Optimal Control of Tumor Growth Model with Dendritic Cells as Immunotherapy

Firmansyah Reskal Motulo, Trisilowati Trisilowati, Abdul Rouf

Abstract


In this paper, optimal control of tumor growth model with dendritic cells as immunotherapy is provided. The model equation can be expressed into nonlinear differential equations which are consist of four compartments namely, tumor cells, CTL cells, helper T cells, and dendritic cells. Dendritic cells as immunotherapy are injected into the body at time t. The aim of this optimal control is to minimize the tumor cells density as well as the cost of dendritic cells to be administered to the body. The optimal control problem is carried out based on Pontryagin's maximum principle and numerical simulation is solved by using Forward-Backward Sweep methods. Simulation results show that control strategy shrinks tumor cells density which is shown by tumor cells density graph that monotonically decreases after applying dendritic cells as immunotherapy.

Keywords: immunotherapy, optimal control, Tumor cell. 


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