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Hopf bifurcation in extended SIR1S (3,8,3)

Determine whether the extended SIR1S mass-action model of type (3,8,3), formed by adding all epidemiologically interpretable linear transfers, admits an Andronov–Hopf bifurcation.

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Background

The basic SIR1S without demography is shown not to admit Hopf bifurcation, but extending the model to include all linear transfer reactions results in a (3,8,3) bimolecular CRN.

The question aims to classify whether this richer model can exhibit oscillatory dynamics via Hopf bifurcation.

References

Open Problem 5. Does the extended SIR1S of type (3,8,3), where we have added all the possible linear transfers (which may all be interpreted epidemiologically, and have in fact appeared individually in the literature), admit Hopf bifurcation?

— 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