State feedback impulsive control of computer worm and virus with saturated incidence

Meng Zhang; Kaiyuan Liu; Lansun Chen; Zeyu Li; Meng Zhang; Kaiyuan Liu; Lansun Chen; Zeyu Li

doi:10.3934/mbe.2018067

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 6: 1465-1478. doi: 10.3934/mbe.2018067

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State feedback impulsive control of computer worm and virus with saturated incidence

Meng Zhang ^{1
,
,},
Kaiyuan Liu ^{2
,},
Lansun Chen ^{3
,},
Zeyu Li ^{4
,}

1.
School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
2.
Anshan Normal University, Anshan 114007, China
3.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
4.
Canvard College, Beijing Technology and Business University, Beijing 101118, China

Received: 22 May 2018 Accepted: 24 July 2018 Published: 01 December 2018
MSC : Primary: 34H15, 34K21; Secondary: 39A23

A state feedback impulsive model is set up to discuss the spreading and control of the computer worm and virus. Considering the transmission features, saturated infectious is adopted to describe the spreading in the model, and all the treatment measures, such as patching operating system and updating antivirus software, are assumed to take effect instantly. Then the model is analyzed with a novel method, and the existence and stability of order-1 limit cycle are discussed. Finally, the numerical simulation is listed to verify the result of the paper.
- Computer worm,
- computer virus,
- state feedback,
- saturated incidence,
- limit cycle
Citation: Meng Zhang, Kaiyuan Liu, Lansun Chen, Zeyu Li. State feedback impulsive control of computer worm and virus with saturated incidence[J]. Mathematical Biosciences and Engineering, 2018, 15(6): 1465-1478. doi: 10.3934/mbe.2018067

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Abstract

A state feedback impulsive model is set up to discuss the spreading and control of the computer worm and virus. Considering the transmission features, saturated infectious is adopted to describe the spreading in the model, and all the treatment measures, such as patching operating system and updating antivirus software, are assumed to take effect instantly. Then the model is analyzed with a novel method, and the existence and stability of order-1 limit cycle are discussed. Finally, the numerical simulation is listed to verify the result of the paper.

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