My publications.

2024

1. Dual CAR-T cell therapy for glioblastoma: strategies to cure tumour diseases based on a mathematical model

   Bodnar, Marek, Piotrowska, Monika Joanna, Bodzioch, Mariusz, Belmonte-Beitia, Juan, and Foryś, Urszula

   Nonlinear Dynamics (2024)

   doi:10.1007/s11071-024-10258-x

2023

1. Travelling waves for low–grade glioma growth and response to a chemotherapy model

   Agnieszka Bartłomiejczyk, Marek Bodnar, Bogdańska, Magdalena U., and Piotrowska, Monika J.

   International Journal of Applied Mathematics and Computer Science 33, 369–381, (2023)

   doi:doi:10.34768/amcs-2023-0041
2. On the Analysis of a Mathematical Model of CAR–T Cell Therapy for Glioblastoma: Insights from a Mathematical Model

   Bodnar, Marek, Foryś, Urszula, Piotrowska, Monika J., Bodzioch, Mariusz, Romero-Rosales, Jose A., and Belmonte-Beitia, Juan

   International Journal of Applied Mathematics and Computer Science 33, 379–394, (2023)

   doi:doi:10.34768/amcs-2023-0027
3. Hopf bifurcation in time-delayed gene expression model with dimers

   Bartłomiejczyk, Agnieszka, and Bodnar, Marek

   Mathematical Methods in the Applied Sciences 46, 12087-12111, (2023)

   doi:10.1002/mma.8961

2022

1. Some remarks on a mathematical model of COVID-19 pandemic with health care capacity

   Krawczyk, Joanna, Kowalewska, Agnieszka, and Bodnar, Marek

   Mathematica Applicanda 50, 23–42, (2022)

   doi:10.14708/ma.v50i1.7113
2. Modeling of drug resistance: Comparison of two hypotheses for slowly proliferating tumors on the example of low-grade gliomas

   Bodnar, Marek, and Foryś, Urszula

   Mathematical Methods in the Applied Sciences 45, 4161–4184, (2022)

   doi:10.1002/mma.7893

2021

1. Evolution of populations with strategy-dependent time delays

   Miękisz, Jacek, and Bodnar, Marek

   Physical Review E 103, 012414, (2021)

   doi:10.1103/PhysRevE.103.012414

2020

1. Cancer as a Killer Tsunami

   Poleszczuk, Jan, Forys, Urszula, Bodnar, Marek, and Piotrowska, Monika

   62–63, (2020)

   doi:10.1007/978-3-030-33471-0_31
2. Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein

   Bartłomiejczyk, Agnieszka, and Bodnar, Marek

   Communications in Nonlinear Science and Numerical Simulation 84, 105166, (2020)

   doi:10.1016/j.cnsns.2020.105166
3. Three-Player Games with Strategy-Dependent Time Delays

   Dynamic Games and Applications 664–675, (2020)

   doi:10.1007/s13235-019-00340-0

2019

1. Mathematical and numerical analysis of low-grade gliomas model and the effects of chemotherapy

   Bodnar, Marek, and Vela-Pérez, María

   Communications in Nonlinear Science and Numerical Simulation 72, 552–564, (2019)

   doi:10.1016/j.cnsns.2019.01.015
2. Mathematical analysis of a generalised model of chemotherapy for low grade gliomas

   Bodnar, Marek, Piotrowska, Monika Joanna, and Bogdańska, Magdalena Urszula

   Discrete & Continuous Dynamical Systems - B 24, 2149–2167, (2019)

   doi:10.3934/dcdsb.2019088
3. Distributed delays in Hes1 gene expression model

   Bodnar, Marek

   24, 2125-2147, (2019)

   doi:10.3934/dcdsb.2019087
4. Analysis of delay dierential equations modelling tumor growth with angiogenesis

   Szlenk, Maja, and Bodnar, Marek

   Mathematica Applicanda 47, 207–217, (2019)

   doi:10.14708/ma.v47i2.6493
5. Some remarks on modelling of drug resistance for low grade gliomas

   Foryś, Urszula, and Bodnar, Marek

   Mathematica Applicanda 47, 151–164, (2019)

   doi:10.14708/ma.v47i2.6487
6. The NF-κB network as an example of a regulatory network with a positive and negative feedback loop

   Grajek, Julia, and Bodnar, Marek

   Mathematica Applicanda 47, 165–176, (2019)

   doi:10.14708/ma.v47i2.6490

2018

1. Mathematical analysis of a generalised p53-Mdm2 protein gene expression model

   Piotrowska, Monika J., Bartłomiejczyk, Agnieszka, and Bodnar, Marek

   Applied Mathematics and Computation 328, 26–44, (2018)

   doi:10.1016/j.amc.2018.01.014
2. Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model

   Piotrowska, Monika J., and Bodnar, Marek

   Communications in Nonlinear Science and Numerical Simulation 54, 389–415, (2018)

   doi:10.1016/j.cnsns.2017.06.003
3. On the nonlocal discretization of the simplified Anderson-May model of viral infection

   Korpusik, Adam, and Bodnar, Marek

   Mathematica Applicanda 46, 109–116, (2018)

   doi:10.14708/ma.v46i1.6395

2017

1. A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications

   Bogdańska, Magdalena U., Bodnar, Marek, Belmonte-Beitia, Juan, Murek, Michael, Schucht, Pphilippe, Beck, Jürgen, and Pérez-García, Victor M.

   Math. Biosci. 288, 1–13, (2017)

   doi:10.1016/j.mbs.2017.02.003
2. Mathematical model for path selection by ants between nest and food source

   Bodnar, Marek, Okińczyc, Natalia, and Vela-Pérez, M.

   Mathematical Biosciences 285, 14–24, (2017)

   doi:10.1016/j.mbs.2016.12.002
3. Angiogenesis model with Erlang distributed delays

   Attia, Emad, Bodnar, Marek, and Foryś, Urszula

   Mathematical Biosciences and Engineering 14, 1–15, (2017)

   doi:10.3934/mbe.2017001
4. A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications

   Bogdańska, Magdalena U., Bodnar, Marek, Piotrowska, Monika J., Murek, Michael, Schucht, Philippe, Beck, Jürgen, Martínez-González, Alicia, and Pérez-García, Víctor M.

   PLOS ONE 12, 1–24, (2017)

   doi:10.1371/journal.pone.0179999

2016

1. Delays do not cause oscillations in a corrected model of humoral mediated immune response

   Bodnar, Marek, and Foryś, Urszula

   Applied Mathematics and Computation 289, 7-21, (2016)

   doi:10.1016/j.amc.2016.05.006
2. Stability analysis of the family of tumour angiogenesis models with distributed time delays

   Bodnar, Marek, and Piotrowska, Monika Joanna

   Communications in Nonlinear Science and Numerical Simulation 31, 124-142, (2016)

   doi:10.1016/j.cnsns.2015.08.002
3. Asymptotic dynamics of some t-periodic one-dimensional model with application to prostate cancer immunotherapy

   Foryś, Urszula, Bodnar, Marek, and Kogan, Yuri

   Journal Of Mathematical Biology 73, 867–883, (2016)

   doi:10.1007/s00285-016-0978-4
4. Deterministic and Stochastic Study for a Microscopic Angiogenesis Model: Applications to the Lewis Lung Carcinoma

   Bodnar, Marek, Guerrero, Pilar, Perez-Carrasco, Ruben, and Piotrowska, Monika J.

   PLOS ONE 11, 1-24, (2016)

   doi:10.1371/journal.pone.0155553

2015

1. Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis

   Wiszniewska-Matyszkiel, Agnieszka, Bodnar, Marek, and Mirota, Fryderyk

   Dynamic Games and Applications 5, 568–598, (2015)

   doi:10.1007/s13235-014-0125-z
2. General model of a cascade of reactions with time delays: global stability analysis

   Bodnar, Marek

   Journal of Differential Equations 259, 777–795, (2015)

   doi:10.1016/j.jde.2015.02.024 arXiv

2014

1. A modified van der Pol equation with delay in a description of the heart action

   Zduniak, Beata, Bodnar, Marek, and Foryś, Urszula

   International Journal of Applied Mathematics and Computer Science 24, 853–863, (2014)

   doi:doi:10.2478/amcs-2014-0063
2. Logistic Equation with Treatment Function and Discrete Delays

   Piotrowska, Monika J., and Bodnar, Marek

   Mathematical Population Studies 21, 166-183, (2014)

   doi:10.1080/08898480.2014.921492
3. Tractable Model of Malignant Gliomas Immunotherapy with Discrete Time Delays

   Piotrowska, Monika J., Bodnar, Marek, and Foryś, Urszula

   Mathematical Population Studies 21, 127-145, (2014)

   doi:10.1080/08898480.2013.804690

2013

1. Logistic type equations with discrete delay and quasi-periodic suppression rate

   Bodnar, Marek, Foryś, Urszula, and Piotrowska, Monika J.

   Appl. Math. Letters 26, 607–611, (2013)

   doi:10.1016/j.aml.2012.12.023
2. A simple model of carcinogenic mutations with time delay and diffusion

   Piotrowska, Monika J., Foryś, Urszula, Bodnar, Marek, and Poleszczuk, Jan

   Mathematical Biosciences and Engineering 10(3), 861–872, (2013)

   doi:10.3934/mbe.2013.10.861
3. Model of tumour angiogenesis – analysis of stability with respect to delays

   Bodnar, Marek, Piotrowska, Monika Joanna, Foryś, Urszula, and Nizińska, Ewa

   Mathematical Biosciences and Engineering 10, 19–35, (2013)

   doi:10.3934/mbe.2013.10.19
4. Gompertz model with delays and treatment: mathematical analysis

   Bodnar, Marek, Piotrowska, Monika J., and Foryś, Urszula

   Mathematical Methods in the Applied Sciences 10, 551–563, (2013)

   doi:10.3934/mbe.2013.10.551
5. Friction dominated dynamics of interacting particles locally close to a crystallographic lattice

   Bodnar, Marek, and Lopez-Velázquez, Juan J.

   Mathematical Methods in the Applied Sciences 36, 1206–1228, (2013)

   doi:10.1002/mma.2672
6. Existence and stability of oscillating solutions for a class of delay differential equations

   Bodnar, Marek, Piotrowska, Monika J., and Foryś, Urszula

   Nonlinear Analysis - Real World Applications 14, 1780-1794, (2013)

   doi:10.1016/j.nonrwa.2012.11.010
7. Mathematical modelling of immune reaction against gliomas: sensitivity analysis and influence of delays

   Piotrowska, Monika J., Bodnar, Marek, Poleszczuk, , and Foryś, Urszula

   Nonlinear Analysis: Real World Applications 14, 1601–1620, (2013)

   doi:10.1016/j.nonrwa.2012.10.020

2012

1. Delay can stabilize: Love affairs dynamics

   Bielczyk, Natalia, Bodnar, Marek, and Foryś, Urszula

   Applied Mathematics and Computation 219, 3923–3937, (2012)

   doi:10.1016/j.amc.2012.10.028
2. About a generalized model of lymphoma

   Chrobak, Joanna M., Bodnar, Marek, and Herrero, Henar

   J. Math. Anal. Appl. 386, 813–829, (2012)

   doi:10.1016/j.jmaa.2011.08.043
3. Stability of delay induced oscillations in gene expression of Hes1 protein model

   Bodnar, Marek, and Bartłomiejczyk, Agnieszka

   Nonlinear Analysis: Real World Applications 13, 2227–2239, (2012)

   doi:10.1016/j.nonrwa.2012.01.017

2011

1. Negativity of delayed induced oscillations in a simple linear DDE

   Foryś, Urszula, Bodnar, Marek, and Poleszczuk, Jan

   Applied Mathematics Letters 24, 982-986, (2011)

   doi:10.1016/j.aml.2011.01.010
2. Stochastic Models of Gene Expression with Delayed Degradation

   Miękisz, Jacek, Poleszczuk, Jan, Bodnar, Marek, and Foryś, Urszula

   Bulletin of Mathematical Biology 73, 2231–2247, (2011)

   doi:10.1007/s11538-010-9622-4
3. Analysis of biochemical reactions models with delays

   Bodnar, Marek, Foryś, Urszula, and Poleszczuk, Jan

   Journal of Mathematical Analysis and Applications 376, 74–83, (2011)

   doi:10.1016/j.jmaa.2010.10.038
4. New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model

   Poleszczuk, Jan, Bodnar, Marek, and Foryś, Urszula

   Mathematical Biosciences and Engineering 8, 591–603, (2011)

   doi:10.3934/mbe.2011.8.591

2009

1. Angiogenesis model with carrying capacity depending on vessel density

   Bodnar, Marek, and Foryś, Urszula

   Journal of Biological Systems 17, 1–25, (2009)

   doi:10.1142/S0218339009002739
2. A model of immune system with time-dependent immune reactivity

   Bodnar, Marek, and Foryś, Urszula

   Nonlinear Analysis: Theory, Methods & Applications 70, 1049–1058, (2009)

   doi:10.1016/j.na.2008.01.031

2008

1. Global stability and the Hopf bifurcation for some class of delay differential equation

   Bodnar, Marek, and Foryś, Urszula

   Mathematical Methods in the Applied Sciences 31, 1197–1207, (2008)

   doi:10.1002/mma.965

2007

1. Three types of simple DDE’s describing tumor growth

   Bodnar, Marek, and Foryś, Urszula

   Journal of Biological Systems 15, 453-471, (2007)

   doi:10.1142/S0218339007002313

2006

1. An integro-differential equation arising as a limit of individual cell-based models

   Bodnar, Marek, and Lopez-Velázquez, Juan J.

   Journal of Differential Equations 222, 341–380, (2006)

   doi:10.1016/j.jde.2005.07.025

2005

1. Derivation of macroscopic equations for individual cell-based models: a formal approach

   Bodnar, Marek, and Lopez-Velázquez, Juan J.

   Mathematical Methods in the Applied Sciences 28, 1757–1779, (2005)

   doi:10.1002/mma.638

2004

1. On the differences and similarities of the first order delay and ordinary differential equations

   Bodnar, Marek

   Journal of Mathematical Analysis and Applications 300, 172–188, (2004)

   doi:10.1016/j.jmaa.2004.06.039

2003

1. Time delays in regulatory apoptosis for solid avascular tumour

   Foryś, Urszula, and Bodnar, Marek

   Mathematical and Computer Modelling 37, 1211–1220, (2003)

   doi:10.1016/S0895-7177(03)00131-6
2. Time delays in proliferation process for solid avascular tumour

   Foryś, Urszula, and Bodnar, Marek

   Mathematical and Computer Modelling 37, 1201–1209, (2003)

   doi:10.1016/S0895-7177(03)80019-5

2002

1. On the norm conservation for the generalized kinetic population models with delay

   Bodnar, Marek

   Mathematical and Computer Modelling 35, 765–778, (2002)

   doi:10.1016/S0895-7177(02)00048-1

2000

1. The nonnegativity of the solutions of delay differential equations

   Bodnar, Marek

   Applied Mathematics Letters 13, 91–95, (2000)

   doi:10.1016/S0893-9659(00)00061-6