We present a delay differential model with optimal control that describes the interactions
of the tumour cells and immune response cells with external therapy. The intracellular
delay is incorporated into the model to justify the time required to stimulate the effector
cells. The optimal control variables are incorporated to identify the best treatment strategy
with minimum side effects by blocking the production of new tumour cells and keeping the
number of normal cells above 75% of its carrying capacity. Existence of the optimal control
pair and optimality system are established. Pontryagin's maximum principle is applicable
to characterize the optimal controls. The model displays a tumour-free steady state and up
to three coexisting steady states. The numerical results show that the optimal treatment
strategies reduce the tumour cells load and increase the effector cells after a few days of
therapy. The performance of combination therapy protocol of immunochemotherapy is
better than the standard protocol of chemotherapy alone.
In this paper, we provide a family of ordinary and delay differential equations to describe the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells, and the rate of influx of IL2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor-dormancy.
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