Marek Bodnar

prof. Marek Bodnar,

Institute of Applied Mathematics and Mechanics
Department of Mathematics, Computer Science and Mechanics
Warsaw University
Banacha 2, 02-097 Warsaw, POLAND
Office room: 5670
Phone: +48 22 55 44 567
Fax: +48 22 55 44 300
e-mail: mbodnar@mimuw.edu.pl
0000-0001-5571-2476.

Fields of interest

retarded functional differential equations, delay differential equations, large systems of interacting particles, mathematical modelling in biology.

Scientific researches are carried on together with Warsaw Biolmat Team.

I am a member of Section of Biomathematics and Game Theory.

Thesis

Positions

My publications:

Papers after referee process:

    Accepted, available on-line:

  1. M. Bodnar, U. Foryś, Modeling of drug resistance: Comparison of two hypotheses for slowly proliferating tumors on the example of low-grade gliomas (2021) doi: 10.1002/mma.7893

    2. Published:

  2. Jacek Miękisz, M. Bodnar, Evolution of populations with strategy-dependent time delays, Phys. Rev. E, 103, (2021) 012414, doi: 10.1103/PhysRevE.103.012414
  3. M. Bodnar, J. Miękisz, R. Vardanyan, Three-Player Games with Strategy-Dependent Time Delays, Dyn. Games Appl., 10 (2020), 664–675, doi: 10.1007/s13235-019-00340-0
  4. A. Bartłomiejczyk, M. Bodnar Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein, Comm. Nonlinear Sci. Num. Sim. 84 (2020), 105166, doi: 10.1016/j.cnsns.2020.105166.
  5. M. Bodnar, M.J. Piotrowska, M.U. Bogdańska, Mathematical analysis of generalised model of chemotherapy for low grade gliomas, Disc. Cont. Dyn. Sys. B 24, 5, (2019), 2149–2167, doi: 10.3934/dcdsb.2019088
  6. M. Bodnar, Distributed delays in Hes1 gene expression model, Disc. Cont. Dyn. Sys. B 24, 5, (2019), 2125–2147, doi: 10.3934/dcdsb.2019087.
  7. M. Bodnar, M. Vela-Pérez, Mathematical and numerical analysis of low grade gliomas model and the effects of chemotherapy Comm. Nonlinear Sci. Num. Sim., 72, (2019), 552–564, doi: 10.1016/j.cnsns.2019.01.015.
  8. M.J. Piotrowska, A. Bartłomiejczyk, M. Bodnar, Mathematical analysis of a generalised p53-Mdm2 protein gene expression model Appl. Math. Comput., 328, (2018), 26–44, doi: 10.1016/j.amc.2018.01.014.
  9. M.J. Piotrowska, M. Bodnar, Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model Comm. Nonlinear Sci. Num. Sim., 54, (2018), 389–415, doi: 10.1016/j.cnsns.2017.06.003.
  10. M.U. Bogdańska, M. Bodnar, M.J. Piotrowska, M. Murek, P. Schucht, J. Beck, A. Martínez-González, V.M. Pérez-García, A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications, PLOS One, 12(8), (2017), e0179999, doi:10.1371/journal.pone.0179999
  11. M.U. Bogdańska, M. Bodnar, J. Belmonte-Beitia, M. Murek, P. Schucht, J. Beck, V.M. Pérez-García, A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications, Math. Biosci., 288, (2017), 1–13, doi:10.1016/j.mbs.2017.02.003
  12. M. Bodnar, N. Okińczyc, M. Vela-Pérez, Mathematical model for path selection by ants between nest and food source, Math. Biosci., 285, (2017), 14–24, doi: 10.1016/j.mbs.2016.12.002
  13. E. Attia, M. Bodnar, U. Foryś, Angiogenesis model with Erlang distributed delays, Math. Biosci. Eng., 14, 1 (2017), 1–15, doi: 10.3934/mbe.2017001
  14. M. Bodnar, U. Foryś, Delays do not cause oscillations in a corrected model of humoral mediated immune response, Appl. Math. Comput., 289 (2016), 7–21, doi: 10.1016/j.amc.2016.05.006
  15. M. Bodnar, P. Guerrero, R. Perez-Carrasco, M.J. Piotrowska, Deterministic and Stochastic Study for a Microscopic Angiogenesis Model: Applications to the Lewis Lung Carcinoma, PLOS One, 11, 5, (2016), e0155553, doi: 10.1371/journal.pone.0155553
  16. U. Foryś, M. Bodnar, Y. Kogan, Asymptotic dynamics of some t-periodic one-dimensional model with application to prostate cancer immunotherapy, J. Math. Biol., 73, 4, (2016), 867–883, doi: 10.1007/s00285-016-0978-4.
  17. M. Bodnar, M.J. Piotrowska, Stability analysis of the family of tumour angiogenesis models with distributed time delays Comm. Nonlinear Sci. Num. Sim., 31, 1–3, (2016), 124–142, doi: 10.1016/j.cnsns.2015.08.002, preprint: arXiv:1502.07862.
  18. A. Wiszniewska-Matyszkiel, M. Bodnar, F. Mirota, Dynamic Oligopoly with Sticky Prices: Off-Steady State Analysis, Dyn. Games Appl., 5, 4, (2015), 568–598, doi: 10.1007/s13235-014-0125-z
  19. M. Bodnar, General model of a cascade of reactions with time delays: global stability analysis, J. Diff. Eqs., 259, 2 (2015), 777–795 doi: 10.1016/j.jde.2015.02.024, preprint: arXiv:1403.5435.
  20. B. Zduniak, M. Bodnar, U. Foryś, Modified van der Pol equation with delay in a~description of the heart action, Int. J. Appl. Math. Comput. Sci., 24, 4, (2014) 853–863 doi: 10.2478/amcs-2014-0063.
  21. M.J. Piotrowska, M. Bodnar, U. Foryś, Tractable model of malignant gliomas immunotherapy with discrete time delays, Math. Popul. Stud.,21, 3, (2014) 166—183 doi: 10.1080/08898480.2013.804690.
  22. M.J. Piotrowska, M. Bodnar, Logistic equation with treatment function and discrete delays, Math. Popul. Stud. 21, 3, (2014) 127–145 doi: 10.1080/08898480.2014.921492.
  23. M. Bodnar, J.J.L. Velazquez, Friction dominated dynamics of interacting particles locally close to a crystallographic lattice, Math. Methods Appl. Sci. 36, 10, (2013), 1206—1228, doi: 10.1002/mma.2672.
  24. M.J. Piotrowska, U. Foryś, M. Bodnar, J. Poleszczuk, A simple model of carcinogenic mutations with time delay and diffusion, Math. Biosci. Eng., 10, 3, (2013), 861–872 doi:10.3934/mbe.2013.10.861.
  25. M. Bodnar, M.J. Piotrowska, U. Foryś, Gompertz model with delays and treatment: mathematical analysis, Math. Biosci. Eng. 10, 3, (2013), 551–563 doi:10.3934/mbe.2013.10.551.
  26. M. Bodnar, U. Foryś, M.J. Piotrowska, Logistic type equations with discrete delay and quasi-periodic suppression rate, Appl. Math. Lett., 26, 6, (2013), 607—611, doi:10.1016/j.aml.2012.12.023.
  27. M. Bodnar, M.J. Piotrowska, U. Foryś, Existence and stability of oscillating solutions for a class of delay differential equations, Non. Anal. Real World Applications, 14, 3, (2013), 1780–1794, doi:10.1016/j.nonrwa.2012.11.010.
  28. M.J. Piotrowska, M. Bodnar, U. Foryś, J. Poleszczuk, Mathematical modelling of immune reaction against gliomas: sensitivity analysis and influence of delays, Non. Anal. Real World Applications, 14, 3, (2013), 1601–1620, doi:10.1016/j.nonrwa.2012.10.020.
  29. M. Bodnar, M.J. Piotrowska, U. Foryś, E. Nizińska, Model of tumour angiogenesis — analysis of stability with respect to delays, Math. Biosci. Eng., 10, 1, (2013), 19–35, doi:10.3934/mbe.2013.10.19.
  30. N. Bielczyk, M. Bodnar, U. Foryś, Delay can stabilize: love affairs dynamics, Appl. Math. Comput. 219, 8, (2012), 3923–3937 doi: 10.1016/j.amc.2012.10.028.
  31. M. Bodnar, A. Bartłomiejczyk, Stability of delay induced oscillations in gene expression of Hes1 protein model, Non. Anal. Real World Applications 13, 5, (2012), 2228–2239, doi:10.1016/j.nonrwa.2012.01.017.
  32. J.M. Chrobak, M. Bodnar, H. Herrero, About a generalized model of lymphoma, J. Math. Anal. Appl. 386, 2, (2012), 813–829, doi:10.1016/j.jmaa.2011.08.043.
  33. U. Foryś, M. Bodnar, J. Poleszczuk, Negativity of delayed induced oscillations in a simple linear DDE, Appl. Math. Lett., 24, 6, (2011), 982–986, doi: 10.1016/j.aml.2011.01.010.
  34. J. Miekisz, J. Poleszczuk, M. Bodnar, U. Foryś, Stochastic models of gene expression with delayed degradation, Bull. Math. Biol., 73 9 (2011), 2231–2247, doi:10.1007/s11538-010-9622-4.
  35. M. Bodnar, U. Foryś, J. Poleszczuk, Analysis of biochemical reactions models with delays J. Math. Anal. Appl. 376, 1 (2011), 74–83 , doi:10.1016/j.jmaa.2010.10.038.
  36. J. Poleszczuk, M. Bodnar, U. Foryś, New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model.,Math. Biosci. Eng., 8, 2, (2011) 591–603, doi:10.3934/mbe.2011.8.591.
  37. M. Bodnar, M.J. Piotrowska, O równaniach różniczkowych z opóźnieniem — teoria i zastosowania, Mat. Stos. 11/52, (2010), 18–56.
  38. M. Bodnar, U. Foryś, Z. Szymańska, Model of AIDS-related tumour with time delay, Appl. Math. (Warsaw), 36, 3, (2009), 263–278, doi:10.4064/am36-3-2.
  39. M. Bodnar, U. Foryś, Angiogenesis model with carrying capacity depending on vessel density, J. Biol. Sys., 17, 1, (2009), 1–25, doi:10.1142/S0218339009002739.
  40. M. Bodnar, U. Foryś, A model of immune system with time-depended immune reactivity, Non. Anal. Th. Meth. Appl., 70, 2, (2009), 1049–1058, doi:10.1016/j.na.2008.01.031.
  41. M. Bodnar, U. Foryś, Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics, Appl. Math. (Warsaw), 36, 3, (2009), 251–262, doi:10.4064/am36-3-1.
  42. M. Bodnar, U. Foryś, Global stability and the Hopf bifurcation for some class of delay differential equation, Math. Methods Appl. Sci., 31, 10, (2008), 1197–1207, doi:10.1002/mma.965.
  43. M. Bodnar, U. Foryś, Three types of simple DDE'S describing tumor growth, J. Biol. Syst., 15, 4, (2007), 453–471, doi:10.1142/S0218339007002313.
  44. M. Bodnar, J.J.L. Velazquez, An integro-differential equation arising as a limit of individual cell-based models, J. Diff. Eqs., 222, 2, (2006), 341–380, doi:10.1016/j.jde.2005.07.025.
  45. M. Bodnar, U. Foryś, Time delay in necrotic core formation, Math. Biosci. Eng., 2, 3, (2005), 461–472.
  46. M. Bodnar, J.J.L. Velazquez, Derivation of macroscopic equations for individual cell-based models: a formal approach, Math. Methods Appl. Sci., 28, 15 (2005), 1757–1779, doi:10.1002/mma.638.
  47. M. Bodnar, On the differences and similarities of the first order delay and ordinary differential equations, J. Math. Anal. Appl., 300, 1, (2004), 172–188, doi:10.1016/j.jmaa.2004.06.039.
  48. U. Foryś, M. Bodnar, Time delays in regulatory apoptosis for solid avascular tumour, Math. Comput. Modelling, 37, 11, (2003), 1211–1220, doi:10.1016/S0895-7177(03)00131-6.
  49. U. Foryś, M. Bodnar, Time delays in in proliferation process for solid avascular tumour, Math. Comput. Modelling, 37, 11, (2003), 1201–1209, doi:10.1016/S0895-7177(03)80019-5.
  50. M. Bodnar, On Norm Conservation for Generalized Kinetic Population Models with Delay, Math. Comput. Modelling, 35,7-8 (2002), 765–778, doi:10.1016/S0895-7177(02)00048-1.
  51. M. Bodnar, On the nonnegativity of solutions of delay differential equations,Appl. Math. Lett., 13,6 (2000), 91–95, doi:10.1016/S0893-9659(00)00061-6.
  52. M. Bodnar, U. Foryś, Behaviour of Marchuk's model depending on time delay, Intern. J. Appl. Math. Comput. Sci. 10, 1, (2000), 97–112.
  53. M. Bodnar, U. Foryś, Periodic dynamics of the model of immune system, Appl. Math. (Warsaw), 27,1 (2000), 113–126.

Papers in conference proceedings after referee process:

  1. A. Bartłomiejczyk, M. Bodnar, Modelling gene expression of a self-regulating protein, Proceedings of the XX National Conference Applications of Mathematics in Biology and Medicine, Łochów, September 23–27, 2014, 9–14.
  2. M. Bogdańska, M. Bodnar, J. Belmonte-Beitia, M. Murek, P. Schucht, J. Beck, V.M. Perez-García, Mathematical model suggests a way to assess low grade glioma malignancy, Proceedings of the XX National Conference Applications of Mathematics in Biology and Medicine, Łochów, September 23–27, 2014, 21–28.
  3. B. Zduniak, M. Bodnar, Mathematical model suggests a way to assess low grade glioma malignancy, Proceedings of the XIX National Conference Applications of Mathematics in Biology and Medicine, Jastrzębia Góra, September 16–20, 2013, 90–95.
  4. M.J. Piotrowska, U. Foryś, M. Bodnar, J. Poleszczuk, Carcinogenesis, mutations, delay and diffusion, Proceedings of the XVIII National Conference Applications of Mathematics in Biology and Medicine, Krynica Morska, September 23–27, 2012, 106–111.
  5. M.J. Piotrowska, U. Foryś, M. Bodnar, Delayed logistic equation with treatment function, Proceedings of the XVII National Conference Applications of Mathematics in Biology and Medicine, Zakopane-Kościelisko, September 1–6, 2011, 66–72.
  6. M. Bodnar, A. Bartłomiejczyk, Delay induced oscillations in gene expression of Hes1 protein model, Proceedings of the XVI National Conference Applications of Mathematics in Biology and Medicine, Krynica, September 14–18, 2010, 18–23.
  7. N. Bielczyk, M. Bodnar, U. Foryś, J. Poleszczuk, Delay can stabilise: love affairs dynamics, Proceedings of the XVI National Conference Applications of Mathematics in Biology and Medicine, Krynica, September 14–18, 2010, 12–17.
  8. M. Bodnar, U. Foryś, Modelling of an immune reaction under the influence of interleukin, Proceedings of the XV National Conference Application of Mathematics in Biology and Medicine, Szczyrk, September 15–19, 2009, 13–19.
  9. M. Bodnar, U. Foryś, Z. Szymańska, A model of AIDS-related tumour with time delay, Proceedings of the XIV National Conference Application of Mathematics in Biology and Medicine, Leszno n. Warsaw, September 16–20, 2008, 12–17.
  10. M. Bodnar, U. Foryś, Hahnfeldt angiogenesis model with time delays, Proceedings of the XIII National Conference Application of Mathematics in Biology and Medicine, Serpelice nad Bugiem, September 18–22, 2007, 19–24.
  11. M. Bodnar, U. Foryś, A model of immune system with time depended immune reactivity, Proceedings of the XII National Conference Application of Mathematics in Biology and Medicine, Koninki, September 25–29, 2006, 19–24.
  12. M. Bodnar, U. Foryś, Time delay in a model of necrotic core formation. Proceedings of the X National Conference Application of Mathematics in Biology and Medicine, Jodłowy Dwór, September 21–25, 2004, 13–18.
  13. M. Bodnar, On some integro-differential models with delay in population dynamics, Proceedings of the VII National Conference Application of Mathematics in Biology and Medicine, Zawoja, September 25–28, 2001, 21–26.
  14. M. Bodnar, U. Foryś, Forest-pest interaction dynamics, Proceedings of the V National Conference Application of Mathematics in Biology and Medicine, Ustrzyki Gorne, September 14–17, 1999, 15–20.
  15. M. Bodnar, U. Foryś, A model of the immune system with stimulation depending on time, Proceedings of the IV National Conference Application of Mathematics in Biology and Medicine, Zwierzyniec, September 15–18, 1998, 12–17.

Papers without referee process and preprints:

  1. M. Bodnar, D. Kuhnke, J. Pedersen, J. Ränäen, G. Haase, A mass reduction for the modulling machine, in Proceedings of 11th ECMI Modeling Week, Milan 1998.

Conferences and Summer schools

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