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Global asymptotic stability of the endemic equilibrium in the IDHKP–IDH ACR system

Prove that the endemic equilibrium of the (5,6,3,1) IDHKP–IDH reaction network is globally asymptotically stable whenever the inequality k3 (k5 + k6) > k4 k6 Stot holds.

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Background

In the IDHKP–IDH ACR system analyzed, the DFE is stable when k3 (k5 + k6) ≤ k4 k6 Stot, and a positive endemic equilibrium exists and is locally stable in the complementary region.

The authors conjecture that local stability extends to global asymptotic stability under the specified parameter condition.

References

Conjecture 1. We conjecture that the EE is globally asymptotically stable when (4.24) holds.

— Stability in Reaction Network Models via an Extension of the Next Generation Matrix Method (2411.11867 - Avram et al., 3 Nov 2024) in Section 4.5