Qualitative analysis and simulation of a nonlinear integro-differential system modeling tumor-immune cells competition

Abstract

This paper deals with a qualitative and computational study of a class of integro-differential model, with a nonlinear growth rate. The model is applied to immunology problems, in particular to the competition between tumors and immune system. Our purpose is to take into account the activity transfer processes between cells. The first part of this paper deals with the modeling, while the second part develops the existence and uniqueness of global solutions to the initial boundary value problem related to the application of the model. Finally, numerical simulations are used to illustrate the results obtained for a dynamic of tumor cells contrasted by the immune system.