Global stability of a pseudorabies virus model with vertical transmission

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 characterized by the basic reproduction number R-0. When R-0 < 1, we show that the disease free equilibrium is unique and globally asymptotically stable. When R-0 > 1 and p(1) >= max{beta, b), using the Lyapunov function method and the theory of competitive system, we obtain the global asymptotical stability of a unique disease endemic equilibrium.