A new approach combining tangent hyperbolic and logistic sigmoid neural networks to model and solve tumor growth dynamics

In this work, we develop a mathematical model that describes tumor growth dynamics by incorporating key biological components such as tumor cells, macrophages (M1 and M2 phenotypes), and the influence of a chemotherapy protocol. The model is designed to capture the nonlinear interactions among these factors, which play a vital role in tumor evolution and the effectiveness of therapeutic strategies. To solve the proposed system, we employ a deep neural network (DNN) architecture that utilizes the complementary characteristics of the hyperbolic tangent and logistic sigmoid activation functions. The logistic sigmoid function effectively models gradual transitions and saturation effects, while the hyperbolic tangent function provides a symmetric nonlinear mapping, enabling the neural network to approximate the complex behavior of tumor development under chemotherapy. This approach offers a robust computational framework to simulate tumor progression and analyze the interplay between drug administration, immune response, and tumor proliferation, thereby shedding light on the potential optimization of therapy strategies. By integrating mathematical modeling and deep learning, this study contributes to the growing body of research aimed at improving the outcomes of cancer treatment.