Open AccessAsymptotic analysis of endemic equilibrium to a brucellosis model
Author(s) -
Ming Tao Li,
Xin Pei,
Juan Zhang,
Li Li
Publication year - 2019
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.2019291
Subject(s) - uniqueness , basic reproduction number , brucellosis , lyapunov function , mathematics , epidemic model , stability (learning theory) , transmission (telecommunications) , mathematical economics , econometrics , biology , computer science , mathematical analysis , physics , medicine , population , virology , nonlinear system , environmental health , quantum mechanics , machine learning , telecommunications
Brucellosis is one of the worlds major infectious and contagious bacterial disease. In order to study different types of brucellosis transmission models among sheep, we propose a deterministic model to investigate the transmission dynamics of brucellosis with the flock of sheep divided into basic ewes and other sheep. The global dynamical behavior of this model is given: including the basic repro-duction number, the existence and uniqueness of positive equilibrium, the global asymptotic stability of the equilibrium. We prove the uniqueness of positive endemic equilibrium through using proof by contradiction, and the global stability of endemic equilibrium by using Lyapunov function. Especially, we give the specific coefficients of global Lyapunov function, and show the calculation method of these specific coefficients. By running numerical simulations for the cases with the basic reproduction number to demonstrate the global stability of the equilibria and the unique endemic equilibrium, re-spectively. By some sensitivity analysis of the basic reproduction number on parameters, we find that vaccination rate of sheep and seropositive detection rate of recessive infected sheep are very important factor for brucellosis.