A Stochastic Immunotherapy Model for Breast Cancer with Pulsed Chemotherapy

Abstract

In this paper, we consider an immunotherapy model for breast cancer with stochastic perturbations and pulsed chemotherapy. By using stochastic Lyapunov analysis and the strong law of large numbers, we first prove the existence, uniqueness and the stochastic ultimate boundedness of the global positive solution for the model. Then we obtain sufficient conditions for the extinction of tumor cells and the persistence of all three kinds of cells for this model. Finally, we use numerical simulations to verify the theoretical results which are obtained in the paper.