Threshold dynamics of an age-space structured brucellosis model with nonlinear incidence rate on a heterogeneous environment

We propose an age-space structured brucellosis model that includes diffusion with heterogeneous coefficients and a general nonlinear incidence rate. The renewal process is used to calculate the next generation operator, and the basic reproduction number R0 is defined by the spectral radius of the next generation operator. We prove that R0 governs the threshold dynamics of the brucellosis model: when R0 < 1 the disease dies out, and when R0 > 1 the disease persists.