Publications

Marek Bodnar

Number of publications: 105

2026

• Agnieszka Kowalewska, Joanna Krawczyk, Marek Bodnar , María Vela-Pérez, Exploring the impact of healthcare capacity and time delays in SIR epidemic model, Mathematics and Computers in Simulation, 241 2026, p. 771-782. See in PBN

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
• Magdalena Szafrańska-Łęczycka, Zuzanna Szymańska , Monika Piotrowska , Marek Bodnar , Urszula Foryś , CAR-T cell therapy for glioblastoma: insight from mathematical modeling, Frontiers in Immunology, 16 2025, p. 1-19. See in PBN
• Emad Attia, Kalina Nec, Marek Bodnar , Urszula Foryś , Distributed delays in a simple neuronal population model of decision-making, Discrete and Continuous Dynamical Systems - Series B, 30 (11) 2025, p. 4136-4161. 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
• Magdalena Szafrańska-Łęczycka, Marek Bodnar , Monika Piotrowska , Mateusz Krukowski, Juan Belmonte-Beitia, Urszula Foryś , Influence of time delay on the dynamics of a mathematical model of CAR-T cell therapy with logistic tumor growth, Discrete and Continuous Dynamical Systems - Series B, 30 2025, p. 4498–4515. 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

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
• Joanna Krawczyk, Agnieszka Kowalewska, Marek Bodnar , Some remarks on a mathematical model of COVID-19 pandemic with health care capacity, Mathematica Applicanda, 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

• Jan Poleszczuk, Urszula Foryś , Marek Bodnar , Monika Piotrowska , Cancer as a Killer Tsunami, The Art of Theoretical Biology, 2020, p. 62-63. See in PBN
• 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, 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, 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, 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, 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, Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine : Jugowice, September 11–15, 2016, 2017. 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
• 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, 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, Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine : Jugowice, September 11–15, 2016, 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, Metody matematyczne w zastosowaniach tom 3, 2015, p. 187-209. 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, Proceedings of the XIX National Conference Applications of Mathematics in Biology and Medicine, 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, 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 , Urszula 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