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Hi, I’m Marek

I am a university professor at The Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw. My main interests are continuous dynamical systems, namely ordinary and delay differential equations, equations with impulses, and sometimes reaction-diffusion equations. I am interested in constructing and analyzing models that describe biological or sociological processes. I study the qualitative properties of the solution of the models and try to relate the results to real situations.

Contact Me

Working place

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)

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)
  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)
  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)

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)
  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)

2021

  1. Evolution of populations with strategy-dependent time delays
    Miękisz, Jacek, and Bodnar, Marek
    Physical Review E 103, 012414, (2021)

2020

  1. Cancer as a Killer Tsunami
    Poleszczuk, Jan, Forys, Urszula, Bodnar, Marek, and Piotrowska, Monika
    62–63, (2020)
  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)
  3. Three-Player Games with Strategy-Dependent Time Delays
    Dynamic Games and Applications 664–675, (2020)

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)
  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)
  3. Distributed delays in Hes1 gene expression model
    Bodnar, Marek
    24, 2125-2147, (2019)
  4. Analysis of delay dierential equations modelling tumor growth with angiogenesis
    Szlenk, Maja, and Bodnar, Marek
    Mathematica Applicanda 47, 207–217, (2019)
  5. Some remarks on modelling of drug resistance for low grade gliomas
    Foryś, Urszula, and Bodnar, Marek
    Mathematica Applicanda 47, 151–164, (2019)
  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)

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)
  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)
  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)

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)
  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)
  3. Angiogenesis model with Erlang distributed delays
    Attia, Emad, Bodnar, Marek, and Foryś, Urszula
    Mathematical Biosciences and Engineering 14, 1–15, (2017)
  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)

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)
  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)
  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)
  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)

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)
  2. General model of a cascade of reactions with time delays: global stability analysis
    Bodnar, Marek
    Journal of Differential Equations 259, 777–795, (2015)

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)
  2. Logistic Equation with Treatment Function and Discrete Delays
    Piotrowska, Monika J., and Bodnar, Marek
    Mathematical Population Studies 21, 166-183, (2014)
  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)

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)
  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)
  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)
  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)
  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)
  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)
  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)

2012

  1. Delay can stabilize: Love affairs dynamics
    Bielczyk, Natalia, Bodnar, Marek, and Foryś, Urszula
    Applied Mathematics and Computation 219, 3923–3937, (2012)
  2. About a generalized model of lymphoma
    Chrobak, Joanna M., Bodnar, Marek, and Herrero, Henar
    J. Math. Anal. Appl. 386, 813–829, (2012)
  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)

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)
  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)
  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)
  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)

2009

  1. Angiogenesis model with carrying capacity depending on vessel density
    Bodnar, Marek, and Foryś, Urszula
    Journal of Biological Systems 17, 1–25, (2009)
  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)

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)

2007

  1. Three types of simple DDE’s describing tumor growth
    Bodnar, Marek, and Foryś, Urszula
    Journal of Biological Systems 15, 453-471, (2007)

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)

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)

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)

2003

  1. Time delays in regulatory apoptosis for solid avascular tumour
    Foryś, Urszula, and Bodnar, Marek
    Mathematical and Computer Modelling 37, 1211–1220, (2003)
  2. Time delays in proliferation process for solid avascular tumour
    Foryś, Urszula, and Bodnar, Marek
    Mathematical and Computer Modelling 37, 1201–1209, (2003)

2002

  1. On the norm conservation for the generalized kinetic population models with delay
    Bodnar, Marek
    Mathematical and Computer Modelling 35, 765–778, (2002)

2000

  1. The nonnegativity of the solutions of delay differential equations
    Bodnar, Marek
    Applied Mathematics Letters 13, 91–95, (2000)

Terminy konsultacji obowiązują w trakcie trwania zajęć dydaktycznych. W dniach wolnych od zajęć dydaktycznych proszę się umawiać indywidualnie.

Konsultacje

semestr zimowy 2024/2025

środy 11:00–11:45 oraz 16:15–17:00, s. 5670

Zapraszam na konsultacje stacjonarnie na wydziale w środy 11:00–11:45 oraz 16:15–17:00, p. 5670. Konsultacje dostępne są także w innych terminach (na przykład przed lub po wykładzie) po wcześniejszym umówieniu się. Możliwe są także konsultacje zdalne (w dowolnym terminie dogodnym dla zainteresowanych i dla mnie) po umówieniu się.

Analiza matematyczna II.1

semestr zimowy 2024/2025

wtorki 12:15–13:45, s. 4420
piątki 12:15–13:45, s. 3180

Terminy kolokwiów: poniedziałek 25 listopada 2024, godziny 14:15-17:30 oraz czwartek 9 stycznia 2025, godziny 14:15-17:30. Więcej informacji o kursie na moodlu.

Modele matematyczne w biologii i naukach społecznych

semestr zimowy i letni 2024/2025

środy 12:15–13:45, s. 5070

Seminarium magisterskie i monograficzne. Więcej informacji o kursie na moodlu.

Conferences, workshops and summer schools
XXIX National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Złoty Potok, Poland, September 2024, talk
Conference on Mathematical Methods and Models in Biosciences (Biomath)
Scottsburgh, South Africa, June 2024, talk
XXVIII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Złoty Potok, Poland, September 2023, talk
The Spanish+Polish Mathematical Meeting
Łodź, Poland, September 2023, invited talk
Conference on Mathematical Methods and Models in Biosciences (Biomath)
Pomorie, Bulgaria, June 2023, talk
XXVII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Wisła, Poland, September 2022, talk
On the Trail of Women in Mathematics -Contemporary Women in Mathematics
Gdańsk, Poland, September 2022, talk
Dynamical Systems and Applications in Life and Social Sciences
Będlewo, Poland, May 2022, talk
XXVI National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Krosno k. Iwonicza Zdrój, Poland, September 2021, talk
SMB 2021 Annual Meeting
on-line, June 2021, talk
XXV National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Jadwisin, Poland, September 2019, talk
Jubilee Congress for the 100th anniversary of the Polish Mathematical Society
Kraków, Poland, September 2019, invited talk
International Congress on Industrial and Applied Mathematics
Valencia, Spain, July 2019, invited talk
Mathematical Methods and Models in Bioscience
Będlewo, Poland, June 2019, invited talk
Joint meeting of the Italian Mathematical Union, the Italian Society of Industrial and Applied Mathematics and the Polish Mathematical Society
Wrocaław, Poland, September 2018, invited talk
XXIV National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Zakopane-Kościelisko, Poland, September 2018
The 11th European Conference on Mathematical and Theoretical Biology
Lisboa, Portugal, July 2018, invited talk
Therapy optimization in glioblastoma: An integrative human data-based approach using mathematical models. Third general meeting
Almagro, Spain, September 2017, invited talk
8th Forum of Polish Mathematical Society
Lublin, Poland, September 2017, talk
XXIII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Jugowice, Poland, September 2017, talk
New Horizons in Optimal Control 2017
Porto, Portugal, July 2017, invited talk
XXV Conference on Differential Equations and Applications / XV Conference on Applied Mathematics
Carthagena, Spain, June 2017, invited talk
Therapy optimization in glioblastoma: An integrative human data-based approach using mathematical models. Second general meeting
Cuenca, Spain, October 2017
XLV Conference of Application of Mathematics
Zakopane-Kościelisko, Poland, September 2016, talk
XXII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Sandomierz, Poland, September 2016, talk
16th Computational and Mathematical Methods in Science and Engineering
Costa Ballena, Spain, July 2016, talk
Mathways into biology
Będlewo, Poland, June 2016
Nonlocal Aspects of Mathematical Biology
Będlewo, Poland, January 2016, talk
XXI National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Regietów, Poland, September 2015, talk
6th Forum of Polish Mathematical Society
Warsaw, Poland, September 2015, talk
Micro and Macro Systems in Life Sciences
Będlewo, Poland, June 2015, talk
Between theory and applications — mathematics in action
Będlewo, Poland, May 2015, plenary lecture
Spring of Differential Equations
Gdańsk, Poland, March 2015, talk
XX National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Łochów, Poland, September 2014, talk
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
Madrid, Spain, July 2014, invited talk
XIX National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Jastrzębia Góra, Poland, September 2013, talk
Between theory and applications — mathematics in action
Będlewo, Poland, May 2013, plenary lecture
Dynamic Days Europe 2012
Gothenburg, Sweeden, September 2012, talk
Mathways into Cancer I
Almagro, Spain, June 2012, talk
XVII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Zakopane-Kościelisko, Poland, September 2011, talk
8th European Conference on Mathematical and Theoretical Biology
Kraków, Poland, June/July 2011, talk
XVI National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Krynica Morska, Poland, September 2010, talk
Workshop on Biomathematics
Madrid, Spain, April 2010
XXI Conference on Differential Equations and Applications / XI Conference on Applied Mathematics
Ciudad Real, Spain, September 2009, talk
XV National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Szczyrk, Poland, September 2009, talk
XIV National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Leszno k. Warszawy, Poland, September 2008, talk
Workshop: From Genetics to Mathematics
Zbąszyń, Poland, October 2007, talk
XIII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Serpelice nad Bugiem, Poland, September 2007, talk
Dynamics Days Europe 2007
Loughborough, United Kingdom, July 2007, talk
XII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Koninki, Poland, September 2006, talk
School and Workshop, From a Microscopic to a Macroscopic Description of Complex Systems
Będlewo, Poland, September 2006, talk
AIMS' Sixth International Conference on Dynamical Systems, Differential Equations and Applications
Poitires, France, June 2006, talk
Workshop on Tumour Modelling
Szczyrk, Poland, Octaber 2005, talk
Conference on Mathematical Models and Methods in Biology and Medicine
Będlewo, Poland, May/June 2005, talk
X National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Święty Krzyż, Poland, September 2004, talk
Linking mathematics and biology in cancer research
Magdeburg, Germany, September 2003, talk
3rd Summer School and Scientific Workshop of RTN Using Mathematical Modelling and Computer Simulation to Improve Cancer Therapy
Propriano, Corse, France, September 2002, talk
VII National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Zawoja, Poland, September 2001, talk
2nd Summer School and Scientific Workshop of RTN Using Mathematical Modelling and Computer Simulation to Improve Cancer Therapy
Propriano, Corse, France, September 2001, talk
1st ESMTB Euro Summer School Spatial Structures in Biology and Ecology: Models and Methods
Martina Franca, Italy, September 2001, communication
1st Summer School and Scientific Workshop of RTN Using Mathematical Modelling and Computer Simulation to Improve Cancer Therapy
Propriano, Corse, France, September 2000, talk
V National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Ustrzyki Górne, Poland, September 1999, talk
European Conference on Mathematical and Theoretical Biology
Amsterdam, Holland, June/July 1999, talk
European Simulation and Modeling
Warsaw, Poland, June 1999, talk
IV National Conference Application of Mathematics in Biology and Medicine (KKZMBiM)
Zwierzyniec, Poland, September 1998, talk
11th ECMI Modeling Week
Milano, Italy, July 1998
V Mathematical Population Dynamics Conference
Zakopane-Kościelisko, Poland, September 1998, talk

Longer stays and some of short visits