Dynamical Analysis of SIR Epidemic Models with Distributed Delay | Zendy

Wencai Zhao | Zendy; Tongqian Zhang | Zendy; Zhengbo Chang | Zendy; Xinzhu Meng | Zendy; Yulin Liu | Zendy

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Dynamical Analysis of SIR Epidemic Models with Distributed Delay

Author(s) -

Wencai Zhao,

Tongqian Zhang,

Zhengbo Chang,

Xinzhu Meng,

Yulin Liu

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/154387

Subject(s) - epidemic model , jacobian matrix and determinant , vaccination , floquet theory , mathematics , perturbation (astronomy) , basic reproduction number , stability (learning theory) , dynamical systems theory , comparison theorem , computer science , medicine , machine learning , virology , physics , population , environmental health , nonlinear system , quantum mechanics

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

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