Immunotherapy plays a major role in tumour treatment, in comparison with other methods of dealing with cancer. The Kirschner-Panetta (KP) model of cancer immunotherapy describes the interaction between tumour cells, effector cells and interleukin-2 which are clinically utilized as medical treatment. The model selects a rich concept of immune-tumour dynamics. In this paper, approximate analytical solutions to KP model are represented by using the differential transform and Adomian decomposition. The complicated nonlinearity of the KP system causes the application of these two methods to require more involved calculations. The approximate analytical solutions to the model are compared with the results obtained by numerical fourth order Runge-Kutta method.
A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences
在这项工作中，我们提出并研究了一个家庭的模型，其中承认作为特殊情况下，一些众所周知的肿瘤免疫系统相互作用的数学模型，与额外的假设，即免疫系统细胞的流入可能是癌细胞的数量的函数。常数，周期和脉冲疗法（以及非扰动系统）的研究分析一般家庭，并通过使用模型Kuznetsov等人。库兹涅佐夫岛A. Makalkin，M. A. Taylor和A. S.佩雷尔森免疫原性肿瘤的非线性动力学：参数估计和全局分叉分析。Bulletin of Mathematical Biology 56（2）：295-321，（1994））。模拟似乎表明，对治疗进行建模的函数的形状仅对于非常高的治疗期$T$值是关键因素，而对于$T$的实际值，癌细胞的根除取决于治疗期的平均值。最后，提出了一些医学推论。
Optimisation of neoadjuvant pembrolizumab therapy for locally advanced MSI-H/dMMR colorectal cancer using data-driven delay integro-differential equations
School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学院）；Department of Immuno-Oncology, Beckman Research Institute, City of Hope（希科医院贝克曼研究所免疫肿瘤学系）
A stochastic agent-based model for simulating tumor-immune dynamics and evaluating therapeutic strategies
School of Software, Tiangong University（天津工业大学软件学院）；School of Mathematical Sciences, Tiangong University（天津工业大学数学科学学院）；Center for Applied Mathematics, Tiangong University（天津工业大学应用数学中心）
