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<p>Colon cancer is a high-risk malignant tumor worldwide. To address the limited efficacy and overlapping toxicity of current chemoimmunotherapy, this study establishes a fractional-order colon cancer model with a core architecture capturing the probiotics-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hbox {CD4}^{+}\)</EquationSource> </InlineEquation>T cells-tumor cells axis. The primary theoretical contributions include: rigorous proof of solution existence and uniqueness through fixed-point theory. Analytical derivation of equilibrium stability conditions using the Routh-Hurwitz criterion. Numerical simulations systematically quantify how the fractional parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation> governs system dynamics and memory effects, while identifying critical drug dosage thresholds for tumor clearance. These findings provide a mathematical foundation for optimizing probiotic-based combination therapies.</p>

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Dynamic stability analysis of a fractional calculus-based colon cancer model with therapeutic interventions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月10日

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  • Ruilei Tai,
  • Zhaoyang Chen,
  • Yanling Zhao,
  • Ruiqing Shi

摘要

Colon cancer is a high-risk malignant tumor worldwide. To address the limited efficacy and overlapping toxicity of current chemoimmunotherapy, this study establishes a fractional-order colon cancer model with a core architecture capturing the probiotics- \(\hbox {CD4}^{+}\) T cells-tumor cells axis. The primary theoretical contributions include: rigorous proof of solution existence and uniqueness through fixed-point theory. Analytical derivation of equilibrium stability conditions using the Routh-Hurwitz criterion. Numerical simulations systematically quantify how the fractional parameter \(\alpha\) governs system dynamics and memory effects, while identifying critical drug dosage thresholds for tumor clearance. These findings provide a mathematical foundation for optimizing probiotic-based combination therapies.