The impact of distributed time delay in a tumor-immune interaction system

The impact of continuously distributed delay has been investigated in this paper to describe the interaction among tumor cells, tumor-specific CD8+T cells, helper T cells and immuno-stimulatory cytokine interleukin-2 (IL-2) through a system of coupled nonlinear ordinary differential equations. We analyze the qualitative properties of the model such as positivity of the solutions and the existence of biologically feasible equilibrium points. Next, we discuss the local asymptotic stability for the delayed and non-delayed system. Our model system experiences Hopf bifurcation with respect to the activation rate lambda(1) of tumor-specific CD8+T cells. The effect of continuously distributed delay involved in immune-activation on the system dynamics of the tumor is demonstrated. Our study reveals that the activation rate of CD8+T cells can prevent the oscillation of tumor-presence equilibria as well as tumor-free equilibria of the system. Then we performed some numerical results and interpret their biological implications to validate our analytical findings. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the impact of continuously distributed delay on the interaction between tumor cells and the immune system, analyzing the properties of the model and the stability of the system. The study reveals that the activation rate of tumor-specific CD8+T cells plays a crucial role in preventing oscillations in the presence or absence of tumors. Additionally, numerical results are provided to validate the findings and interpret their biological implications.