Mathematical modeling and analysis of tumor-immune system interaction by using Lotka-Volterra predator-prey like model with piecewise constant arguments

Abstract

In this study, we present a Lotka-Volterra predator-prey like model for the interaction dynamics of tumor-immune system. The model consists of system of differential equations with piecewise constant arguments and based on the model of tumor growth constructed by Sarkar and Banerjee. The solutions of differential equations with piecewise constant arguments leads to system of difference equations. Sufficient conditions are obtained for the local and global asymptotic stability of a positive equilibrium point of the discrete system by using Schur-Cohn criterion and a Lyapunov function. In addition, we investigate periodic solutions of discrete system through Neimark-Sacker bifurcation and obtain a stable limit cycle which implies that tumor and immune system undergo oscillation.