OPTIMAL CONTROL OF TUMOR-LYMPHATIC MODEL WITH IMMUNO-CHEMOTHERAPY

Jingnan Wang; Li Xu

doi:10.11948/20220553

2023 Volume 13 Issue 5

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Jingnan Wang, Li Xu. OPTIMAL CONTROL OF TUMOR-LYMPHATIC MODEL WITH IMMUNO-CHEMOTHERAPY[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2703-2719. doi: 10.11948/20220553

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Jingnan Wang, Li Xu. OPTIMAL CONTROL OF TUMOR-LYMPHATIC MODEL WITH IMMUNO-CHEMOTHERAPY[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2703-2719. doi: 10.11948/20220553

OPTIMAL CONTROL OF TUMOR-LYMPHATIC MODEL WITH IMMUNO-CHEMOTHERAPY

Jingnan Wang^1, ,,
Li Xu^1,

1.
Department of applied mathematics, Harbin University of Science and technology, Harbin, 150080, China

Author Bio: Email: xuli_0220@163.com (L. Xu)
Corresponding author: Email: wangjingnan@hrbust.edu.cn (J. Wang)

Abstract

Abstract

To find optimal methods to inhibit tumors, we propose a tumor-lymphocyte immune optimal model with immuno-chemotherapy. Firstly, we investigate the therapeutic effects of high-dose single immunotherapy and high-dose single chemotherapy for tumor logistic growth, respectively. Furthermore, we apply the optimal control theory to investigate the optimal control problem of immuno-chemotherapy to eliminate tumors, maximize the remaining number of lymphocytes and minimize the cost caused by drugs over a finite time interval. The necessary and sufficient conditions for the existence of optimal control are also discussed. Finally, the numerical results indicate that the effect of immuno-chemotherapy with strong killing rate to tumors and weak killing rate to immune cells is the most effective strategy in inhibiting tumor growth.
- Tumor-lymphatic model /
- immuno-chemotherapy /
- optimal control /
- stability
MSC: 34H05, 92B05

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