Abstract
To analyze the effect of a therapeutic program that provides intermittent suppression of cancer cells, we suppose that the Gompertz stochastic diffusion process is influenced by jumps that occur according to a probability distribution, producing instantaneous changes of the system state. In this context a jump represents an application of the therapy that leads the cancer mass to a return state randomly chosen. In particular, constant and exponential intermittence distribution are considered for different choices of the return state. We perform several numerical analyses to understand the behavior of the process for different choices of intermittence and return point distributions.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Albano, G., Giorno, V.: A stochastic model in tumor growth. J. Theor. Biol. 242(2), 229–236 (2006)
Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals Series and Products. Academic Press, Amsterdam (2007)
Hirata, Y., Bruchovsky, N., Aihara, K.: Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer. J. Theor. Biol. 264, 517–527 (2010)
Lo, C.F.: Stochastic Gompertz model of tumor cell growth. J. Theor. Biol. 248, 317–321 (2008)
Migita, T., Narita, T., Nomura, K.: Activation and Therapeutic Implications in Non-Small Cell Lung Cancer. Cancer Research 268, 8547–8554 (2008)
Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G.: An outline of theoretical and algorithmic approches to first passage time problems with applications to biological modeling. Math. Japonica 50, 247–322 (1999)
Tanaka, G., Hirata, Y., Goldenberg, S.L., Bruchovsky, N., Aihara, K.: Mathematical modelling of prostate cancer growth and its application to hormone therapy. Phil. Trans. R. Soc. A 368, 5029–5044 (2010)
Wang, J., Tucker, L.A., Stavropoulos, J.: Correlation of tumor growth suppression and methionine aminopetidase-2 activity blockade using an orally active inhibitor. In: Matthews, B.W. (ed.) Global pharmaceutical Research and Development, Abbott Laboratories, University of Oregon, Eugene, OR (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giorno, V., Spina, S. (2013). A Stochastic Gompertz Model with Jumps for an Intermittent Treatment in Cancer Growth. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory - EUROCAST 2013. EUROCAST 2013. Lecture Notes in Computer Science, vol 8111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53856-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-53856-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53855-1
Online ISBN: 978-3-642-53856-8
eBook Packages: Computer ScienceComputer Science (R0)