Global stability for an endogenous-reactivated tuberculosis model with Beddington-DeAngelis incidence, distributed delay and relapse

Abstract

In this article, 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 (LTBI), as well as relapse. The basic reproduction number R0 is defined, and the globally asymptotic stability of disease-free equilibrium is shown when R0 <1, while if R0 >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. The effect on the protection levels of susceptible and infectious individuals is discussed as well.