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. Baar et al., 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 return to the stochastic model and calculate the probability of complete T cells exhaustion. 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.

癌症的过继细胞转移疗法目前正在全面开发中，数学建模在这一领域起着至关重要的作用。我们研究了Baar等人开发的随机模型。Baar等人，2015年，针对黑色素瘤皮肤癌的免疫疗法建模。首先，我们根据小鼠肿瘤生长的生物学数据估算模型确定性极限的参数。通过随机近似期望最大化算法估计非线性混合效应模型。利用估计的参数，我们返回到随机模型并计算完全T细胞衰竭的可能性。我们表明，对于一些相关的参数值，早期复发是由于随机波动（完全T细胞衰竭）引起的，其可能性不可忽略。然后，