A Stochastic Gompertz Model with Jumps for an Intermittent Treatment in Cancer Growth

  • Virginia Giorno
  • Serena Spina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8111)


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.


Return State Return Distribution Therapeutic Program Intermittent Treatment Return Point 
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  1. 1.
    Albano, G., Giorno, V.: A stochastic model in tumor growth. J. Theor. Biol. 242(2), 229–236 (2006)MathSciNetGoogle Scholar
  2. 2.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals Series and Products. Academic Press, Amsterdam (2007)zbMATHGoogle Scholar
  3. 3.
    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)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lo, C.F.: Stochastic Gompertz model of tumor cell growth. J. Theor. Biol. 248, 317–321 (2008)CrossRefGoogle Scholar
  5. 5.
    Migita, T., Narita, T., Nomura, K.: Activation and Therapeutic Implications in Non-Small Cell Lung Cancer. Cancer Research 268, 8547–8554 (2008)CrossRefGoogle Scholar
  6. 6.
    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)zbMATHGoogle Scholar
  7. 7.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Virginia Giorno
    • 1
  • Serena Spina
    • 2
  1. 1.Dipartimento di Studi e Ricerche Aziendali, (Management & Information Technology)Università di SalernoFiscianoItaly
  2. 2.Dipartimento di MatematicaUniversità di SalernoFiscianoItaly

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