Global stability of a pseudorabies virus model with vertical transmission | Zendy

Yuhua Long | Zendy; Yining Chen | Zendy

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Global stability of a pseudorabies virus model with vertical transmission

Author(s) -

Yuhua Long,

Yining Chen

Publication year - 2020

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2020283

Subject(s) - pseudorabies , lyapunov function , virus , stability theory , virology , stability (learning theory) , basic reproduction number , equilibrium point , transmission (telecommunications) , biology , mathematics , control theory (sociology) , physics , computer science , mathematical analysis , medicine , differential equation , quantum mechanics , nonlinear system , population , artificial intelligence , telecommunications , environmental health , control (management) , machine learning

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 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{ 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.

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