Bautin bifurcation in a minimal model of immunoediting

TL;DR

This paper analyzes a minimal immunoediting model, proving the existence of Bautin bifurcations, which enriches the understanding of immune surveillance phases through advanced bifurcation theory.

Contribution

It demonstrates the presence of Bautin bifurcations in a minimal immunoediting model, completing the bifurcation scenario and linking mathematical results to immunoediting phases.

Findings

Existence of Bautin bifurcations in the model

Connection of bifurcation scenarios to immunoediting phases

Extension of previous bifurcation analysis in immunoediting models

Abstract

One of the simplest model of immune surveillance and neoplasia was proposed by Delisi and Resigno. Later Liu et al proved the existence of non-degenerate Takens-Bogdanov bifurcations defining a surface in the whole set of five positive parameters. In this paper we prove the existence of Bautin bifurcations completing the scenario of possible codimension two bifurcations that occur in this model. We give an interpretation of our results in terms of the three phases immunoediting theory:elimination, equilibrium and escape.