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Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation

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  • Yong Dam Jeong
  • Kwang Su Kim
  • Yunil Roh
  • Sooyoun Choi
  • Shingo Iwami
  • Il Hyo Jung

Abstract

Cancer chemotherapy has been the most common cancer treatment. However, it has side effects that kill both tumor cells and immune cells, which can ravage the patient’s immune system. Chemotherapy should be administered depending on the patient’s immunity as well as the level of cancer cells. Thus, we need to design an efficient treatment protocol. In this work, we study a feedback control problem of tumor‐immune system to design an optimal chemotherapy strategy. For this, we first propose a mathematical model of tumor‐immune interactions and conduct stability analysis of two equilibria. Next, the feedback control is found by solving the Hamilton–Jacobi–Bellman (HJB) equation. Here, we use an upwind finite‐difference method for a numerical approximate solution of the HJB equation. Numerical simulations show that the feedback control can help determine the treatment protocol of chemotherapy for tumor and immune cells depending on the side effects.

Suggested Citation

  • Yong Dam Jeong & Kwang Su Kim & Yunil Roh & Sooyoun Choi & Shingo Iwami & Il Hyo Jung, 2022. "Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:2158052
    DOI: 10.1155/2022/2158052
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    References listed on IDEAS

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    1. Richard Bellman, 1954. "On some applications of the theory of dynamic programming to logistics," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(2), pages 141-153, June.
    2. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
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    Cited by:

    1. Sooyoun Choi & Yunil Roh & Yong Dam Jeong & Il Hyo Jung, 2025. "Prevention of EMT‐Mediated Metastasis via Optimal Modulation Strategies for the Dysregulated WNT Pathway Interacting With TGF‐β," Complexity, John Wiley & Sons, vol. 2025(1).

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