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Existence of ME models with equivalent WR–ZD mass-action realizations

Identify whether there exist mathematical epidemiology models that admit equivalent mass-action kinetic realizations which are both weakly reversible and have deficiency zero, thereby inheriting the associated dynamical properties from CRN theory.

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Background

Weakly reversible deficiency-zero networks enjoy powerful structural and dynamical results, including complex-balanced equilibria and robust stability properties.

The authors pose whether any ME models can be recast exactly as WR–ZD mass-action systems, connecting ME dynamics to the tractable CRN class and enabling use of existing translation algorithms.

References

Open Problem Are there ME models which admit equivalent MAK WR-ZD representations?

— Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them (2411.00488 - Avram et al., 1 Nov 2024) in Open Problem, Subsection “Finding Weakly Reversible and Zero Deficiency (WR-ZD/WR0) Representations of an ODE, Using TowardZ”