# American Institute of Mathematical Sciences

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December  2018, 15(6): 1465-1478. doi: 10.3934/mbe.2018067

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

 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

* Corresponding author: Meng Zhang

Received  May 22, 2018 Accepted  July 24, 2018 Published  September 2018

Fund Project: Lansun Chen is supported by NSFC of China (No.11671346, No.61751317), and Meng Zhang is supported by NSFC of China (No.11701026).

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.

Citation: Meng Zhang, Kaiyuan Liu, Lansun Chen, Zeyu Li. State feedback impulsive control of computer worm and virus with saturated incidence. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1465-1478. doi: 10.3934/mbe.2018067
##### References:

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##### References:
Successor function $F(A) = c-a$
Trajectory of uncontrolled system. The parameter values: $K = 0.06, \beta = 0.09, \alpha = 8.2, \mu = 0.01$
region $G$
Case of $N_A$ coinciding with $A$
Case of $0<\sigma_1<\sigma_1^*$
Case of $\sigma_1^*<\sigma_1<1$
The successor function is monotonically decreasing
${S_1},{S_2},\cdots ,{S_{k+1}},{S_{k + 2}},\cdots$ are the subsequent points of ${S_0},{S_1},\cdots ,{S_k},{S_{k + 1}},\cdots$ respectively
Establish coordinate system $(s,n)$ on point $A$
Subplot (a) is the trajectory of system (1) and (b) and (c) are time series of $S$ and $I$ respectively
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