zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The triplex vaccine effects in mammary carcinoma: a nonlinear model in tune with SimTriplex. (English) Zbl 06118750
Summary: This paper deals with the mathematical modeling of the mammary carcinoma-immune system competition elicited by an external stimulus represented by three different protocols of the triplex vaccine [C. De Giovanni, et al., Immunoprevention of HER-2/neu transgenic mammary carcinoma through an interleukin 12-engineered allogeneic cell vaccine, Cancer Research 64 (2004) 4001 -- 4009]. The presented model is composed of nonlinear ordinary differential equations based on parameters and cell populations. A qualitative analysis of the asymptotic behavior of the model and numerical simulations are able to depict preclinical experiments on transgenic mice in tune with the SimTriplex model [F. Pappalardo, F. Castiglione, P.L. Lollini, S. Motta, Modelling and simulation of cancer immunoprevention vaccine, Bioinformatics 21 (2005) 2891 -- 2897]. The results are of great interest both in the applied and theoretical sciences.

92C60Medical epidemiology
Full Text: DOI
[1] Bar-Yam, Y.: Dynamics of complex systems, Studies in nonlinearity (2003) · Zbl 1074.37041
[2] Bianca, C.; Bellomo, N.: Towards a mathematical theory of complex biological systems, Series in mathematical biology and medicine 11 (2011) · Zbl 1286.92003
[3] Bianca, C.; Pennisi, M.: Immune system modelling by top-down and bottom-up approaches, International mathematical forum 7, 109-128 (2012) · Zbl 1250.92017
[4] Eftimie, R.; Bramson, J. L.; Earn, D. J. D.: Interactions between the immune system and cancer: a brief review of non-spatial mathematical models, Bulletin of mathematical biology 73, 2-32 (2011) · Zbl 1209.92028 · doi:10.1007/s11538-010-9526-3
[5] Baker, C. T. H.; Bocharov, G. A.; Paul, C. A. H.: Mathematical modelling of the interleukin-2 T-cell system: a comparative study of approaches based on ordinary and delay differential equations, Journal of theoretical medicine 2, 117-128 (1997) · Zbl 0904.92022 · doi:10.1080/10273669708833012
[6] Perelson, A. S.; Weisbuch, G.: Immunology for physicists, Reviews of modern physics 69, 1219-1268 (1997)
[7] Přiikrylovà, D.; Jìlek, M.; Waniewski, J.: Mathematical modeling of the immune response, (1992)
[8] De Giovanni, C.: Immunoprevention of HER-2/neu transgenic mammary carcinoma through an interleukin 12-engineered allogeneic cell vaccine, Cancer research 64, 4001-4009 (2004)
[9] Pappalardo, F.; Castiglione, F.; Lollini, P. L.; Motta, S.: Modelling and simulation of cancer immunoprevention vaccine, Bioinformatics 21, 2891-2897 (2005)
[10] Jorcyk, C. L.; Kolev, M.; Tawara, K.; Zubik-Kowal, B.: Experimental versus numerical data for breast cancer progression, Nonlinear analysis: RWA 13, 78-84 (2012) · Zbl 1238.92021
[11] Ko, W.; Ahn, I.: Diffusive tumor-immune interaction systems under immunotherapy, Nonlinear analysis: RWA 12, 3035-3045 (2011) · Zbl 1231.35270 · doi:10.1016/j.nonrwa.2011.05.005
[12] Wang, K.; Fan, A.; Torres, A.: Global properties of an improved hepatitis B virus model, Nonlinear analysis: RWA 11, 3131-3138 (2010) · Zbl 1197.34081 · doi:10.1016/j.nonrwa.2009.11.008
[13] Tao, Y.: Global existence for a haptotaxis model of cancer invasion with tissue remodeling, Nonlinear analysis: RWA 12, 418-435 (2011) · Zbl 1205.35144 · doi:10.1016/j.nonrwa.2010.06.027
[14] Alemani, D.: Combining cellular automata and lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition, Journal of immunological methods (2012)
[15] Ahn, I.; Park, J.: Drug scheduling of cancer chemotherapy based on natural actor--critic approach, Biosystems 106, 121-129 (2011)
[16] Clare, S. E.; Nakhlis, F.; Panetta, J. C.: Molecular biology of breast cancer metastasis. The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer, Breast cancer research 2, 430-435 (2000)
[17] Roitt, I.: Essential immunology, (1994)
[18] Haslam, S. Z.; Woodward, T. L.: Epithelial-cell-stromal-cell interactions and steroid hormone action in normal and cancerous mammary gland, Breast cancer research 5, 208-215 (2003)
[19] Lollini, P. L.; Motta, S.; Pappalardo, F.: Discovery of cancer vaccination protocols with a genetic algorithm driving an agent based simulator, BMC bioinformatics 7 (2006)
[20] Palladini, A.: In silico modeling and in vivo efficacy of cancer preventive vaccinations, Cancer research 70, 7755-7763 (2010)
[21] Pappalardo, F.; Cincotti, A.; Motta, S.; Pennisi, M.: Agent based modeling of atherosclerosis: a concrete help in personalized treatments, Lecture notes in artificial intelligence 5755, 386-396 (2009)
[22] Pappalardo, F.; Musumeci, S.; Motta, S.: Modeling immune system control of atherogenesis, Bioinformatics 24, 1715-1721 (2008)
[23] Pennisi, M.; Pappalardo, F.; Motta, S.: Agent based modeling of lung metastasis-immune system competition, Lecture notes in computer science 5666, 1-3 (2009)
[24] Pennisi, M.; Pappalardo, F.; Palladini, A.; Nicoletti, G.; Nanni, P.; Lollini, P. -L.; Motta, S.: Modeling the competition between lung metastases and the immune system using agents, BMC bioinformatics 11, No. Suppl. 7 (2010)
[25] M. Pennisi, C. Bianca, F. Pappalardo, S. Motta, Modeling artificial immunity against mammary carcinoma, in: Proc. 10th Int. Conf. on Math. Meth. in Sci. and Eng., CMMSE 2010, 2010, pp. 753--756, ISBN: 978-84-613-5510-5.
[26] Bianca, C.; Pennisi, M.; Motta, S.; Ragusa, M. A.: Immune system network and cancer vaccine, AIP conference Proceedings 1389, 945-948 (2011)
[27] Schlub, T. E.: Comparing the kinetics of NK cells, CD4, and CD8 T cells in murine cytomegalovirus infection, Journal of immunology 187, 1385-1392 (2011)
[28] Lollini, P. L.; Motta, S.; Pappalardo, F.: Modeling tumor immunology, Mathematical models and methods in applied sciences 16, 1091-1124 (2006) · Zbl 1099.92036 · doi:10.1142/S0218202506001479
[29] Alarcon, T.; Byrne, H.; Maini, P.: A cellular automation model for tumor growth in inhomogeneous environment, Journal of theoretical biology 225, 257-274 (2003)
[30] Gerlee, P.; Anderson, A.: Evolution of cellmotility in an individual-based model of tumor growth, Journal of theoretical biology 259, 67-83 (2009)
[31] Pappalardo, F.; Motta, S.; Lollini, P. L.; Mastriani, E.: Analysis of vaccine’s schedule using models, Cell immunology 244, 137-140 (2004)
[32] Malet, D.; De Pillis, L.: A cellular automatamodel of tumor-immune system interactions, Journal of theoretical biology 239, 334-350 (2006)
[33] Nowak, M. A.; Sigmund, K.: Evolutionary dynamics of biological games, Science 303, 793-799 (2004)
[34] Bianca, C.: Mathematical modeling for keloid formation triggered by virus: malignant effects and immune system competition, Mathematical models and methods in applied sciences 21, 389-419 (2011) · Zbl 1218.35236 · doi:10.1142/S021820251100509X
[35] Bellouquid, A.; De Angelis, E.: From kinetic models of multicellular growing systems to macroscopic biological tissue models, Nonlinear analysis: RWA 12, 1111-1122 (2011) · Zbl 1203.92020 · doi:10.1016/j.nonrwa.2010.09.005
[36] Bianca, C.: Kinetic theory for active particles modelling coupled to Gaussian thermostats, Applied mathematical sciences 6, 651-660 (2012) · Zbl 1250.82025
[37] Bianca, C.; Fermo, L.: Bifurcation diagrams for the moments of a kinetic type model of keloid-immune system competition, Computers and mathematics with applications 61, 277-288 (2011) · Zbl 1211.37102 · doi:10.1016/j.camwa.2010.11.003
[38] He, Y.; Rappuoli, R.; De Groot, A. S.; Chen, R. T.: Emerging vaccine informatics, Journal of biomedicine and biotechnology (2010)
[39] Drucis, K.; Kolev, M.; Majdaa, W.; Zubik-Kowal, B.: Nonlinear modeling with mammographic evidence of carcinoma, Nonlinear analysis: RWA 11, 4326-4334 (2010) · Zbl 1197.92026 · doi:10.1016/j.nonrwa.2010.05.017
[40] Coscia, V.: On the mathematical theory of living systems I: Complexity analysis and representation, Mathematical and computer modelling 54, 1919-1929 (2011) · Zbl 1235.92006
[41] Coscia, V.; Fermo, L.; Bellomo, N.: On the mathematical theory of living systems II: The interplay between mathematics and system biology, Computers and mathematics with applications 62, 3902-3911 (2011) · Zbl 1236.92005