Dynamics of cancer cells with immunotherapy and virotherapy

Abstract

Oncology is the science that deals with the prevention, diagnosis and study the different possible remedies in order to treat and fight the cancer disease. In this paper, immunotherapy and virotherapy are included to mathematical new model which expresses the interaction between tumor, immunity elements (Cytotoxic T cell and Interleukin-2 (IL-2)) and oncolytic virus. After the well-posedness of model, we show that the disease-free equilibrium point (DFE) and the endemic equilibrium point can exist under specific conditions depending on treatment parameters: adoptive cellular therapy (ACT) or IL-2 treatment or the case of oncolytic virus treatment (OVT) and combined treatments. We will also discuss the local stability of the equilibrium points. The oncolytic dynamic will be analyzed numerically by using MATLAB software in order to interpret the different cancer evolution situations. A set of numerical results are obtained in order to show the performance of each treatment to reduce the size and the speed of tumor proliferation, although it leaves treatment residues for a long time.