Analysis of a tumor growth model with treatments

In this paper, we conduct a mathematical analysis of a tumor growth model with treatments.The model consists of a system that describes the evolution of metastatic tumors and the number of cells present in the primary tumor.The former evolution is described by a transport equation, and the latter by an ordinary differential equation of Gompertzian type.The two dynamics are coupled through a nonlocal boundary condition that takes into account the tumor colonization rate.We prove an existence result where the main difficulty is to handle the coupling and to take into account the time discontinuities generated by treatment terms.The proof is based on a Banach fixed point theorem in a suitable functional space.We also develop a computational code based on the method of characteristics and present numerical tests that highlight the effects of different therapies.