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Chaos in Cancer Tumor Growth Model with Commensurate and Incommensurate Fractional-Order Derivatives
Nadjette Debbouche1, Adel Ouannas1, Giuseppe Grassi2
1Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria.
Computational and Mathematical Methods in Medicine
|May 31, 2022
Summary
This study introduces a novel fractional-order differential equation model for cancer growth dynamics. The research reveals chaotic behaviors in tumor-immune system interactions, offering insights for improved cancer therapies.
Area of Science:
- Mathematical Oncology
- Dynamical Systems Theory
- Fractional Calculus
Background:
- Understanding tumor-immune system dynamics is crucial for developing effective cancer treatments.
- Existing models may not fully capture the complex interactions within the tumor microenvironment.
Purpose of the Study:
- To propose a new mathematical model for cancer growth dynamics using fractional-order differential equations.
- To investigate the chaotic behaviors inherent in tumor-immune system interactions.
- To contribute novel insights into cancer progression and potential therapeutic strategies.
Main Methods:
- Development of a novel cancer growth model based on fractional-order differential equations.
- Analysis of system dynamics, including commensurate and incommensurate fractional orders.
- Utilizing bifurcation diagrams, Lyapunov exponents, and phase plots to characterize model behavior.
Main Results:
- The proposed fractional-order model exhibits complex and chaotic dynamics.
- Chaotic behaviors were observed in both commensurate and incommensurate cases, indicating system sensitivity.
- Bifurcation diagrams and Lyapunov exponents confirmed the presence of chaos.
Conclusions:
- Fractional-order modeling provides a powerful framework for analyzing intricate tumor-immune dynamics.
- The identified chaotic behaviors suggest potential for complex, unpredictable tumor progression.
- These findings can inform the design of more sophisticated and targeted cancer therapies.
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