The discrete age-structured SEIT model with application to tuberculosis transmission in China

Age plays an important role in the transmission of some infectious diseases. A discrete SEIT model with age-structure is formulated and studied. The basic reproduction number, R0R0, of the model is defined. It is proved that R0=1R0=1 is a threshold to determine the disease extinction or persistence. The disease-free equilibrium is globally stable (unstable) if R0<1R0<1 (if R0>1R0>1). There exists an endemic equilibrium, and the system is uniformly persistent if R0>1R0>1. The numerical simulation demonstrates that the endemic equilibrium may be globally asymptotically stable. The model is applied to describe tuberculosis (TB) transmission in China. The total number of the population, the incidence rate, the prevalent rate and its age structure match the statistical data well.