
Colorectal cancer exhibits complex dynamics driven by genomic heterogeneity, microbiome instability, and environmental exposures.Traditional tumor models often neglect these factors, limiting their ability to predict patient-specific treatment outcomes. In thiswork, we develop a structured population model treating colorectal cancer as a complex adaptive system, where tumor cells arecharacterized by a genomic radiosensitivity trait. The model incorporates nonlinear tumor growth, radiotherapy and chemotherapyeffects, phenotypic plasticity, and environmental interactions. We establish well-posedness, positivity, and boundedness of solutionsusing functional analysis techniques. An optimal control framework is formulated to determine personalized radiochemotherapyprotocols that minimize tumor burden while penalizing treatment toxicity. Analytical results reveal conditions for tumor eliminationand characterize evolutionary selection toward resistant subpopulations. Numerical simulations demonstrate the impact of genomicvariation on treatment response, highlight the emergence of therapy-resistant traits, and show that adaptive, personalized protocolsoutperform standard treatment schedules. This study provides a rigorous mathematical foundation for precision oncology, linkingtumor heterogeneity, environmental factors, and genomic information to optimized therapy design.
colorectal cancer, complex adaptive system, structured population model, optimal control, genomic radiosensitivity, personalized therapy, mathematical oncology
colorectal cancer, complex adaptive system, structured population model, optimal control, genomic radiosensitivity, personalized therapy, mathematical oncology
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