Analysis of global behavior in a diffusive tuberculosis epidemic model structured by ages of latency and infection

This work investigates the global threshold dynamics of a novel tuberculosis (TB) model with spatial-diffusion and dual age structures (tracking both latent infection and active disease stages), incorporating key biological complexities like fast/slow progression and immune decline. A key initiative is the integration of post-exposure interventions to assess their potential impact on TB control. Analytically, we establish the model’s well-posedness applying the fixed point theory and contradiction method, and derive the reproduction number ( R 0 ) using renewal theory. Our primary theoretical result establishes the global asymptotic stability of the steady states, proven via the Lyapunov functionals, which reveals that transmission dynamics are entirely determined by R 0 : the disease is ultimately eliminated if R 0 ≤ 1; whereas the spread of TB will stabilize in an endemic state if R 0 > 1. Numerical simulations, calibrated with annual TB case data from China (2008-2023), confirm these dynamic behaviors. They further demonstrate that population mobility exacerbates epidemics, a risk overlooked in non-spatial models. Crucially, the findings show that enhancing post-exposure vaccination can effectively curb the surge in new TB cases, highlighting its important role in controlling outbreaks.