An immune system-tumour interactions model with discrete time delay: model analysis and validation

TL;DR

This paper presents a mathematical model of tumor-immune interactions with discrete time delay, analyzing its properties and validating it with experimental data to better understand tumor progression dynamics.

Contribution

It introduces a generalized delay differential equation model for tumor-immune interactions, analyzing stability and bifurcations, and validates the model with experimental data.

Findings

Model exhibits stability switches depending on delay parameter

Analytical results align with experimental tumor progression data

Numerical simulations illustrate complex dynamics of tumor-immune interactions

Abstract

In this article a generalized mathematical model describing the interactions between malignant tumour and immune system with discrete time delay incorporated into the system is considered. Time delay represents the time required to generate an immune response due to the immune system activation by cancer cells. The basic mathematical properties of the considered model, including the global existence, uniqueness, non-negativity of the solutions, the stability of steady sates and the possibility of the existence of the stability switches, are investigated when time delay is treated as a bifurcation parameter. The model is validated with the sets of the experimental data and additional numerical simulations are performed to illustrate, extend, interpret and discuss the analytical results in the context of the tumour progression.