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Weak reversibility in ME models (definition-dependent open question)

Determine whether weak reversibility can occur in mathematical epidemiology models under an appropriate formal definition of ME as a subclass of CRNs; clarify the dependence of this property on the adopted ME model definition.

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Background

The authors discuss structural CRN properties (e.g., zero deficiency, weak reversibility) and their relation to ME models. They note zero deficiency likely never occurs in ME and raise the status of weak reversibility as uncertain, contingent on how ME models are defined.

Resolving this open question hinges on first formalizing ME models within CRN terms (see Open Problem 1) and then testing weak reversibility for that class.

References

The answer to this natural question was not at all obvious, since some important features in CRN examples, like zero deficiency (ZD) may probably never occur in ME (this is a consequence of the global attractor conjecture), and others, like weak-reversibilty, seem also impossible (this is an open question, whose answer depends on how we define ME models; our proposed definition is stated in Open Problem (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 1.1