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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 4514935, 13 pages
https://doi.org/10.1155/2017/4514935
Research Article

Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate

1School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China
2Department of Computer, Liaocheng College of Education, Liaocheng 252004, China

Correspondence should be addressed to Zizhen Zhang; moc.361@adiahzzz

Received 14 July 2016; Accepted 1 September 2016; Published 4 January 2017

Academic Editor: Xiao-Jun Yang

Copyright © 2017 Zizhen Zhang and Limin Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A four-compartment computer virus propagation model with two delays and graded infection rate is investigated in this paper. The critical values where a Hopf bifurcation occurs are obtained by analyzing the distribution of eigenvalues of the corresponding characteristic equation. In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. Finally, some numerical simulations are also carried out to justify the obtained theoretical results.