Abstract
We propose a new model for computer worms propagation, using dynamic quarantine and a nonlinear infection rate. The dynamic quarantine is based in epidemic disease control methods and in the principle ‘assume guilty before proven inocent’. This means that the host is blocked whenever its behavior looks suspicious. After a short time, the quarantined computer is released. The nonlinear infection rate is used to capture the dynamics of overcrowded infectious networks and high viral loads. We simulate numerically the model for distinct values of the quarantine times. We observe that increasing the quarantine time decreases the number of infectious hosts in the network.
REFERENCES
- 1.Capasso V., A generalization of the Kermack-McKendrick deterministic epidemic model, Mathematical Biosciences 42(1–2) 43–61 (1978). 10.1016/0025-5564(78)90006-8 [DOI] [Google Scholar]
- 2.Gan C., Yang X., Liu W., Zhu Q., Zhang X., An epidemic model of computer viruses with vaccination and generalized nonlinear incidence rate, Appl. Math. Comput. 22 265–274 (2013). 10.1016/j.amc.2013.07.055 [DOI] [Google Scholar]
- 3.Hethcote H.W., van den Driessche P., Some epidemiological models with nonlinear incidence, J. Math. Biol. 29(3) 271–287 (1991). 10.1007/BF00160539 [DOI] [PubMed] [Google Scholar]
- 4.Kephart J.O., White S.R.. Directed-graph epidemiological models of computer viruses, IEEE Symposium on Security and Privacy 343–359 (1991). [Google Scholar]
- 5.Li T., Guan Z., Wang Y., Bifurcation dynamics of a worm model with nonlinear incidence rates, Proceedings of the Control and Decision Conference (CCDC), 2011 Chinese, 3326–3328 (2011). 10.1109/CCDC.2011.5968832 [DOI] [Google Scholar]
- 6.Liu W.-m., Hethcote H.W., Levin S.A.. Dynamical behavior of epidemiological models with nonlinear incidence rates, J. Math. Biol. 25 359–380 (1987). 10.1007/BF00277162 [DOI] [PubMed] [Google Scholar]
- 7.Szor P., The Art of Computer Virus Research and Defense, Addison-Wesley Professional; (2005). [Google Scholar]
- 8.Wang F.W., Zhang Y.K., Wang C.G., Ma J.F., Moon S.J., Stability analysis of a SEIQV epidemic model for rapid spreading worms, Comput Secur, 29(4) 410–418 (2009). 10.1016/j.cose.2009.10.002 [DOI] [Google Scholar]
- 9.Yang W., Chang G.-r., Yao Y., Shen X.-m., Stability analysis of P2P Worm Propagation Model with Dynamic Quarantine Defense, Journal of Networks, 6(1) 153–162 (2011). 10.4304/jnw.6.1.153-162 [DOI] [Google Scholar]
- 10.Yang L.-X., Yang X., A new epidemic model for computer viruses, Commun. Nonl. Sci. Numer. Simul., 19(6) 1935–1944 (2014). 10.1016/j.cnsns.2013.09.038 [DOI] [Google Scholar]
- 11.Yao Y., Guo L., Guo H., Yu G., Gao F.-x., Tong X.-j.., Pulse quarantine strategy of internet worm propagation: Modeling and analysis, Computers & Electrical Engineering, 38(5) 1047–1061 (2012). 10.1016/j.compeleceng.2011.07.009 [DOI] [Google Scholar]
- 12.Yao Y., Xie X.-w., Guo H., Gao F.-x., Yu G., The Worm Propagation Model with Dual Dynamic Quarantine Strategy, Intelligent Computing and Information Science Communications in Computer and Information Science, 135 497–502 (2011). 10.1007/978-3-642-18134-4_79 [DOI] [Google Scholar]
- 13.Zhang Y.K., Wang F.W., Zhang Y.Q., Ma J.F., Worm propagation modeling and analysis based on quarantine, Proceedings of the 3rd international conference on information security (InfoSecu’04) 69–75 (2004). 10.1145/1046290.1046305 [DOI] [Google Scholar]
- 14.Zou C.C., Gong W., Towsley D., Worm propagation modeling and analysis under dynamic quarantine defense, WORM’03 Proceedings of the 2003 ACM workshop on Rapid malcode 51–60 (2003). 10.1145/948187.948197 [DOI] [Google Scholar]