Abstract
In this paper, the propagation of a nonlinear delay SIR epidemic using the double epidemic hypothesis is modeled. In the model, a system of impulsive functional differential equations is studied and the sufficient conditions for the global attractivity of the semi-trivial periodic solution are drawn. By use of new computational techniques for impulsive differential equations with delay, we prove that the system is permanent under appropriate conditions. The results show that time delay, pulse vaccination, and nonlinear incidence have significant effects on the dynamics behaviors of the model. The conditions for the control of the infection caused by viruses A and B are given.
Keywords: Double epidemic hypothesis, Permanence, Nonlinear incidence, Time delay, SIR epidemic model
Footnotes
This project was supported by the National Natural Science Foundation of China (No. 30870397) and National Basic Research Program of China (973 Program) (No. 2006CB403207-4).
Contributor Information
Xinzhu Meng, Email: mxz721106@sdust.edu.cn.
Zhenqing Li, Email: lizq@ibcas.ac.cn.
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