The impact of age and environment on tuberculosis transmission

This paper presents a tuberculosis transmission model incorporating age structure and dual time delays to examine the joint effects of environmental pathways and infection-stage heterogeneity. Theoretical analysis establishes threshold dynamics dominated by the basic reproduction number R₀, demonstrating that when R₀<1, the system is globally asymptotically stable at the disease-free equilibrium E₀ regardless of variations in τ ₁ and τ ₂. When R₀>1, the system is globally asymptotically stable at the endemic equilibrium E* under conditions where τ ₁=τ ₂=0 or τ ₁=τ ₂=τ >0. Numerical simulations not only validate these global stability conclusions but also reveal the differential regulatory effects of dual time delays. This study clarifies the regulatory mechanism of dual age-dependent infection delays on tuberculosis transmission, providing a dynamical basis for formulating relevant prevention and control strategies.