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.
- delay differential equations — I am investigating systems of
ordinary differential equation with time delays. As far I have been
considering only constant delay. I was studying an integro-differential
equations with delay;
- large systems of interacting particles — I am looking for a macroscopic
equation (partial differential equation or integro-differential equation)
which can describe an evolution of a macroscopic density of the particle
system
Scientific researches are carried on together with Warsaw Biolmat Team.
I am a member of Section of Biomathematics and Game Theory.
Thesis
- Habilitation: "Analysis of mathematical properties of delay differential equations that appear in mathematical models of tumour growth or in models of immune system."
- Ph.D. thesis: "Properties of the
solution to DDE versus properties of the solution to ODE", tutor:
Mirosław Lachowicz;
- Master thesis: "Marchuk's Model with
immune reactivity depending on time", tutor: Urszula Foryś;
Positions
- October 1st, 2015 – now — associate professor at the Institute of Applied
Mathematics and Mechanics, Warsaw University
- July 1st, 2011 – September 30th, 2015 — assistant professor at the Institute of Applied
Mathematics and Mechanics, Warsaw University
- February 1st, 2010 – June 30th, 2011 — visiting professor at the Institute for the Mathematical Sciences of the Consejo Superior de Investigaciones Cientificas, Madrid, Spain in the framework of the project of Spanish Ministry of Science and Education, project no. SB2009-0074
- October 1st, 2004 – January 31st, 2010 — assistant professor at the Institute of Applied
Mathematics and Mechanics, Warsaw University
- October 1st, 2001 – 30th, September 2004 — instructor at Institute of Applied
Mathematics and Mechanics, Warsaw University
- March 1st, 2002 – September 30th, 2003 — post-doc position at
Faculty of Mathematic
Complutense University in Madrid in the framework
of 5th RTN Using Mathematical
Modelling and Computer Simulation to Improve Cancer Therapy
- September 1998 – September 2001 — Ph.D studies at the Faculty of
Mathematics, Informatics and Mechanics, Warsaw University
My publications:
Papers after referee process:
Accepted, available on-line:
- 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
Published:
- Jacek Miękisz, M. Bodnar, Evolution of populations with strategy-dependent time delays, Phys. Rev. E, 103, (2021) 012414, doi: 10.1103/PhysRevE.103.012414
- 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
- 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.
- 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
- M. Bodnar, Distributed delays in Hes1 gene expression model, Disc. Cont. Dyn. Sys. B 24, 5, (2019), 2125–2147, doi: 10.3934/dcdsb.2019087.
- 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.
- 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.
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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.
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M. Bodnar, M.J. Piotrowska, O równaniach różniczkowych z opóźnieniem — teoria i zastosowania, Mat. Stos. 11/52, (2010), 18–56.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M. Bodnar, U. Foryś, Time delay in necrotic core formation, Math. Biosci. Eng., 2, 3, (2005), 461–472.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M. Bodnar, U. Foryś, Behaviour of Marchuk's model depending on time delay, Intern. J. Appl. Math. Comput. Sci. 10, 1, (2000), 97–112.
- 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:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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:
- 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
- June 1998 — V Mathematical Population Dynamics
Conference, Zakopane (Poland), talk;
- July — ECMI (European Consortium
for Mathematics in Industry) 11-th ECMI Modeling Week, Milano (Italy)
- September 1998 — IV National Conference
Application of Mathematics in Biology and Medicine
(KKZMBiM), Zwierzyniec, talk;
- June 1999 — ESM (European Simulation and
Modeling) Conference, Warsaw (Poland), talk;
- June/July 1999 — TMBT (Theoretical and
Mathematics in Biology and Medicine) Conference in
Amsterdam (Holland), poster;
- September 1999 — V KKZMBiM in Ustrzyki Górne, talk;
- June 2000 — 1st Summer School and Scientific Workshop of RTN
Using Mathematical Modelling and Computer
Simulation to Improve Cancer Therapy, Propriano (Corse, France), talk;
- 1st ESMTB Euro Summer School Spatial Structures in
Biology and Ecology: Models and Methods, Martina Franca (Italy),
communication;
- September 2001 — 2nd Summer School and Scientific Workshop of RTN
Using Mathematical Modelling and Computer
Simulation to Improve Cancer Therapy, Propriano (Corse, France), talk;
- September 2001 — VII KKZMBiM, Zawoja (Poland), talk;
- September 2002 — 2nd Summer School and Scientific Workshop of RTN
Using Mathematical Modelling and Computer
Simulation to Improve Cancer Therapy, Propriano (Corse, France), talk;
- September 2003 — Linking mathematics and biology in cancer research,
Magdeburg (Germany), talk;
- September 2004 — X KKZMBiM, Jodłowy Dwór (Poland), talk;
- May/June 2005 — Conference on Mathematical Models and Methods in Biology and Medicine, Będlewo (Poland), talk
- October 2005, Workshop on Tumour Modelling, Szczyrk (Poland), talk
- June 2006 — AIMS' Sixth International Conference on
Dynamical Systems, Differential Equations and Applications, Poitires (France), talk
- September 2006 — School and Workshop, From a Microscopic to a Macroscopic Description of Complex Systems, Będlewo (Poland), talk
- September 2006 — XII KKZMBiM, Serpelice nad Bugime (Poland), talk
- July 2007 — Dynamics Days Europe 2007, Loughborough University (Great Britain), talk
- September 2007 — XIII KKZMBiM, Serpelice nad Bugiem (Poland), talk
- October 2007 — Workshop: From Genetics to Mathematics, Zbąszyń (Poland)
- September 2008 — XIV KKZMBiM, Leszno n. Warsaw (Poland), talk
- September 2009 — XV KKZMBiM, Szczyrk (Poland), talk
- September 2009 — XXI CEDYA/XI CMA, Cuidad Real (Spain), talk
- April 2010 — Workshop on Biomathematics, Madrid (Spain)
- September 2010 — XVI KKZMBiM, Krynica (Poland), talk
- June/July 2011 — 8th European Conference on Mathematical and Theoretical Biology, Kraków (Poland)), talk
- September 2011 — XVII KKZMBiM, Zakopane-Kościelisko (Poland), talk
- June 2012 — Workshop "Mathways into cancer", Almagro (Spain), talk
- September 2012 — Dynamic Days Europe 2012, Gothenburg (Sweden), organisation of mini-symposia, talk
- May 2013 — Mathways into Cancer II, Carmona (Spain), talk
- June 2013 — Between theory and applications — mathematics in action, Będlewo (Poland), inviated speaker
- September 2013 — XIX KKZMBiM, Jastrzębia Góra (Poland), talk
- July 2014 — AIMS' 10th International Conference on Dynamical Systems, Differential Equations and Applications, Madird (Spain), invited talk in special session and contributed talk
- September 2014 — XX KKZMBiM, Łochów (Poland), organiser
- March 2015 — Spring of Differential Equations, Gdańsk (Poland), talk
- May 2015 — Between theory and applications — mathematics in action, Będlewo (Poland), inviated speaker
- June 2015 — Micro and Macro Systems in Life Sciences, Będlewo (Poland), talk