A Mathematical Model of Gene Therapy for the Treatment of Cancer - Mathematical Methods and Models in Biomedicine - page 370

the practice of which is even younger. As with the development of any therapy,
questions relating to which gene to target, or what combination of therapies
can be used (immunotherapy plus gene therapies) is important. A recent paper
reviewed the importance of pairing high-throughput experimental studies together
with computational systems biology studies to help determine the optimal answers
to these questions [ 23 ]. Excitingly, these types of studies can lead to personalized
medical treatment, which one would expect from medicine in the twenty first
century.
In this work, we begin by offering a small step in using mathematical models to
make predictions that could be useful to experimentalists and clinicians working in
the area of tumor-immune interactions and the development of treatment protocols.
To this end, we simplified an existing model describing tumor-immune dynamics [ 7 ]
by merging the effector molecule equation (for IL-2) into the effector cell equation,
and allowing for time-varying inputs representing several options for immunother-
apy and gene therapy. Sufficient global stability conditions of the cancer-free state
were derived and tested numerically. Since the conditions are sufficient, further
numerical analysis was performed to investigate regions of the parameter space
where the system clears the cancer, even when sufficient conditions are not satisfied.
Our results suggest that the source term of TIL cells, s 1 , in combination with the
cancer clearance term, a , provide the optimal treatment combination: high levels
of both will clear the tumor. Further investigation is necessary to establish whether
this is a viable immunotherapy/gene therapy option in the clinical setting. We are
working now on deriving necessary conditions for the stability of the cancer-free
state for the model system ( 5 ) in the general time-dependent therapy case.
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