Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

TL;DR

This paper uses a semi-analytic homotopy analysis method to study how activating immune cells affects tumor dynamics, revealing that immune activation can lead to chaos or tumor extinction depending on stochastic factors.

Contribution

It introduces the Step Homotopy Analysis Method (SHAM) for solving nonlinear cancer models and demonstrates its application in analyzing immune activation effects on tumor extinction.

Findings

Increased immune activation induces chaotic tumor dynamics in deterministic models.

Stochastic effects facilitate tumor extinction with immune activation.

Early immune activation is crucial for effective cancer therapy.

Abstract

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems - the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.