Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 13, Issue 1, Pages 376-384Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2011.07.048
Keywords
Anti-virus ability; Stability; Bifurcation; Bistable states
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Funding
- NSFC [90818028, 10771227]
- NCET of Educational Ministry of China [NCET-05-0759]
- Fundamental Research Funds for the Central Universities [CDJXS10181130]
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In this paper, we propose a novel computer virus propagation model and study its dynamic behaviors; to our knowledge, this is the first time the effect of anti-virus ability has been taken into account in this way. In this context, we give the threshold for determining whether the virus dies out completely. Then, we study the existence of equilibria, and analyze their local and global asymptotic stability. Next, we find that, depending on the anti-virus ability, a backward bifurcation or a Hopf bifurcation may occur. Finally, we show that under appropriate conditions, bistable states may be around. Numerical results illustrate some typical phenomena that may occur in the virus propagation over computer network. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.
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