Open AccessGlobal stability of a pseudorabies virus model with vertical transmission
Author(s) -
Long Ye,
Yi Ning 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.