A comprehensive mathematical model for cancer metastasis induction: Qualitative analysis and numerical experiments

Abstract

Tumors pose a significant threat to human health, and traditional treatment methods have limitations in controlling their growth and spread. This article utilizes combined mathematical and physical models to investigate tumor diffusion and development laws, particularly focusing on the microenvironment induction stage in tumor treatment research. By analyzing tumor metastasis and microenvironment formation, new insights and methods are proposed. We have conducted rigorous theoretical proof and numerical simulations on the proposed mathematical model. The research emphasizes the interaction between tumor cells and the microenvironment, providing a scientific basis and guidance for tumor treatment and offering a fresh perspective for tumor diagnosis. Mathematically, the model contributes a rigorous analysis of a strongly coupled convection-diffusion-chemotaxis system with mass conservation constraints, including proofs of global existence and uniqueness. The framework is also generalizable to other biological systems involving immune cell recruitment and microenvironment remodeling, such as inflammation-induced tissue repair or autoimmune cell infiltration.

The authors' abstract, as published at the source. Applied Mathematics and Computation, 2026 · DOI ↗