Abstract
In this paper the interaction between cancer and immunological system is analysed. The model is a modification of a one proposed by de Vladar and Gonzales. For our model the stability is analysed. Furthermore, the effect of a therapy schedule with fixed concentration is investigated. Mathematically, the effect of therapy is viewed as a moderating term both for tumor cell growth rate and for T-cells death rate. In conclusion, a systematic computational analysis is associated to the obtained theoretical results.
Keywords
Work performed under partial support by MIUR (PRIN 2005) G.N.C.S-INdAM.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Albano, G., Giorno, V.: A stochastic model in tumor growth. J. Theor. Biol. 242(2), 229–236 (2006)
de Vladar, H.P., Gonzalez, J.A.: Dynamic response of cancer under the influence of immunological activity and therapy. J. Theor. Biol. 227(3), 335–348 (2004)
Dunn, G., Bruce, A., Ikeda, H., Old, L., Schreiber, R.: Cancer immunoediting: from immunosurveillance to tumor escape. Nat. Immunol. 3(11), 991–998
Galach, M.: Dynamics of the tumor-immune system competition-the effect of time delay. Int. J. Appl. Math. Comput. Sci. 13(3), 395–406 (2004)
Kozusko, F., Bajzer, Z.: Combining Gompertzian growth and cell population dynamics. Mathematical Biosciences (2003) 185, 153–167 (2004)
Loddo, R., Busonera, B., La Colla, P., Filona, R., Buonerba, M., Saturnino, C.: N,No (4,5-dihydro-1H-imidazol-2-yl)3-aza-1,10-decane-diamine and N,No (4,5-dihydro-1H-imidazol-2-yl)3-aza-1,10-dodecane-diamine antagonize cell proliferation as selective ligands towards the topoisomerase II, J. Pharmacy and Pharmacology (in press) (2006)
de Pillis, L.G., Radunskaya, A.: A mathematical model of immune response to tumor invasion. Computational Fluid and Solid Mechanics (2003)
Stepanova, N.: Course of the immune reaction during the development of a malignant tumor. Biophysics 24, 917–923 (1980)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Albano, G., Giorno, V., Saturnino, C. (2007). A Prey-Predator Model for Immune Response and Drug Resistance in Tumor Growth. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2007. EUROCAST 2007. Lecture Notes in Computer Science, vol 4739. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75867-9_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-75867-9_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75866-2
Online ISBN: 978-3-540-75867-9
eBook Packages: Computer ScienceComputer Science (R0)