Threshold Dynamics of an Age--Space Structured Brucellosis Model with Nonlinear Incidence Rate on a Heterogeneous Environment

Abstract

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 $\mathcal{R}_0$ is defined by the spectral radius of the next generation operator. We prove that $\mathcal{R}_0$ governs the threshold dynamics of the brucellosis model: when $\mathcal{R}_0<1$ the disease dies out, and when $\mathcal{R}_0>1$ the disease persists.