On the global stability of an age-structured tuberculosis transmission model with relapse

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.