  Adoptive T cell based immunotherapy is gaining significant traction in cancer
treatment. Despite its limited success, so far, in treating solid cancers, it
is increasingly successful, demonstrating to have a broader therapeutic
potential. In this paper we develop a mathematical model to study the efficacy
of engineered T cell receptor (TCR) T cell therapy targeting the E7 antigen in
cervical cancer cell lines. We consider a dynamical system that follows the
population of cancer cells, TCR T cells, and IL-2. We demonstrate that there
exists a TCR T cell dosage window for a successful cancer elimination that can
be expressed in terms of the initial tumor size. We obtain the TCR T cell dose
for two cervical cancer cell lines: 4050 and CaSki. Finally, a combination
therapy of TCR T cell and IL-2 treatment is studied. We show that certain
treatment protocols can improve therapy responses in the 4050 cell line, but
not in the CaSki cell line.
