Global dynamics in a model for anthrax transmission in animal populations

Abstract

In this paper, we propose a deterministic model to study the transmission dynamics of anthrax disease, which includes live animals, carcasses, spores in the environment and vectors. We derive three biologically plausible and insightful quantities (reproduction numbers) that determine the stability of the equilibria. We carry out rigorous mathematical analysis on the model dynamics, the global stability of the disease-free and vector-free equilibrium, the disease-free equilibrium and the vector-free disease equilibrium is proved. The global stability of the endemic equilibrium as the basic reproduction number is greater than one is derived in the special case in which the disease-related death rate is zero. The possibility of backward bifurcation is briefly discussed. Numerical analyses are carried out to understand the transmission dynamics of anthrax and investigate effective control strategies for the outbreaks of the disease. Our studies suggest that the larval vector control measure should be taken as early as possible to control the vector population size, a vaccination policy and an animal carcass removal policy are useful methods to control the prevalence of the diseases in infected animal populations, the adult vector control measure is also necessary to prevent the transmission of anthrax.