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    This study introduces an iterative algorithm for optimizing lung cancer drug delivery. The ecological model and HJB equation demonstrate an effective strategy for inhibiting cancer cell growth.

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    Area of Science:

    • Oncology
    • Mathematical Biology
    • Pharmacology

    Background:

    • Lung cancer cell proliferation and apoptosis are complex processes influenced by the immune system and drug interventions.
    • Developing optimal drug delivery schemes is crucial for effective cancer treatment.
    • Existing models may not fully capture the ecological dynamics of cancer cell growth under treatment.

    Purpose of the Study:

    • To propose an extend-policy iterative algorithm for an optimal drug delivery scheme targeting lung cancer.
    • To develop an ecological containment model for lung cancer cells considering immune system interactions and drug effects.
    • To establish the Hamilton-Jacobi-Bellman (HJB) equation for biological tissue damage in the context of lung cancer treatment.

    Main Methods:

    • Construction of an ecological containment model for lung cancer cells.
    • Analysis of cell proliferation-apoptosis dynamics under chemotherapeutic and immunological agents.
    • Derivation of the HJB equation incorporating lung cancer cell concentration and drug dosage.
    • Application of an extend-policy iterative algorithm for optimization.

    Main Results:

    • The proposed algorithm effectively addresses the ecological evolving-lung cancer cells growth inhibition problem.
    • The developed model accurately mimics cancer cell dynamics under various interventions.
    • Simulation experiments validated the effectiveness of the optimized drug delivery scheme.

    Conclusions:

    • The extend-policy iterative algorithm provides a robust method for optimizing lung cancer drug delivery.
    • The ecological model and HJB equation offer valuable insights into cancer treatment dynamics.
    • The study demonstrates a promising approach for personalized and effective lung cancer therapy.