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Global asymptotic stability of the unique endemic equilibrium in SIR1S when R0 > 1

Establish whether the unique endemic equilibrium of the SIR1S model is globally asymptotically stable whenever the basic reproduction number R0 exceeds 1.

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Background

For SIR1S, the authors derive a rational univariate representation showing one positive endemic equilibrium when R0 > 1 and discuss local stability via Routh–Hurwitz analysis.

They pose the global stability question for the unique endemic equilibrium in the R0 > 1 regime.

References

Open Problem 7. For R0 > 1, is the unique endemic point of SIR1S globally asymptotically stable?

— Stability in Reaction Network Models via an Extension of the Next Generation Matrix Method (2411.11867 - Avram et al., 3 Nov 2024) in Section 5.1