### Mathematical Biosciences and Engineering

2020, Issue 5: 5234-5249. doi: 10.3934/mbe.2020283
Research article

# Global stability of a pseudorabies virus model with vertical transmission

• Received: 11 June 2020 Accepted: 23 July 2020 Published: 05 August 2020
• 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.

Citation: Yuhua Long, Yining Chen. Global stability of a pseudorabies virus model with vertical transmission[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5234-5249. doi: 10.3934/mbe.2020283

### Related Papers:

• 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.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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