Mathematical modeling of the effect of early detection in breast cancer treatment

Introduction Early detection is a cornerstone of cancer control, yet its quantitative influence on tumor–immune interactions remains underexplored in mathematical oncology. Methods We formulated a nonlinear tumor–immune interaction model consisting of two coupled ordinary differential equations for tumor growth and immune response. Early detection was represented by a saturating function (Michealis-Menten term) dependent on tumor size and awareness level. The system was nondimensionalized to reduce parameters and ease analysis. Equilibria were derived, and both local and global stability were analyzed. Numerical simulations, phase portraits, bifurcation and sensitivity analyses were conducted to assess system behavior and parameter influence. Results Two biologically meaningful equilibria were identified. Stability analyses established the conditions for sustained tumor-free states. Simulations demonstrated that higher awareness significantly enhances early detection, thereby suppressing tumor growth. Phase portraits revealed stable tumor–immune dynamics, while sensitivity results highlighted awareness- and detection-related parameters as the most critical for tumor control. Discussion The model quantifies the role of awareness-driven early detection in shaping tumor–immune outcomes. Results underscore the importance of public awareness campaigns, screening initiatives, and early intervention strategies for effective cancer management. This framework bridges mathematical modeling and policy, offering understanding into optimizing awareness-based control measures.