Dynamical Analysis of SIR Epidemic Models with Distributed Delay

SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction number R is got. In order t...

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Veröffentlicht in:Journal of Applied Mathematics 2013-01, Vol.2013 (2013), p.579-593-054
Hauptverfasser: Meng, Xinzhu, Zhang, Tongqian, Chang, Zhengbo, Liu, Yulin, Zhao, Wencai
Format: Artikel
Sprache:eng
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Zusammenfassung:SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction number R is got. In order to study the important role of vaccination to prevent diseases, the model with distributed delay under impulsive vaccination is formulated. And the sufficient conditions of globally asymptotic stability of “infection-free” periodic solution and the permanence of the model are obtained by using Floquet’s theorem, small-amplitude perturbation skills, and comparison theorem. Lastly, numerical simulation is presented to illustrate our main conclusions that vaccination has significant effects on the dynamical behaviors of the model. The results can provide effective tactic basis for the practical infectious disease prevention.
ISSN:1110-757X
1687-0042
DOI:10.1155/2013/154387