A fractional mathematical examination on breast cancer progression for the healthcare system of Jordan

Abstract

Breast cancer remains a significant public health challenge worldwide, with rising incidence rates in both developed and developing nations. This study presents a fractional mathematical model to examine the progression of breast cancer within the healthcare system of Jordan. The proposed model integrates fractional calculus to account for the non-linear dynamics and long-memory effects characteristic of biological systems. It employs a compartmental framework, categorizing women into six states: Susceptible, Preclinical, Clinical, Treatment, Remission, and Death. Transition rates between these states are derived from local epidemiological data to ensure relevance to Jordan’s healthcare context. The model is analyzed for stability, disease-free equilibrium (DFEP), and endemic equilibrium (EEP), using fractional differential equations to explore the dynamics of breast cancer progression. Numerical solutions are obtained using the Modified Fractional Euler Method (MFEM), showcasing the impact of various parameters on disease spread and treatment outcomes. Results emphasize the utility of fractional-order models in capturing the intricate interplay of biological and clinical factors influencing breast cancer dynamics. This study provides valuable insights for policymakers and healthcare professionals, facilitating the optimization of resource allocation and the development of targeted intervention strategies in Jordan.