Discretization of a mathematical model for tumor-ımmune system ınteraction with piecewise constant arguments

Abstract

The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor and immune cells. The model consists of differential equations with piecewise constant arguments and based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is obtained a system of difference equations from the system of differential equations. In order to get local and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a consequence of Neimark-Sacker bifurcation.