This paper proposes and analyzes a class of fractional optimal control problems for lung cancer therapy, which combines surgical intervention with the administration of autologous ex vivo expanded immune T lymphocytes. The proposed combined therapy facilitates tumor cell elimination, enhances patient survival rates, and—by leveraging autologous expanded immune cells—minimizes adverse effects, thereby enabling the effective treatment of cancer patients at minimal cost. In the treatment process, according to the individual differences of patients, the treatment plan should be adjusted promptly, such as adjusting the use of immunotherapy drugs or deciding whether a second operation is needed, to achieve personalized precision medicine and maximize the treatment effect. In the numerical solution part, $ L1 $ discretization and the Adams-Bashforth-Moulton method were used to solve fractional differential equations, and the sensitivity analysis of parameters were carried out by the Latin hypercube sampling method to determine the robustness of the model. In the control part, a genetic algorithm was used to control the input $ u(t) $. We found the optimal $ u(t) $ to minimize the target value.
Citation: Wen Fang, Xuewen Tan, Yanbin Feng. Analysis and optimization control of lung cancer treatment based on surgical resection and immune cell therapy[J]. Networks and Heterogeneous Media, 2025, 20(2): 356-386. doi: 10.3934/nhm.2025017
This paper proposes and analyzes a class of fractional optimal control problems for lung cancer therapy, which combines surgical intervention with the administration of autologous ex vivo expanded immune T lymphocytes. The proposed combined therapy facilitates tumor cell elimination, enhances patient survival rates, and—by leveraging autologous expanded immune cells—minimizes adverse effects, thereby enabling the effective treatment of cancer patients at minimal cost. In the treatment process, according to the individual differences of patients, the treatment plan should be adjusted promptly, such as adjusting the use of immunotherapy drugs or deciding whether a second operation is needed, to achieve personalized precision medicine and maximize the treatment effect. In the numerical solution part, $ L1 $ discretization and the Adams-Bashforth-Moulton method were used to solve fractional differential equations, and the sensitivity analysis of parameters were carried out by the Latin hypercube sampling method to determine the robustness of the model. In the control part, a genetic algorithm was used to control the input $ u(t) $. We found the optimal $ u(t) $ to minimize the target value.
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Wen Fang, Xuewen Tan, Yanbin Feng. Analysis and optimization control of lung cancer treatment based on surgical resection and immune cell therapy[J]. Networks and Heterogeneous Media, 2025, 20(2): 356-386. doi: 10.3934/nhm.2025017
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