**AUTHORS:**Xiaochuan Hu, Sophia R. J. Jang

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**ABSTRACT:**
We apply optimal control theory to a model of interactions between cancer cells, CD4+ T cells,
cytokines and host cells to devise best immunotherapies for treating cancer. The CD4+ T cells cannot
kill cancer cells directly but use the cytokines produced to suppress tumor growth. The immunotherapy
implemented is modeled as a control agent and it can be either transferring of CD4+ T cells, cytokines or
both. We establish existence and uniqueness of the optimal control. The optimal treatment strategy is
then solved numerically under different scenarios. Our numerical results provide best protocols in terms
of strengths and timing of the treatments.

**KEYWORDS:**
Cytokine, Immunotherapy, Ordinary Differential equations, Optimal Control, Tumor

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