Porcine pseudorabies infection is an acute infectious disease caused by pseudorabies virus. In this paper, we formulate a mathematical susceptible-incubating-infected-treated (SEIT) model with vertical transmission. The existence and stability of the equilibrium points of the model are characteri-zed by the basic reproduction number ℜ0. When ℜ0 < 1, we show that the disease free equilibrium is unique and globally asymptotically stable. When ℜ0 > 1 and p1 ≥ max{β, b}, using the Lyapunov function method and the theory of competitive system, we obtain the global asymptotical stability of a unique disease endemic equilibrium.
Keywords: basic reproduction number; equilibrium; global stability; pseudorabies virus model.