Rank-one NGM shortcut yields only part of the boundary (conjecture)

Determine whether the rank-one next-generation matrix (NGM) shortcut generally yields only part of the boundary of the disease-free equilibrium (DFE) stability domain, or characterize when it can recover the full boundary.

Background

The paper compares a full NGM construction with a rank-one shortcut in an EnvZ–OmpR ACR network. In that example, the shortcut recovered only part of the DFE stability boundary, suggesting limitations of the method.

The authors explicitly conjecture this partial accuracy is typical, motivating a formal assessment of the shortcut’s scope.

References

We conjecture therefore that the rank one shortcut adopted below yields only part of the boundary of the stability domain (see also Open question 1).

— Stability in Reaction Network Models via an Extension of the Next Generation Matrix Method (2411.11867 - Avram et al., 3 Nov 2024) in Section 4.4