marek Bodnar , Monika Piotrowska , Mathematical analysis of the model describing chemotherapy of brain tumours, XXIII National Conference on Applications of Mathematics in Biology and Medicine, Jugowice, Poland, 11 September 2017 - 15 September 2017. See in PBN
• Marek Bodnar , Natalia Okińczyc, Maria Vela-Perez, Mathematical model for path selection by ants between nest and food source, Mathematical Biosciences, 285 2017, p. 14-24. See in PBN
• Magdalena Bogdańska, Marek Bodnar , Monika Piotrowska , Michael Murek, Philpp Schucht, Juergen Beck, Alicia Martınez-Gonzalez, Victor Manuel Perez-Garcia, P10.02 Malignant transformation of low-grade gliomas. Prognostic implications from mathematical model, Neuro-Oncology, 19 (suppl_3) 2017, p. iii85. See in PBN
• Marek Bodnar , Urszula Foryś , Two models of drug resistance for low grade gliomas: comparison of the models dynamics, 2017. See in PBN

2016

• Marek Bodnar , Urszula Foryś , Yuri Kogan, Asymptotic dynamics of some t-periodic one-dimensional model with application to prostate cancer immunotherapy, Journal of Mathematical Biology, 2016. See in PBN
• Marek Bodnar , Urszula Foryś , Delays do not cause oscillations in a corrected model of humoral mediated immune response, Applied Mathematics and Computation, 2016. See in PBN
• Marek Bodnar , Pilar Guerro, Ruben Perez-Carrasco, Monika Piotrowska , Deterministic and Stochastic Study for a Microscopic Angiogenesis Model: Applications to the Lewis Lung Carcinoma, PLoS ONE, 2016. See in PBN
• Marek Bodnar , Monika Piotrowska , Magdalena Bogdańska, Mathematical model of malignant transformation of gliomas, XXII Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Sandomierz, Poland, 5 September 2016 - 9 September 2016. See in PBN
• Marek Bodnar , Monika Piotrowska , Stability analysis of the family of tumour angiogenesis models with distributed time delays, Communications in Nonlinear Science and Numerical Simulation, 2016. See in PBN
• Marek Bodnar , Monika Piotrowska , Tumour-immune system interaction model with Erlang distributed delays, 16th International Conference Computational and Mathematical Methods in Science and Engineering, Rota, Cadiz, Spain, 4 July 2016 - 8 July 2016. See in PBN

2015

• Marek Bodnar , Monika Piotrowska , Agnieszka Bartłomiejczyk, Analysis of the p53 protein gene expression model, XXI Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Regietów, Poland, 22 September 2015 - 26 September 2015. See in PBN
• Emad Attia, Marek Bodnar , Urszula Foryś , Angiogenesis model with Erlang distributed delay in vessels formation, XXI Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Regietów, Poland, 22 September 2015 - 26 September 2015. See in PBN
• Marek Bodnar , Fryderyk Mirota, Agnieszka Wiszniewska-Matyszkiel , Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis, Dynamic Games and Applications, 2015. See in PBN
• Marek Bodnar , General model of a cascade of reactions with time delays: global stability analysis, Journal of Differential Equations, 2015. See in PBN
• Marek Bodnar , Monika Piotrowska , Magdalena Bogdańska, Modeling chemotherapy for low grade gliomas, XXI Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Regietów, Poland, 22 September 2015 - 26 September 2015. See in PBN
• Paulina Rowińska, Marek Bodnar , Periodic solutions in a mathematical model of the temperature sex determination with periodic floods, XXI Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Regietów, Poland, 22 September 2015 - 26 September 2015. See in PBN
• Marek Bodnar , Monika Piotrowska , Różne oblicza równania logistycznego, 2015. See in PBN

2014

• Marek Bodnar , Monika Piotrowska , Logistic Equation with Treatment Function and Discrete Delays, Mathematical Population Studies, 2014. See in PBN
• Marek Bodnar , Matematyka małżeństwa, DELTA, 8 (483) 2014, p. 9-11. See in PBN
• Jurgen Beck, Juan Belmonte-Beitia, Marek Bodnar , Magdalena Bogdańska, Michael Murek, Victor M. Perez-Garcia, Philippe Schucht, Mathematical model suggests a way to assess low grade glioma malignancy, XX Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Łochów, Poland, 23 September 2014 - 27 September 2014. See in PBN
• Marek Bodnar , Modele reakcji biochemicznych z opóźnionym argumentem: nieujemność rozwiązań i stabilność oscylacji, 2014. See in PBN
• Agnieszka Bartłomiejczyk, Marek Bodnar , Modelling gene expression of a self-regulating protein, XX Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Łochów, Poland, 23 September 2014 - 27 September 2014. See in PBN
• Marek Bodnar , Urszula Foryś , Beata Jackowska-Zduniak, Modified van der Pol equation with delay in a description of the heart action, International Journal of Applied Mathematics and Computer Science, 2014. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Proceedings of the Twentieth National Conference on Applications of Mathematics in Biology and Medicine - Łochów 23-27 September 2014, 2014. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Tractable Model of Malignant Gliomas Immunotherapy with Discrete Time Delays, Mathematical Population Studies, 2014. See in PBN

2013

• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Jan Poleszczuk, A simple model of carcinogenic mutations with time delay and diffusion, Mathematical Biosciences and Engineering, 2013. See in PBN
• Marek Bodnar , Beata Jackowska-Zduniak, A ventricular tachycardia and av nodal double response tachycardia in a modified van der Pol equation, Proceedings of the Nineteenth National Conference Applications of Mathematics in Biology and Medicine, , 16 - 20 September 2013, Jastrzębia Góra, Poland, 16 September 2013 - 20 September 2013. See in PBN
• Marek Bodnar , Beata Zduniak, A ventricular tachycardia and AV nodal double response tachycardia in modified van der Pol equation, 2013. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Existence and stability of oscillating solutions for a class of delay differential equations, Nonlinear Analysis: Real World Applications, 2013. See in PBN
• Marek Bodnar , Juan Velazquez, Friction dominated dynamics of interacting particles locally close to a crystallographic lattice, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 36 (10) 2013, p. 1206-1228. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Gompertz model with delays and treatment: mathematical analysis, Mathematical Biosciences and Engineering, 2013. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Logistic type equations with discrete delay and quasi-periodic suppression rate, Applied Mathematics Letters, 2013. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Jan Poleszczuk, Mathematical modelling of immune reaction against gliomas: Sensitivity analysis and influence of delays, Nonlinear Analysis: Real World Applications, 2013. See in PBN
• Marek Bodnar , Urszula Foryś , Ewa Nizińska, Monika Piotrowska , Model of tumour angiogenesis - analysis of stability with respect to delays, Mathematical Biosciences and Engineering, 2013. See in PBN

2012

• Marek Bodnar , J. Chrobak, H. Herrero, About a generalized model of lymphoma, Journal of Mathematical Analysis and Applications, 2012. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Jan Poleszczuk, Carcinogenesis, mutations, delay and diffusion, XVIII Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Krynica Morska, Poland, 23 September 2012 - 27 September 2012. See in PBN
• Natalia Bielczyk, Marek Bodnar , Urszula Foryś , Delay can stabilize: Love affairs dynamics, Applied Mathematics and Computation, 2012. See in PBN
• Agnieszka Bartłomiejczyk, Marek Bodnar , Stability of delay induced oscillations in gene expression of Hes1 protein model, Nonlinear Analysis: Real World Applications, 2012. See in PBN

2011

• Marek Bodnar , Urszula Foryś , Jan Poleszczuk, Analysis of biochemical reactions models with delays, Journal of Mathematical Analysis and Applications, 2011. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Delayed logistic equation with treatment function, XVII Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Zakopane - Kościelisko, Poland, 1 September 2011 - 6 September 2011. See in PBN
• Marek Bodnar , Urszula Foryś , Jan Poleszczuk, Negativity of delayed induced oscillations in a simple linear DDE, Applied Mathematics Letters, 2011. See in PBN
• Marek Bodnar , Urszula Foryś , Jan Poleszczuk, New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model, Mathematical Biosciences and Engineering, 2011. See in PBN
• Marek Bodnar , Urszula Foryś , Monika Piotrowska , Jan Poleszczuk, Proceedings of the XVII National Conference on Application of Mathematics in Biology and Medicine, 2011. See in PBN
• Marek Bodnar , Urszula Foryś , Jacek Miękisz , Jan Poleszczuk, Stochastic Models of Gene Expression with Delayed Degradation, Bulletin of Mathematical Biology, 2011. See in PBN

2010

• Natalia Bielczyk, Marek Bodnar , Urszula Foryś , Jan Poleszczuk, Delay can stabilise: love affairs dynamics, XVI Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Krynica Morska, Poland, 14 September 2010 - 18 September 2010. See in PBN
• Agnieszka Bartłomiejczyk, Marek Bodnar , Delay induced oscillations in gene expression of Hes1 protein model, XVI Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Krynica, Poland, 14 September 2010 - 18 September 2010. See in PBN
• Marek Bodnar , Monika Piotrowska , O równaniach różniczkowych z opóźnieniem - teoria i zastosowania, Mathematica Applicanda (Matematyka Stosowana). Annales Societatis Mathematicae Polonae Series III, 2010. See in PBN
• Marek Bodnar , Ekaterina Kutafina, Mariusz Ziółko, Proceedings of the XVI National Conference on Application of Mathematics in Biology and Medicine, 2010. See in PBN

2009

• Marek Bodnar , Urszula Foryś , A model of immune system with time-dependent immune reactivity, Nonlinear Analysis, Theory, Methods and Applications, 2009. See in PBN
• Marek Bodnar , Urszula Foryś , Angiogenesis model with carrying capacity depending on vessel density, Journal of Biological Systems, 2009. See in PBN
• Marek Bodnar , Urszula Foryś , Influence of time delays on the hahnfeldt et al. angiogenesis model dynamics, Applicationes Mathematicae, 2009. See in PBN
• Marek Bodnar , Urszula Foryś , Zuzanna Szymańska , Model of AIDS-related tumour with time delay, Applicationes Mathematicae, 2009. See in PBN
• Marek Bodnar , Urszula Foryś , Modelling of an immune reaction under the influence of interleukin, XV Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Szczyrk, Poland, 15 September 2009 - 19 September 2009. See in PBN

2008

• Marek Bodnar , Urszula Foryś , Global stability and Hopf bifurcation for a general class of delay differential equations, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2008. See in PBN
• Marek Bodnar , Urszula Foryś , Zuzanna Szymańska , Model of AIDS-related tumour with time delay, XIV Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Leszno k. Warszawy, Poland, 16 September 2008 - 20 September 2008. See in PBN
• Marek Bodnar , Urszula Foryś , Proceedings of the XIV National Conference on Application of Mathematics in Biology and Medicine, 2008. See in PBN
• Marek Bodnar , Zbiór zadań z matematyki dla biologów, 2008. See in PBN

2007

• Marek Bodnar , Urszula Foryś , Hahnfeldt angiogenesis model with time delays, XIII Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Serpelice nad Bugiem, Poland, 18 September 2007 - 22 September 2007. See in PBN
• Marek Bodnar , Matematyka a krokodyle, proporcja płci i przetrwania gatunku, DELTA, 2007. See in PBN
• Marek Bodnar , Urszula Foryś , Three types of simple DDE's describing tumor growth, Journal of Biological Systems, 2007. See in PBN

2006

• Marek Bodnar , Urszula Foryś , A model of immune system with time-depended immune reactivity, 2006. See in PBN
• Marek Bodnar , Juan Jose Lopez Velazquez, An integro-differential equation arising as a limit of individual cell-based models, Journal of Differential Equations, 2006. See in PBN

2005

• Marek Bodnar , Juna Jose Lopez Velazquez, Derivation of macroscopic equations for individual cell-based models: A formal approach, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2005. See in PBN
• Marek Bodnar , Urszula Foryś , Time delay in necrotic core formation, Mathematical Biosciences and Engineering, 2005. See in PBN

2004

• Marek Bodnar , On the differences and similarities of the first order delay and ordinary differential equations, Journal of Mathematical Analysis and Applications, 2004. See in PBN
• Marek Bodnar , Urszula Foryś , Time delay in a model of necrotic core formation, X Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Jodłowy Dwór, Poland, 21 September 2004 - 25 September 2004. See in PBN

2003

• Marek Bodnar , Urszula Foryś , Time delays in proliferation process for solid avascular tumour, MATHEMATICAL AND COMPUTER MODELLING, 2003. See in PBN
• Marek Bodnar , U. Foryś, Time delays in regulatory apoptosis for solid avascular tumour, MATHEMATICAL AND COMPUTER MODELLING, 2003. See in PBN

2002

• Marek Bodnar , Norm conservation for generalized kinetic population models with delay, MATHEMATICAL AND COMPUTER MODELLING, 2002. See in PBN
• Marek Bodnar , On the norm conservation for the generalized kinetic populatuion models with delay., MATHEMATICAL AND COMPUTER MODELLING, 2002. See in PBN

2001

• Marek Bodnar , On some integro-differential models with delay in population dynamics., VII Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Zawoja, Poland, 25 September 2001 - 28 September 2001. See in PBN

2000

• Urszula Foryś , Marek Bodnar , Behaviour of Solutions to Marchuk's Model Depending on a Time Delay, International Journal of Applied Mathematics and Computer Science, 2000. See in PBN
• Marek Bodnar , Urszula Foryś , Periodic dynamics in a model of immune system., Applicationes Mathematicae, 2000. See in PBN
• Marek Bodnar , The nonnegativity of the solutions of delay differential equations., Applied Mathematics Letters, 2000. See in PBN

1999

• Marek Bodnar , Urszula Foryś , Forest-pest interaction dynamics, V Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Ustrzyki Górne, Poland, 14 September 1999 - 17 September 1999. See in PBN

1998

• Marek Bodnar , Urszula Foryś , A model of the immune system with stimulation depending on time, IV Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie, Zwierzyniec, Poland, 15 September 1998 - 18 September 1998. See in PBN

Others

• Marek Bodnar , Beata Zduniak, A ventricular tachycardia and AV nodal double response tachycardia in modified van der Pol equation, Proceedings of the XIX National Conference Applications of Mathematics in Biology and Medicine. See in PBN
• Agnieszka Bartłomiejczyk, Marek Bodnar , Analysis of a gene expression model, Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine : Jugowice, September 11–15, 2016. See in PBN
• Jan Poleszczuk, Urszula Foryś , Marek Bodnar , Monika Piotrowska , Cancer as a Killer Tsunami, The Art of Theoretical Biology, , p. 62-63. See in PBN
• Magdalena Bogdańska, Marek Bodnar , Monika Piotrowska , Mathematical analysis of the model describing chemotherapy of brain tumours, Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine : Jugowice, September 11–15, 2016. See in PBN
• Marek Bodnar , Monika Piotrowska , Różne oblicza równania logistycznego, Metody matematyczne w zastosowaniach tom 3, , p. 187-209. See in PBN
• Marek Bodnar , Urszula Foryś , Two models of drug resistance for low grade gliomas: comparison of the models dynamics, Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine : Jugowice, September 11–15, 2016. See in PBN