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CRN relevance of varying-population ME models and existence of CRN classes with ACR-like endemic formulas

Investigate whether varying total population epidemic models and their intermediate approximations are of interest within chemical reaction network theory, and determine whether there exist CRN classes for which endemic susceptible concentrations satisfy absolute concentration robustness and for which R0–susceptible relationships analogous to those established for SIR-PH(-FA/IA) models hold.

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Background

The authors connect ME models with CRN absolute concentration robustness (ACR), where certain species (e.g., susceptibles) take invariant concentrations at steady state independent of totals.

They ask if varying-population ME models fit naturally into CRN frameworks and whether CRN classes exist that exhibit the same endemic-susceptible and R0 relationships found in SIR-PH models.

References

Open Problem Are varying total population models and their intermediate approximations of interest in CRN? Are there particular classes of CRN models where formulas similar to \eqr{sEACR} and \eqr{R0fr} hold (which include for example the ACR examples provided in )?

— Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them (2411.00488 - Avram et al., 1 Nov 2024) in Open Problem, Subsection “SIR-PH-FA Meets ACR”