Dynamics of an Anthrax Model with Distributed Delay

In this paper, we consider global stability for an anthrax model with distributed delay. The model incorporates vaccination and carcass disposal. The basic reproduction number of the anthrax model is derived, which completely determine the stability of equilibria. By using the direct Lyapunov method and constructing appropriate Lyapunov functional, the global stability for the anthrax epidemic model with distributed delay is investigated. It is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the unique endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. In addition, numerical simulation results are presented to demonstrate the analytical findings.