Global stability of a pseudorabies virus model with vertical transmission

Abstract

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 $\Re_0$. When $\Re_0<1$, we show that the disease free equilibrium is unique and globally asymptotically stable. When $\Re_0>1$ and $p_{1}\geq\max\{\beta,b\}$, using the Lyapunov function method and the theory of competitive system, we obtain the global asymptotical stability of a unique disease endemic equilibrium.

Keywords

• pseudorabies virus model
• basic reproduction number
• equilibrium
• global stability