A mathematical model for the quantitative analysis of cancer–immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells (Ivano et al. in J Clin Investig 119(8):2143–2159, 2009). The existence of transcritical bifurcation, which has been proved using Sotomayor theorem, provides strong biological implications. Through numerical simulations, it has been illustrated that under certain therapy (like monoclonal antibody therapy), which is capable of altering the parameters of the system, cancer-free state can be obtained.

中文翻译：

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考虑抗体作用的癌症免疫系统数学模型。

考虑到抗体的作用，本文提出了一种定量分析癌症-免疫相互作用的数学模型。该模型基于临床证据，该证据表明抗体可以直接杀死癌细胞（Ivano等人，《临床研究杂志》 119（8）：2143-2159，2009）。使用Sotomayor定理证明的跨临界分叉的存在提供了强大的生物学意义。通过数值模拟，已经表明，在能够改变系统参数的某些疗法（如单克隆抗体疗法）下，可以获得无癌状态。