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<p>We present a mathematical model describing the interactions between cancer cells, cytotoxic T lymphocytes (CTLs), and monocytes within the tumor microenvironment. The model incorporates key immunological mechanisms, including tumor antigenicity, the Allee effect, and monocyte-mediated immune activation via MHCI cross-dressing. Using systems of nonlinear ordinary differential equations (ODEs), we derive analytical expressions for equilibrium points, evaluate their stability, and characterize bifurcations, such as saddle-node, Hopf, Bogdanov–Takens, and Bautin. A reduced model via quasi-steady-state approximation (QSSA) is also proposed, preserving the core dynamic structure to facilitate bifurcation analysis. A central finding of our study is the critical role of the monocyte-mediated T cell activation rate, denoted by the parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>, which encapsulates the immunostimulatory potential of inflammatory monocytes presenting tumor antigens via MHCI cross-dressing. Numerical continuation corroborates the existence of multiple codimension-two organizing centers, delineating parameter regimes of tumor clearance, immune-mediated control, bistability, sustained oscillations, and inevitable escape. Our results quantitatively characterize the critical role of the monocyte-T-cell activation rate (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>) and the Allee threshold (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>) in tipping the balance between immune surveillance and tumor persistence. This framework provides actionable bifurcation-based criteria for designing combination immunotherapies that enhance antigen presentation or monocyte functionality to shift the system toward tumor-eliminating attractors.</p>

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Immune Modulation in the Tumor Microenvironment: Bifurcation Analysis of Cancer-CTL-Monocyte Dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月24日

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  • Eymard Hernandez-Lopez,
  • Russell Milne,
  • Xiunan Wang

摘要

We present a mathematical model describing the interactions between cancer cells, cytotoxic T lymphocytes (CTLs), and monocytes within the tumor microenvironment. The model incorporates key immunological mechanisms, including tumor antigenicity, the Allee effect, and monocyte-mediated immune activation via MHCI cross-dressing. Using systems of nonlinear ordinary differential equations (ODEs), we derive analytical expressions for equilibrium points, evaluate their stability, and characterize bifurcations, such as saddle-node, Hopf, Bogdanov–Takens, and Bautin. A reduced model via quasi-steady-state approximation (QSSA) is also proposed, preserving the core dynamic structure to facilitate bifurcation analysis. A central finding of our study is the critical role of the monocyte-mediated T cell activation rate, denoted by the parameter \(\beta \) β , which encapsulates the immunostimulatory potential of inflammatory monocytes presenting tumor antigens via MHCI cross-dressing. Numerical continuation corroborates the existence of multiple codimension-two organizing centers, delineating parameter regimes of tumor clearance, immune-mediated control, bistability, sustained oscillations, and inevitable escape. Our results quantitatively characterize the critical role of the monocyte-T-cell activation rate ( \(\beta \) β ) and the Allee threshold ( \(\gamma \) γ ) in tipping the balance between immune surveillance and tumor persistence. This framework provides actionable bifurcation-based criteria for designing combination immunotherapies that enhance antigen presentation or monocyte functionality to shift the system toward tumor-eliminating attractors.