Impact of chemotherapy in a tumor-immune interaction model with allee effect

Brain metastases are a serious clinical problem because they grow rapidly, spread quickly, and often respond poorly to standard treatments. In this study, we develop a mathematical model that includes immune response, chemotherapy effects, and population-threshold behavior through the Allee effect. The model consists of a nonlinear system of five coupled ordinary differential equations describing tumor cells, damaged cells, necrotic tissue, immune cells, and drug concentration. We study the equilibrium points and stability of the system and support the results with numerical simulations and sensitivity analysis. The findings show that even small changes in treatment intensity or initial tumor size can lead to different long-term outcomes. Another key point is the balance between chemotherapy and the immune system. If this balance is disrupted, treatment may become less effective. Finally, the Allee effect introduces a threshold that determines whether the tumor continues to grow or begins to decline.