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Classify SEIR-type models admitting Hopf bifurcation

Identify which SEIR-type bimolecular CRN models with four species and maximal rank, restricted to transfer reactions and infection reactions S + E -> 2E and S + I -> I + E, admit an Andronov–Hopf bifurcation.

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Background

The authors define SEIR-type in CRN terms and seek a classification of which such systems can undergo Hopf bifurcations. Prior work has partially classified minimal bimolecular networks, but a comprehensive classification for this SEIR-type class remains open.

This problem targets a structural understanding of oscillatory epidemiological models within the CRN framework.

References

Open Problem 6. Identify which SEIR-type models admit Hopf bifurcation, where we define SEIR-type to mean CRN bimolecular models with 4 species and maximal rank, and only reactions of transfer and of infections of the types S + E -> 2E, S+I->I+E.

— 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