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Permanence of a delayed SIR epidemic model with general nonlinear incidence rate
Author(s) -
Jiang Zhichao,
Ma Wanbiao
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3083
Subject(s) - mathematics , epidemic model , nonlinear system , stability (learning theory) , hopf bifurcation , incidence (geometry) , control theory (sociology) , mathematical economics , bifurcation , control (management) , demography , geometry , computer science , population , physics , quantum mechanics , machine learning , artificial intelligence , sociology
In this paper, a SIR model with two delays and general nonlinear incidence rate is considered. The local and global asymptotical stabilities of the disease‐free equilibrium are given. The local asymptotical stability and the existence of Hopf bifurcations at the endemic equilibrium are also established by analyzing the distribution of the characteristic values. Furthermore, the sufficient conditions for the permanence of the system are given. Some numerical simulations to support the analytical conclusions are carried out. At last, some conclusions are given. Copyright © 2014 John Wiley & Sons, Ltd.