The local and global dynamics of a general cancer tumor growth model with multiphase structure

TL;DR

This paper conducts a phase-space analysis of a multiphase tumor growth model with immune response, examining stability, boundedness, and basins of attraction to understand tumor dynamics and potential outcomes.

Contribution

It provides a detailed mathematical analysis of a three-cell population tumor model, including conditions for stability and the behavior of solutions with multipoint initial conditions.

Findings

Trajectories tend to equilibrium points under certain conditions.

Conditions for stability of healthy and death equilibria are derived.

Biological implications of tumor growth dynamics are discussed.

Abstract

We present a phase-space analysis of a mathematical model of tumor growth with an immune responses. We consider mathematical analysis of the model equations with multipoint initial condition regarding to dissipativity, boundedness of solutions, invariance of non-negativity, local and global stability and the basins of attractions. We derive some features of behavior of one of three-dimensional tumor growth models with dynamics described in terms of densities of three cells populations: tumor cells, healthy host cells and effector immune cells. We found 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 points-the healthy equilibrium point, the "death" equilibrium point have been examined. Biological implications of our results are discussed.