| Abstract: |
| In this talk, we study an optimal control problem of delay differential model to describe the dynamics of tumor-immune interactions in presence of immuno-chemotherapy.
The model includes time-lags in the mitotic phase to justify the time required to stimulate the effector cells and for the effector cells to develop a suitable response to the tumor cells. By applying optimal control theory, we seek to minimize the cost function associated with the immuno-chemotherapy and to reduce load of tumor cells. Optimality conditions and characterization of the control are also discussed. We numerically approximate the solution of the optimal control problem by solving the state system forward and adjoint system backward in time. The numerical simulations show that the combination of immuno-chemotherapy protocol reduces the tumor load in few months of therapy.
Keywords: DDEs, Epidemiology; Immunology; Physiology; Optimal control; Parameter estimation; Sensitivity; Time-lags; Tumor-immune system |
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