Dynamic Study of Carbon-Nitrogen Competition Between the Malignant and Secondary Tumour for Breast Cancer in The Metastasis Process

Metastasis, a major cause of cancer treatment failure, remains poorly understood despite extensive research.This paper employs mathematical modelling to address the crucial question of how tumour cells, including those associated with breast cancer, survive, and initiate secondary growth in nutrient-limited environments.A four-equation model is developed, focusing on the competition between primary and metastatic tumours for carbon and nitrogen.Parameters are estimated from biological data, emphasizing the model's relevance to breast cancer metastasis.Results indicate that the carbon-to-nitrogen (C:N) ratio plays a pivotal role, with tumours having a higher optimal C:N ratio outcompeting others in nutrient-limited conditions.Comparative analyses with existing models are presented, and experimental validations, particularly in the context of breast cancer, are proposed.This study contributes insights into metastasis dynamics, laying the groundwork for further experimental exploration.