On the dynamics of a cancer tumor growth model with multiphase structure

TL;DR

This paper analyzes a mathematical tumor growth model with immune response, exploring stability, boundedness, and equilibrium conditions to understand tumor-immune dynamics and potential outcomes.

Contribution

It provides a comprehensive phase-space analysis of a multiphase tumor growth model, including stability conditions and bounds for immune cell populations, which is novel in the context of multipoint initial conditions.

Findings

Boundaries for immune cell populations established

Conditions for convergence to equilibrium identified

Different tumor-immune equilibrium states characterized

Abstract

In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of solutions, invariance of non-negativity, nature of equilibria, local and global stability will be investigated. We study some features of behavior of one three-dimensional tumor growth model with dynamics described in terms of densities of three cells populations: tumor cells, healthy host cells and effector immune cells. We find the upper and lower bounds for the effector immune cells population. Further, we derive sufficient conditions under which trajectories from the positive domain of feasible multipoint initial conditions tend to one of equilibrium points. Here cases of the small tumor mass equilibrium point; the healthy equilibrium point; the "death" equilibrium point are examined. Biological implications of our results are considered