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.
Work performed under partial support by MIUR (PRIN 2005) G.N.C.S-INdAM.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-540-75867-9_22
Publisher Name: Springer, Berlin, Heidelberg
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