Global dynamics of a degenerate reaction-diffusion model for Brucellosis transmission

Abstract

The effective control of brucellosis is critically important for global public health and the economy. This paper presents a novel degenerate reaction-diffusion model for brucellosis, incorporating spatiotemporal heterogeneity, human behavior dynamics and a multi-stage latent period. The well-posedness of the model is rigorously analyzed, and the basic reproduction number $R_0$ is derived via the next-generation operator method. A threshold result based on the $R_0$ is established: global asymptotic stability of the disease-free equilibrium is proven for $R_0<1$, while disease persistence is rigorously demonstrated for $R_0>1$. The global asymptotic stability of the disease-free equilibrium for $R_0=1$ is further proven under spatial heterogeneity. Furthermore, the global attractiveness of the endemic equilibrium under spatiotemporal homogeneity is established through the construction of a Lyapunov function. Numerical simulations identify critical drivers of brucellosis transmission, including human behavior adaptation, latent period staging, and grazing intensity, providing significant insights for brucellosis control strategies.