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 R0. 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 R₀ > 1, the uniform persistence of the model is established. Moreover, using appropriate Lyapunov functionals and LaSalle’s invariance principle, it is proven that if R₀ < 1, then the disease-free equilibrium is globally asymptotically stable, while the endemic equilibrium of the model is globally asymptotically stable when R₀ > 1. Furthermore, to illustrate the theoretical results, we establish some numerical simulations.