Analysis of an age-structured tuberculosis model with time delay in incomplete treatment and the latent period of two stages

Since people with other chronic diseases will shorten the incubation period of TB, which means that their immune capacity is weaker and they are more susceptible to infection, this article considers dividing the incubation period into two stages: fast and slow. Furthermore, this paper also takes into account the influence of latent age and the distribution delay of incomplete treatment on the transmission of TB. By analyzing the existence of equilibrium points, the asymptotic smoothness of solutions, and the uniform persistence of the system, based on the definition of the basic reproduction number, this paper verifies the local and global asymptotic stability of the system.