Modeling and analysis of the effects of antivirus software on an infected computer network.

*(English)*Zbl 1364.68064Summary: In this paper, a nonlinear mathematical model for cleaning an infected computer network by using antivirus software is proposed and analyzed. In the modeling process, the total number of nodes in the network are divided in three subclasses, namely, the number of susceptible nodes, number of infected nodes and the number of protected nodes. A variable representing the number of antivirus softwares, assumed to be proportional to number of infected nodes, is also considered in the model which interacts with other nodes bilinearly to conduct the cleaning process. The model is analyzed by using stability theory of differential equations and computer simulation. The analysis shows that it is possible to clean the computer network under certain condition which depend upon the inflow rate of infected nodes in the computer network, the rate of interaction of infected nodes with susceptible nodes and their interactions with antivirus software, etc. It is found that the entire network can be cleaned eventually if the antivirus software is applied on the network, where a separate class of protected nodes is formed. The computer simulation confirms the analytical results.

##### MSC:

68M10 | Network design and communication in computer systems |

34D20 | Stability of solutions to ordinary differential equations |

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\textit{J. B. Shukla} et al., Appl. Math. Comput. 227, 11--18 (2014; Zbl 1364.68064)

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##### References:

[1] | Bailey, N. T.J., The mathematical theory of infectious diseases and its applications, (1975), Griffin London · Zbl 0334.92024 |

[2] | Hethcote, H. W., Qualitative analysis of communicable disease models, Math. Biosci., 28, 335-336, (1976) · Zbl 0326.92017 |

[3] | Hethcote, H. W., One thousand and one epidemic models, (Levin, S. A., Frontier of Mathematical Biology, (1994), Springer New York) · Zbl 0819.92020 |

[4] | Hethcote, H. W., The mathematics of infectious diseases, SIAM Rev., 42, 4, 599-653, (2000) · Zbl 0993.92033 |

[5] | May, R. M.; Anderson, R. M., Population biology of infectious diseases, part 2, Nature, 280, 455-461, (1979) |

[6] | Mishra, B. K.; Navneet Jha, SEIQRS model for the transmission of malicious objects in computer network, Appl. Math. Model., 34, 710-715, (2010) · Zbl 1185.68042 |

[7] | Mishra, B. K.; Saini, D. K., SEIRS epidemic model with delay for transmission of malicious objects in computer networks, Appl. Math. Comp., 188, 2007, 1476-1482, (2007) · Zbl 1118.68014 |

[8] | Newman, M. E.J.; Forrest, S.; Balthrop, J., Email networks and the spread of computer viruses, Phy. Rev. E, 66, 035101-035104, (2002) |

[9] | Singh, S.; Shukla, J. B.; Chandra, P., Mathematical modelling and analysis of the spread of carrier dependent infectious diseases: effects of cumulative density of environmental factors, Int. J. Biomath., 2, 2, 213-228, (2009) · Zbl 1342.92282 |

[10] | Yuan, H.; Chen, G., Network virus-epidemic model with the point-to-group information propagation, Appl. Math. Comp., 206, 357-367, (2008) · 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.