| Our Publications within RTN Project
|
| S.D. Angus and M.J. Piotrowska, Towards a 3D Cellular Automaton Model of Mulicellular Spheroids. Proc. XIV National Conference on Application of
Mathematics in Biology and Medicine, Leszno,17-20 September 2008, 6-11, WMIM UW, 2008. |
| L. Arlotti, A. Deutsch, M. Lachowicz, On a discrete Boltzmann-type model of swarming, Math. Comput. Model., 41 (10), 1193-1201, 2005. |
| J. Banasiak, M. Lachowicz, M. Moszyński, Chaotic behavior of semigroups related to the process of gene amplification-deamplification
with cell proliferation, Math. Biosci., 206, 200-215, 2007. |
| J. Banasiak, M. Lachowicz, M. Moszyński, Semigroups for generalized birth-and-death equations in l^p spaces, Semigroup Forum, 73, 175-193, 2006. |
| M. Bodnar, U. Foryś, Angiogenesis model with carrying capacity depending on vessel density, J. Biol. Sys., 17(1), 1–25, 2009. |
| M. Bodnar, U. Foryś, Three types of simple DDE'S describing tumor growth, J. Biol. Syst., 15, 453–471, 2007. |
| M. Bodnar, J.J.L. Velazquez, An integro-differential equation arising as a limit of individual cell-based models,
J. Diff. Equations., 222 (2), 341 – 380, 2006. |
| M. Bodnar, U. Foryś, Time delay in necrotic core formation, Math. Bio. Eng., 2 (3), 461 – 472, 2005. |
| C. Morales-Rodrigo, Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours
Mathematical and Computer Modelling, 47 (5-6), 604-613, (2008). |
| T. Cieslak, C. Morales-Rodrigo, Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume
filling effect. Existence and uniqueness of global-in-time solutions, Topoligical Methods in Nonlinear Analysis, 29(2), 361-382, 2007. |
| T. Cieslak, P. Laurencot, C. Morales-Rodrigo, Global existence and convergence to steady-states in a chemorepulsion system, preprint, Banach Center Publications. |
| U. Foryś, Comparison of the models for carcinogenesis mutations - one-stage case. Proceedings of the tenth National Conference on Applications of Mathematics in Biology and Medicine; Święty Krzyż, 22-25 September 2004. |
| U. Foryś, Stability analysis and comparison of the models for carcinogenesis mutations in the case of two stages of mutations,
Journal of Applied Analysis, 11(2), 283-302, 2005. |
| U. Foryś, Time delays in one-stage models for carcinogenesis mutations. Proceeding of the 11th National Conference on Application of Mathematics
in Biology and Medicine, Zawoja, 21-24, September 2005, 13-18. |
| U. Foryś, Y. Kheifetz, Y. Kogan, Critical-point analysis for three-variable cancer angiogenesis models. Math. Biosci. Eng., 2(3), 511-525, 2005. |
| U. Foryś, A. Mokwa-Borkowska, Solid tumour growth. Analysis of necrotic core formation. Math. Comp. Modell., 42, 593-600, 2005. |
| U. Foryś, J. Waniewski, P. Zhivkov, Anti-tumor immunity and tumor anti-immunity in a mathematical model of tumor immunotherapy. J. Biol. Sys., 14(1), 1-18, 2006. |
| J. Gomułkiewicz, J. Miękisz, S. Miękisz, Ion Transport Through Cell Membrane Channels, preprint. |
| M. Kolev, E. Kozlowska, M. Lachowicz, A mathematical model for single cell cancer - immune system dynamics, Math. Comput. Model., 41, 10, 1083-1095, 2005. |
| R. Kowalczyk, Preventing Blow-up in a Chemotaxis Model. J. Math. Anal. Appl. 305, 566-588, 2005. |
| R. Kowalczyk, Z. Szymańska, On the global existence of solutions to an aggregation model, J. Math. Anal. Appl., 343, 379-398, 2008. |
| M. Lachowicz, Links Between Microscopic and Macroscopic Descriptions. In Multiscale Problems in the Life Science. From Microscopic to Macroscopic, pp. 201-268, Springer, 2008. |
| M. Lachowicz, A model of swarming and its macroscopic limit. Proc. 10th Natianal Conf. on Application of matheamtics in Biology and Medicine, 113-117, University of Cpomputer Enguneering and Telecommunications in Kielce, 2004. |
| M. Lachowicz, General population systems. Macroscopic limit of a class of stochastic semigroups, J. Math. Anal. Appl., 307/2, 585-605, 2005. |
| M. Lachowicz, Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours, Math. Models Methods Appl. Sci., 15, 1667-1683, 2005. |
| M. Lachowicz, Stochastic semigroups and coagulation equations, Ukrainian Math. J., 57, 6, 770-777, 2005. |
| M. Lachowicz, Towards Microscopic and Nonlocal Models of Tumour Invasion of Tissue. In: Selected Topics in Cancer Modeling. Genesis, Evolution Immune Competition and Therapy,
pp.49-63, Birkhauser, 2008. |
| M.J. Piotrowska, S.D. Angus: A Quantitative Cellular Automaton Model of in vitro Multicellular Spheroid Tumour Growth, Journal of
Theoretical Biology, 258, 165-178, 2009. |
| M.J. Piotrowska, E. Mamontov, A. Peterson and A. Koptyug, A model and simulation for homeorhesis in the motion of a single individual.
Math. and Comp. Modelling 48, 1122-1142, 2008. |
| M.J. Piotrowska, Hopf Bifurcation in a Solid Avascular Tumour Growth Model with two Discrete Delays. Math. and Comp. Modelling 47, 597-603, 2008. |
| M.J. Piotrowska, H. Enderling, M. C. Mackey and U. an der Heiden, Mathematical Modelling of Stem Cells Related to Cancer.
In: Cancer and Stem Cells, pp. 11-36, Eds.: T. Dittmar, K. S. Zaenker, NovaScience Publisher, Hauppauge, NY, 2008. |
| M.J. Piotrowska, A remark on the ODE with two discrete delays. J. Math. Anal. Appl. 329, 664-676, 2007. |
| M.J. Piotrowska, D. Widera, C. Kaltschmidt, B. Kaltschmidt and U. an der Heiden, Mathematical model for NF-kappaB driven
proliferation of adult neural stem cells. Cell Proliferation 39(6), 441-455, 2006. |
| M.J. Piotrowska: Activator - Inhibitor System with Delay and Pattern Formation. Math. and Comp. Modelling 42, 123-131, 2005. |
| M.J. Piotrowska, U. Foryś, Time Delays in Sold Avascular Tumour Growth. Proceedings of the Tenth National
Conference on Applications of Mathematics in Biology and Medicine; Święty Krzyż, 22-25 September 2004. |
| Z. Szymanska, C. Morales-Rodrigo, M.Lachowicz, M.A.J. Chaplain, Mathematical modelling of cancer invasion of tissue:
the role and effect of nonlocal interactions, Math. Models Methods Appl. Sci., 19, 257-281, 2009. |
| Szymańska, Z., Urbański, J., Marciniak-Czochra, A., Mathematical modelling of the influence
of heat shock proteins on cancer invasion of tissue, J. Math. Biol., 58(4-5), 819-44, 2009. Epub 2008 Sep 20. |
| Z. Velkov, M. Kolev, A. Tadjer, Modeling and statistical analysis of DPPH scavenging activity of phenolics, Collect. Czech. Chem. Commun. 72(11), 1461-1471, 2007. |
| Our Old Publications
|
| L. Arlotti, N. Bellomo, M. Lachowicz, Kinetic equations modelling population dynamics, Transport Theory Statist. Physics, 29, (1-2), 2000, 125-139. |
| L. Arlotti, N. Bellomo, E. De Angelis, M. Lachowicz, Generalized Kinetic Models in Applied Sciences. Lecture Notes on Mathematical Problems, World Sci., New Jersey 2003. |
| L. Arlotti, A. Gamba, M. Lachowicz, A kinetic model of tumor - immune system cellular interactions, J. Theoret. Medicine, 4 (1), 2002, 39-50. |
| L. Arlotti, M. Lachowicz, Qualitative analysis of an equation modelling tumor - host dynamics, Math. Comput. Model., 23, (6), 1996, 11-29. |
| N. Bellomo, M. Lachowicz, J. Polewczak, On a mathematical model in theoretical immunology, Appl. Math. Lett., 10, (4), 1997, 53-58. |
| J. Banasiak, M. Lachowicz, Chaotic linear dynamical systems with applications, The Proceedings of the 2nd International Conference on Semigroups of Operators:
Theory and Applications SOTA 2, Rio de Janeiro, 10-14 September 2001, Eds. C. Kubrusly, N. Levan, and M. da Silveira, Optimization Software, Los Angeles, 2002, 32-44. |
| J. Banasiak, M. Lachowicz, Topological chaos for birth - and - death - type models with proliferation, Math. Models Methods Appl. Sci., 12, 6, 2002, 755-775. |
| J. Banasiak, M. Lachowicz, M. Moszyński, Topological chaos: When topology meets medicine, Appl. Math. Lett., 16, 2003, 303-308. |
| M. Bodnar, 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. |
| M. Bodnar, Norm conservation for generalized kinetic population models with delay, Math. Comput. Modelling, 35, 7-8, 2002, 765-778. |
| 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, 25-28 September 2001, 21-26. |
| M. Bodnar, On the blow-up of solutions of delay differential equations. preprint RW 00-16 (83), November 2000, Institute of Applied Mathematics and Mechanics, Warsaw University |
| M. Bodnar, On the nonnegativity of solutions of delay differential equations, Appl. Math. Lett., 13,6 (2000), 91-95. |
| 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, 15-18 September 1998, 12-17 |
| M. Bodnar, U. Foryś, A model of immune system with time-depended immune reactivity, Non. Anal. Th. Meth. Appl., 70, 2, 2009, 1049–1058 |
| 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, Forest-pest interaction dynamics, Proceedings of the V National Conference Application of Mathematics in Biology and Medicine, Ustrzyki Górne, 14-17 września 1999, 15-20 |
| M. Bodnar, U. Foryś, Periodic dynamics of the model of immune system, Appl. Math. (Warsaw), 27(1), 2000, 113-126 |
| U. Foryś, Analysis of the model of coral reefs colony, proceeding of the IX National Conference on Mathematics Applied to Biology and Medicine, Piwniczna, 2003. |
| U. Foryś, Biological delay systems and the Mikhailov criterion of stability (accepted to J. Biol. Sys., preprint On the Mikhailov criterion and stability of delay differential equations, RW 01-14 (97) November 2001, Institute of Applied Mathematics and Mechanics, Warsaw University). |
| U. Foryś, Discrete mathematical model of an immune system, in Mathematical Population Dynamics, 2, Wuerz Publishing, 1995, 167 - 182. |
| U. Foryś, Global analysis of Marchuk's model in a case of strong immune system, J. Biol. Sys., 8 (4) (2000), 331 - 346. |
| U. Foryś, Global analysis of Marchuk's model in a case of weak immune system, Math. Comp. Modelling, 25 (6) (1997), 97 - 106. |
| U. Foryś, Global analysis of Marchuk's model of an immune system in some special cases, in proceedings of the I National Conference on Mathematics Applied to Biology and Medicine, Zakopane, 1995. |
| U. Foryś, Global analysis of the initial value problem for a system of ODE modeling the immune system after vaccinations, Math. Comp. Modelling, 29 (1999), 79 - 85. |
| U. Foryś, Global stability for some type of delay equations (accepted to Appl. Math. Letters, preprint RW 03-02 (123) January 2003, Institute of Applied Mathematics and Mechanics, Warsaw University). |
| U. Foryś, Hopf bifurcation in Marchuk's model of immune reactions, Math. Comp. Modelling, 34 (2001), 725-735. |
| U. Foryś, Interleukin mathematical model of an immune system, J. Biol. Sys., 3 (1995), 889 - 902. |
| U. Foryś, Marchuk's model of immune system dynamics with application to tumour growth, J. Theor. Medicine, 4 (1) (2002), 85-93. |
| U. Foryś, Mathematical model of an immune system in a case of vaccination, in proceedings of the II National Conference on Mathematics Applied to Biology and Medicine, Zakopane, 1996. |
| U. Foryś, Mathematical model of an immune system with random time of reaction, Appl. Math. (Warsaw) 21 (4) (1993), 521 - 536. |
| U. Foryś, Modele matematyczne w epidemiologii i immunologii, Matematyka Stosowana. Matematyka dla spoeczenstwa, 1 (2000). |
| U. Foryś, Professor Wiesaw Szlenk (1935 - 1995), Appl. Math. (Warsaw), 27 (1) (2000), 1 - 20. |
| U. Foryś, Professor Wiesaw Szlenk - life and activity, in proceedings of the IV National Conference on Mathematics Applied to Biology and Medicine, Zwierzyniec, 1998. |
| U. Foryś, Some remarks on the stability of chronic state in Marchuk's model depending on time delay, in proceedings of the VI National Conference on Mathematics Applied to Biology and Medicine, Zawoja, 2000. |
| U. Foryś, Time delays in avascular tumour growth, proceeding of the VII National Conference on Mathematics Applied to Biology and Medicine, Zawoja, 2001. |
| U. Foryś, The mathematical model of immune system with random time of reaction, in Lecture notes of the ICB seminars. Biosystems, ICB Warsaw 1992, 162 - 186. |
| U. Foryś, M. Bodnar, Time delays in in proliferation process for solid avascular tumour, Math. Comput. Modelling, 37 (2003) |
| U. Foryś, M. Bodnar, Time delays in regulatory apoptosis for solid avascular tumour, Math. Comput. Modelling, 37 (2003) |
| U. Foryś, M. Kolev, Time delays in proliferation and apoptosis for solid avascular tumour (accepted to Banach Center Publications, preprint RW 02-10 (110), August 2002, Institute of Applied Mathematics and Mechanics, Warsaw University). |
| U. Foryś, R. Kowalczyk, Qualitative analysis on the initial value problem to the logistic equation with delay, Math. Comp. Modelling, 35 (2002), 1-13. |
| U. Foryś, A. Marciniak-Czochra, Delay logistic equation with diffusion, proceedings of the VIII National Conference on Mathematics Applied to Biology and Medicine, Łajs, 2002. |
| U. Foryś, A. Marciniak-Czochra, Logistic equations in tumour growth modelling, Int. J. Appl. Math. Comp. Sci, 13 (3) (2003), 317-326. |
| U. Foryś, A. Mokwa-Borkowska, Solid tumour growth. Analysis of necrotic core formation (preprint RW 03-01 (122), January, 2003, Institute of Applied Mathematics and Mechanics, Warsaw University). |
| U. Foryś, J. Nowak, A. Mokwa-Borkowska, Some remarks on coral reefs, mathematical modelling and organic architecture of the future, proceedings of the VIII National Conference on Mathematics Applied to Biology and Medicine, Łajs, 2002. |
| U. Foryś, N. Żołek, A model of immune system after vaccinations, ARI, 50 (1998), 180 - 184. |
| U. Foryś, N. Żołek, Complementary analysis of the initial value problem for system of ODE modelling immune system after vaccinations, Appl. Math. (Warsaw), 27 (1) (2000), 103 - 111. |
| M. Lachowicz, Competition tumor - immune system, Proceedings of the Sixth National Conference on Application of Mathematics in Biology and Medicine, Zawoja, September 12-15, 2000, 89-93. |
| M. Lachowicz, Describing competitive systems at the level of interacting individuals, Proceedings of the Eighth National Conference on Application of Mathematics in Biology and Medicine, Łajs, September 24-27, 2002, 95-100. |
| M. Lachowicz, From microscopic to macroscopic description for generalized kinetic models, Math. Models Methods Appl. Sci., 12, 7, 2002, 985-1005. |
| M. Lachowicz, From microscopic to macroscopic descriptions of complex systems, Compt. Rend. Acad. Sci. Paris, Serie IIb, 2003, to appear. |
| M. Lachowicz, Nonlocal coagulation and fragmentation, Proceedings of the Fifth National Conference on Application of Mathematics in Biology and Medicine, Ustrzyki Górne, September 14-17, 1999, 93-98. |
| M. Lachowicz, Modele matematyczne w biologii, Matematyka Stosowana - Matematyka dla społeczeństwa, 1, 42, 2000, 3-34. |
| M. Lachowicz, On bilinear kinetic equations. Between micro and macro description of biological populations, Mathematical Modelling of Population Dynamics, Banach Center Publ., 217-230, 2004. |
| M. Lachowicz, Ph. Laurencot, D. Wrzosek, On the Oort-Hulst-Safranov coagulation equation and its relation to the Smoluchowski equation, SIAM J. Math. Anal., 34, 6, 2003-1421. |
| M. Lachowicz, D. Wrzosek, A nonlocal coagulation-fragmentation model, Appl. Math. (Warsaw), 27, (1), 2000, 45-66. |
| M. Lachowicz, D. Wrzosek, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci., 11, no. 8, 2001, 1393-1409. |
| M. Lachowicz, D. Wrzosek, Matematyczne modele zjawisk przyrodniczych, Matematyka, Społeczeństwo, Nauczanie, OKM, 15, 1995, 4 - 15. |
