Nonlinear Model for Cancer Dynamics
DOI:
https://doi.org/10.54536/ajamr.v2i1.7397Keywords:
Chaos Theory, Delay Differential Equations, Dynamical Systems, Nonlinear Model, TumorAbstract
This study proposes a nonlinear model for cancer dynamics over a 12-month period, using delay differential equations (DDEs) inspired by the Lorenz system. The modeling focuses solely on the internal evolution of the tumor, excluding any interaction with the immune system or clinical treatments, and emphasizes cellular proliferation, mutation, and angiogenesis. The model progressively incorporates the delay parameter τ, which represents biological memory effects, allowing for the analysis of dynamic transitions in the system from stability to chaotic behavior. The approach employs tools from chaos theory, bifurcation analysis, and dynamic systems, with tumor behavior graphically represented through phase portraits (z(t)×y(t)). Numerical simulations were carried out using the fourth-order Runge-Kutta method, implemented in Python, and supported by the NumPy, SciPy, and Matplotlib libraries. The results show that cancer can evolve from a stable state to highly disordered dynamics as time progresses and memory effects intensify, reflecting patterns observed in aggressive tumors. This model contributes to a deeper understanding of the complexity of tumor growth and may serve as a foundation for future predictive strategies in precision medicine.
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