期刊
APPLIED MATHEMATICAL MODELLING
卷 37, 期 16-17, 页码 8225-8236出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2013.03.051
关键词
Malware; Epidemic model; Time delay; Hopf bifurcation; Stability
资金
- National Natural Science Foundation of China [60973114, 61170249, 61003247]
- Natural Science Foundation project of CQCSTC [2009BA2024]
- State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University [2007DA10512711206]
A variable infection rate is more realistic to forecast dynamical behaviors of malware (malicious software) propagation. In this paper, we propose a time-delayed SIRS model by introducing temporal immunity and the variable infection rate. The basic reproductive number R-0 which determines whether malware dies out is obtained. Furthermore, using time delay as a bifurcation parameter, some necessary and sufficient conditions ensuring Hopf bifurcation to occur for this model are derived. Finally, numerical simulations verify the correctness of theoretical results. Most important of all, we investigate the effect of the variable infection rate on the scale of malware prevalence and compare our model with stationary analytical model by simulation. According to simulating results, some strategies that control malware rampant are given, which may be incorporated into cost-effective antivirus policies for organizations to work quite well in practice. (C) 2013 Elsevier Inc. All rights reserved.
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