In this paper, the therapeutic interactions are discussed with the aid of a mathematical model and piecewise differentiation technique. The model is based on the interaction between cell populations in therapeutic stress and cell populations in neoplastic transformation, referring specifically to triple-negative breast cancer (TNBC). The proposed computational approach provides an opportunity for the qualitative and parametric analysis of the clinical trials in question. The proposed mathematical model is based on the analysis of cell–cell interactions according to a logic that examines pathological stress and its influence on the dynamics of the cell population involved in tumor pathology. Detailed literature review and dynamical analysis of the proposed hypothesis are provided in this paper. The existence and non-negativity of the solutions are exploited, the hypothesis is stabilized; it is then further demonstrated with the aid of the piecewise derivative and the relevant application of the formula of Newton interpolation.

在本文中，治疗相互作用在数学模型和分段微分技术的帮助下进行了讨论。该模型基于治疗应激细胞群与肿瘤转化细胞群之间的相互作用，特别是指三阴性乳腺癌 (TNBC)。拟议的计算方法为相关临床试验的定性和参数分析提供了机会。所提出的数学模型基于根据检查病理应激及其对肿瘤病理学中涉及的细胞群动力学的影响的逻辑对细胞-细胞相互作用的分析。本文提供了所提出假设的详细文献回顾和动态分析。利用解的存在性和非负性，稳定假设；然后借助分段导数和牛顿插值公式的相关应用进一步论证。