Geometric Ergodicity of a Stochastic Reaction–Diffusion Tuberculosis Model with Varying Immunity Period

Considering the effects of spatial diffusion and environmental noise, this paper establishes a stochastic reaction–diffusion tuberculosis (TB) model that includes varying immunity period. Compared to the classical TB models, the TB models driven by stochastic partial differential equations are more versatile. Mathematically, the boundness of moment on the solutions is given. Furthermore, the regularity of an invariant measure and the unique geometric ergodicity of model are proved by the generalized coupling method. Some numerical simulations are also displayed, which demonstrate the effectiveness of theories.