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Dynamic analysis and optimal control of a stochastic tumor-immune model

Author

Listed:
  • Wang, Xi
  • Liu, Zijian
  • Tan, Yuanshun
  • Mu, Yu

Abstract

Competition between tumor cells and normal tissue cells due to limited resources is considered as a key dynamic in tumor development. Therefore, in this paper, we develop a stochastic model of the interaction between tumor cells, helper T cells, effector cells, and host cells. The existence and uniqueness of the global positive solutions, stochastic eventual boundedness, and stochastic persistence of the model are proved by establishing appropriate Lyapunov functions. Additionally, we derive the threshold condition for tumor cell extinction and investigate the system’s steady-state distribution. Furthermore, we obtain the optimal control strategy through stochastic control theory. The results and numerical simulations demonstrate that stochastic perturbations can inhibit tumor cell growth, the control strategy can accelerate tumor extinction while reducing damage to effector cells, and increasing the competition coefficient of normal tissue cells against tumor cells can accelerate tumor extinction.

Suggested Citation

  • Wang, Xi & Liu, Zijian & Tan, Yuanshun & Mu, Yu, 2026. "Dynamic analysis and optimal control of a stochastic tumor-immune model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 244(C), pages 45-69.
    • Handle: RePEc:eee:matcom:v:244:y:2026:i:c:p:45-69
    DOI: 10.1016/j.matcom.2025.12.010
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