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Marek Bodnar, Ph.D.

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

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.

Thesis

• 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

• July 1st, 2011 – now — 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

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

My publications:

Papers after referee process:

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. M. Bodnar, M.J. Piotrowska, O równaniach różniczkowych z opóźnieniem — teoria i zastosowania, Mat. Stos. 11/52, (2010), 18–56.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. M. Bodnar, U. Foryś, Time delay in necrotic core formation, Math. Biosci. Eng., 2, 3, (2005), 461–472.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. 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.
22. M. Bodnar, U. Foryś, Behaviour of Marchuk's model depending on time delay, Intern. J. Appl. Math. Comput. Sci. 10, 1, (2000), 97–112.
23. 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. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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:

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.

Preprints:

1. M. Bodnar, An integro-differential equation arising as a limit of an individual cell-based models: the case of bounded domain, preprint of Institute of Applied Mathematics and Mechanics Warsaw University, No. 181, 2008.
2. M. Bodnar, U. Foryś›, A model of the immune system with time-dependent immune reactivity, preprint of Institute of Applied Mathematics and Mechanics Warsaw University, RW 99-04 (52), February 1999.

mbodnar@mimuw.edu.pl