| Abstract: |
| This work explores a mathematical model of tumor-immune
interactions that incorporates Allee effects to capture the nuances of
cooperative tumor growth. Through bifurcation analysis and numerical
continuation, we identify and characterize saddle-node, Hopf, Bautin,
and Bogdanov-Takens bifurcations, further establishing a formal proof
of a codimension-three bifurcation within a biologically relevant
parameter space. The findings provide a theoretical foundation for
understanding the critical transitions between the elimination,
equilibrium, and escape phases of cancer immunoediting, highlighting
the underlying mechanisms that drive clinical outcomes. |
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