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Mathematical Modeling of Cancer Inhibition Through Localized Radiation Therapy

In: Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells

Author

Listed:
  • Ibrahim Nali

    (University of Szeged, Bolyai Institute)

  • Attila Dénes

    (University of Szeged, Bolyai Institute
    National Laboratory for Health Security)

  • Abdessamad Tridane

    (United Arab Emirates University, Emirates Center for Mobility Research)

Abstract

This study investigates the possibility of halting the spread of cancer within tissue by acting on a small, targeted area through radiation therapy. Using reaction-diffusion equations, we model the dynamics of cancer proliferation, which are represented by traveling wave solutions. These waves illustrate how cancer cells invade healthy tissue. We propose a method to block this invasion by calculating the critical gap length L ∗ $$L^*$$ , which represents the minimum area where radiation can effectively stop the wave of cancerous growth. By adapting the geometric approach of Lewis and Keener, we apply a localized dose of radiation, creating a barrier to the spread of cancer cells. Numerical simulations are performed to support our theoretical findings, offering potential applications to improve localized radiation treatments to prevent the progression of cancer within affected tissues.

Suggested Citation

  • Ibrahim Nali & Attila Dénes & Abdessamad Tridane, 2025. "Mathematical Modeling of Cancer Inhibition Through Localized Radiation Therapy," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, pages 135-145, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-97461-8_7
    DOI: 10.1007/978-3-031-97461-8_7
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