Dynamical Analysis of Breast Cancer Progression with Noise Effects and Impulsive Therapeutic Interventions

Abstract

Breast cancer remains one of the most prevalent cancers globally and is a leading cause of cancer-related mortality in women. This study investigates the dynamics of interactions among healthy, cancer and immune cells through an impulsive model incorporating chemotherapy and immunotherapy's effects, under the influence of stochastic perturbations. The combined effects of periodic treatments and stochastic variations are analyzed, offering valuable insights into disease progression and therapeutic strategies. The model is constructed using three auxiliary equations to establish the existence, positivity, and uniqueness of solutions. The global stability of the system's solutions is demonstrated through the construction of a Lyapunov function, while the boundedness of the solution's expectation is verified using a comparison theorem for impulsive equations. Criteria for the extinction and non-persistence of healthy cells, cancer cells, and immune populations are derived, along with conditions for the weak and stochastic persistence of cancer cells. Numerical simulations are conducted to support the theoretical findings, highlighting the biological implications of the results.