Global properties of a general dynamic model for animal diseases: A case study of brucellosis and tuberculosis transmission

Animal diseases such as brucellosis and tuberculosis can be transmitted through an environmentally mediated mechanism, but the topics of most modeling work are based on infectious contact and direct transmission, which leads to the limited understanding of the transmission dynamics of these diseases. In this paper, we propose a new deterministic model which incorporates general incidences, various stages of infection and a general shedding rate of the pathogen to analyze the dynamics of these diseases. Under the biologically motivated assumptions, we derive the basic reproduction number _R0$R_0$, show the uniqueness of the endemic equilibrium, and prove the global asymptotically stability of the equilibria. Some specific examples are used to illustrate the utilization of our results. In addition, we elaborate the epidemiological significance of these results, which are very important for the prevention and control of animal diseases.