Mathematical model that describes breast cancer and immune interactions were presented using system of differential equations to provide analytic and nnmeric framework of cancer-immune dynamics. Four types of immune c...Mathematical model that describes breast cancer and immune interactions were presented using system of differential equations to provide analytic and nnmeric framework of cancer-immune dynamics. Four types of immune cells-CTLs (cytotoxic T lymphocytes), macrophages, NK (natural killer) and helper T cells-known to play the most significant roles in developing breast cancer immunity were modeled using differential equations. The model was then applied to different cancer growth rates and simulated using MATLAB software tool. The parameters of the model were based on experimental and clinical results from published articles. Results supported clinical studies that maximal breast cancer immunity depends mostly on each of the four immune cell types chosen. It was observed that for a given breast cancer growth rate, there was an optimal activation that maximized the response of the immune system. The effectiveness of the immune system resulted in the decrease in breast cancer killing rates. These results highlighted the importance of immune system activations in breast cancer development and treatment. Therefore, the model and its simulation provided a robust framework to better understand breast cancer progression and response to the immune system.展开更多
文摘Mathematical model that describes breast cancer and immune interactions were presented using system of differential equations to provide analytic and nnmeric framework of cancer-immune dynamics. Four types of immune cells-CTLs (cytotoxic T lymphocytes), macrophages, NK (natural killer) and helper T cells-known to play the most significant roles in developing breast cancer immunity were modeled using differential equations. The model was then applied to different cancer growth rates and simulated using MATLAB software tool. The parameters of the model were based on experimental and clinical results from published articles. Results supported clinical studies that maximal breast cancer immunity depends mostly on each of the four immune cell types chosen. It was observed that for a given breast cancer growth rate, there was an optimal activation that maximized the response of the immune system. The effectiveness of the immune system resulted in the decrease in breast cancer killing rates. These results highlighted the importance of immune system activations in breast cancer development and treatment. Therefore, the model and its simulation provided a robust framework to better understand breast cancer progression and response to the immune system.