Mathematical modeling of cancer response to immunotherapy

Mathematical modelling plays a crucial role in studying cancer, providing insights into the growth of cancer and its response to various therapies. In this paper, we introduce a modified model representing the interaction between cancer, immune effector cells, and the growth factor IL-2. We analyze this model in terms of its local stability. Equilibrium solutions are found along with their stability conditions. The theoretical analysis shows that the model has two equilibrium points: the tumor-free equilibrium point, $ Q_1 $ Q1, and the positive equilibrium point, $ Q_2 $ Q2. The existence and the local stability of both points depend on the values of the threshold parameter $ R_0 $ R0 and the cancer death rate $ c_1 $ c1. Furthermore, our analysis indicates that under certain conditions, cancer can be significantly reduced. Additionally, we conduct some numerical simulations to show the consistency with the theoretical results and demonstrate the benefits of increasing treatment terms in eradicating cancer.