Mathematical model of mestastasis involving immunotherapy with CAR T cells

The essence of cancer is characterized by the disordered growth of cells having the ability to invade tissues and injured adjacent organs. Classified as a world health problem, cancer lies among the four leading death causes worldwide, being metastasis responsible for over 90% of all cancer-related deaths. In order to eradicate the disease, several therapies are under development, being the immunotherapy on prominence for not causing severe damages to the normal cells, reinforcing the patient's immune system so it can better fight the cancer cells. Using differential equations, in this work, we proposed a mathematical model of mestastasis involving immunotherapy with CAR T cells. In the model, metastasis is modeled as a migratory phenomenon, where two populations of cancer cells coexist and develop in two different locations.Through numerical simulations, we studied the tumor dynamics in different scenarios, where these were obtained by varying the initial condition of the tumor cells and in the amount of CAR T cells used.