## A novel computer virus propagation model and its dynamics.(English)Zbl 1255.68058

Summary: By taking into account the fact that, in general, a computer immediately possesses infectivity as soon as it is infected, a novel computer virus propagation model, known as the SLBS model, is established. It is proved that the dynamic behaviour of the model is determined by a threshold $$R_0$$. Specifically, the virus-free equilibrium is globally asymptotically stable if $$R_0\leq 1$$, whereas the virulent equilibrium is globally asymptotically stable if $$1<R_0\leq 4$$. It is conjectured that the virulent equilibrium is also globally asymptotically stable if $$R_0>4$$. These results suggest some effective strategies for eradicating computer viruses distributed in the Internet.

### MSC:

 68N99 Theory of software 37N99 Applications of dynamical systems
Full Text:

### References:

 [1] DOI: 10.1016/0167-4048(87)90122-2 [2] DOI: 10.1016/j.amc.2010.07.064 · Zbl 1209.68139 [3] DOI: 10.1109/6.275061 [4] DOI: 10.1016/j.nonrwa.2010.12.030 · Zbl 1220.34069 [5] DOI: 10.1016/j.amc.2007.02.004 · Zbl 1117.92052 [6] DOI: 10.1016/j.apm.2009.06.011 · Zbl 1185.68042 [7] DOI: 10.1016/j.nonrwa.2010.05.018 · Zbl 1203.94148 [8] DOI: 10.1016/j.amc.2011.03.041 · Zbl 1219.68080 [9] DOI: 10.1016/j.amc.2006.11.012 · Zbl 1118.68014 [10] DOI: 10.1016/j.amc.2009.03.023 · Zbl 1185.68133 [11] DOI: 10.1016/j.chaos.2011.10.003 · Zbl 1343.34186 [12] DOI: 10.1016/j.nonrwa.2011.07.048 · Zbl 1238.34076 [13] Robinson R. C., An Introduction to Dynamical Systems: Continuous and Discrete (2004) · Zbl 1073.37001 [14] Szor P., The Art of Computer Virus Research and Defense (2005) [15] DOI: 10.1016/j.cose.2009.10.002 [16] DOI: 10.1016/j.amc.2008.09.025 · Zbl 1162.68404
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.