Stability of SIRS via deficiency-one theory

Analyze the local and global stability properties of the mass-action SIRS reaction network using the deficiency-one theory of chemical reaction network theory (CRNT), determining what deficiency-one results can certify about disease-free and endemic equilibria.

Background

The SIRS model is a foundational ME system that the authors present in CRN form, noting its deficiency is 1 and that classical ME results give unique interior equilibria and global stability under certain conditions.

The open problem invites the application of deficiency-one theorems to SIRS to potentially yield structured, CRNT-based stability conclusions beyond example-specific ME analyses.

References

Open Problem 2. Analyze the stability of SIRS using deficiency one theory.

— Stability in Reaction Network Models via an Extension of the Next Generation Matrix Method  (2411.11867 - Avram et al., 2024) in Section 2.2