Abstract
Age and infection age have significant influence on the transmission of infectious diseases, such as HIV/AIDS and TB. A discrete SEIT model with age and infection age structures is formulated to investigate the dynamics of the disease spread. The basic reproduction number R0 is defined and used as the threshold parameter to characterize the disease extinction or persistence. It is shown that the disease-free equilibrium is globally stable if R0 < 1, and it is unstable if R0 > 1. When R0 > 1, there exists an endemic equilibrium, and the disease is uniformly persistent. The stability of the endemic equilibrium is investigated numerically.
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