Global Stability for an Endogenous-Reactivated Tuberculosis Model with Beddington-DeAngelis Incidence, Distributed Delay and Relapse

A tuberculosis (TB) epidemic model with Beddington-DeAngelis incidence and distributed delay is proposed to characterize the interaction between latent period, endogenous reactivation, treatment of latent TB infection, as well as relapse. The basic reproduction number R-0 is defined, and the globally asymptotic stability of disease-free equilibrium is shown when R-0 < 1, while if R-0 > 1 the globally asymptotic stability of endemic equilibrium is also acquired. Theoretical results are validated through performing numerical simulations, wherein we detect that TB dynamic behavior between models with discrete and distributed delays could be same and opposite, and TB is more persistent in the model with distributed delay. Besides, increasing the protection level of susceptible and infectious individuals is crucial for the control of TB.