GLOBAL DYNAMICS OF AN AGE-STRUCTURED TUBERCULOSIS MODEL WITH A GENERAL NONLINEAR INCIDENCE RATE

In this paper, we consider an age-structured tuberculosis model with a general nonlinear incidence rate. It is shown that the global transmission dynamics of the disease is completely controlled by the basic reproduction number [Formula: see text]. The local asymptotic stability of the disease-free and endemic equilibria of the model is obtained by linearization and analyzing the corresponding characteristic equations. Then, under [Formula: see text], the uniform persistence of the model is established. Moreover, using appropriate Lyapunov functionals and LaSalle’s invariance principle, it is proven that if [Formula: see text], then the disease-free equilibrium is globally asymptotically stable, while the endemic equilibrium of the model is globally asymptotically stable when [Formula: see text]. Furthermore, to illustrate the theoretical results, we establish some numerical simulations.