Periodic solutions for small and large delays in a tumor-immune system model

Abstract

In this paper we study the Hopf bifurcation for the tumor-immune system model with one delay. This model is governed by a system of two differential equations with one delay. We show that the system may have periodic solutions for small and large delays for some critical value of the delay parameter via Hopf bifurcation theorem bifurcating from the non trivial steady state.

Keywords

• Tumor-Immune system competition
• delayed differential equations
• stability
• Hopf bifurcation
• periodic solutions.