Maximum generalized-Hopf codimension in the nonlinear-incidence SIRS model
For the SIRS epidemic model with nonlinear incidence rate , where and are arbitrary real numbers, determine the largest possible codimension of a generalized Hopf bifurcation at an admissible positive equilibrium, as the remaining model parameters and vary. In particular, decide whether codimension five is maximal, or whether an admissible codimension-six generalized Hopf point exists.
References
Primary source
Additional references
- A codimension-5 Hopf bifurcation yielding 5 limit cycles in a SIRS epidemic model with nonlinear incidence rate — arXiv — Pei Yu, Wanyue Tang, Yanni Zeng
Progress summary
A new preprint reports a five-cycle bifurcation, but whether five is the maximum remains open.
The problem asks for the largest generalized-Hopf codimension in this nonlinear-incidence SIRS model. The latest claim establishes examples with three, four, and five cycles and offers evidence, but not a proof, that six is impossible.
Known results
An earlier study analyzes Hopf and related bifurcations in a nonlinear-incidence SIRS model and computes the first four focal values, but does not settle the maximum-codimension question.
September 2026 five-cycle claim
Pei Yu, Wanyue Tang, and Yanni Zeng report rigorously certified generalized-Hopf points producing three, four, and five limit cycles, together with obstructions to codimension six. This is specialist-preprint evidence for five-cycle existence, not a proof of maximality, and remains unverified in the scan.
Current status (as of October 2026): Five-cycle existence is claimed in a recent preprint, while codimension-six nonexistence and hence maximality at five remain open.
Solutions 0
No solutions have been posted yet.