  Adoptive Cell Transfer therapy of cancer is currently in full development and
mathematical modeling is playing a critical role in this area. We study a
stochastic model developed by Baar et al. in 2015 for modeling immunotherapy
against melanoma skin cancer. First, we estimate the parameters of the
deterministic limit of the model based on biological data of tumor growth in
mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic
Approximation Expectation Maximization algorithm. With the estimated
parameters, we head back to the stochastic model and calculate the probability
that the T cells all get exhausted during the treatment. We show that for some
relevant parameter values, an early relapse is due to stochastic fluctuations
(complete T cells exhaustion) with a non negligible probability. Then, focusing
on the relapse related to the T cell exhaustion, we propose to optimize the
treatment plan (treatment doses and restimulation times) by minimizing the T
cell exhaustion probability in the parameter estimation ranges.
