Abstract
We reconsider the model presented in Cao et al. (2020, doi:10.1002/mma.6156), where the global asymptotic stability (GAS) of the endemic steady state (ESS) was unresolved when ℜ0 > 1. We recompute the existence of ESS in detail, re‐establish the GAS of the disease‐free steady state (DFSS) in a simple and direct manner, and, furthermore, resolve the GAS of ESS, which was left as an open problem in the above paper. We adopt the method of Lyapunov functional with a key skill of selecting some novel appropriate kernel functions.
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