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Modeling and optimal control of cancer-immune system 85

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most importantly T cells, but also natural killer (NK) cells, both of which
are capable of destroying cancer cells directly. The main role of ACI is that
the T cells are collected from a patient and grown in the laboratory. This
increases the number of T cells that are able to kill cancer cells or fight infec-
tions. These T cells are given back to the patient to help the IS to fight dis-
ease. This can be done in two ways, either by (i) a lymphokine-activated
killer cell therapy (LAK therapy) or by a tumor infiltrating lymphocyte ther-
apy (TIL) (Dunn et al., 2002). However, we should mention that the com-
mon side effects of IL-2 treatment include weight gain and low blood
pressure, which can be treated with other medications (Rihan et al.,
2014b; Preziosi, 2003).
Chemotherapy and radiotherapy are also common cancer therapies that
have been developed to fight cancer (Lackie, 2010). The basic idea behind
chemotherapy is to kill cancerous cells faster than healthy cells, while radio-
therapy uses radiation to kill cancerous cells. Immunotherapy is used as a
maintenance therapy following a combination of chemotherapy or radio-
therapy, and in some circumstances it is used as a single agent to treat cancer
(de Pillis et al., 2006, 2008). The combination is due to the fact that the che-
motherapy treatment kills both cancerous and healthy cells and therefore it
depletes the patient’s IS, making the patient prone to dangerous infections.
For this and other reasons, it is desirable to strengthen the IS after an
immune-depleting course of chemotherapy. Additionally, recruiting the
body’s own defense to fight cancer can be a powerful treatment strategy.
Therefore, maintaining a strong IS, by combining immunotherapy and che-
motherapy, may be essential to successfully fighting cancer. However, the
query now is how to most effectively combine cancer immunotherapy
and chemotherapy. Rihan et al. (2019) study an optimal control problem
(OCP) of delay differential model to describe the dynamics of tumor-
immune interactions in presence of immuno-chemotherapy. The model
includes constant delays 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.
Mathematical models, based on ordinary differential equations, delay dif-
ferential equations (DDEs), and partial differential equations, have proven to
be useful tools in analyzing and understanding IS interactions with viral,

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T cell: A type of white blood cell that is of key importance to the IS and is at the core of
adaptive immunity, the system that tailors the body’s immune response to specific patho-
gens. T cells are like soldiers who search out and destroy the targeted invaders.