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

• * Corresponding author: Meng Zhang
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.

Mathematics Subject Classification: Primary: 34H15, 34K21; Secondary: 39A23.

 Citation: • • Figure 1.  Successor function $F(A) = c-a$

Figure 2.  Trajectory of uncontrolled system. The parameter values: $K = 0.06, \beta = 0.09, \alpha = 8.2, \mu = 0.01$

Figure 3.  region $G$

Figure 4.  Case of $N_A$ coinciding with $A$

Figure 5.  Case of $0<\sigma_1<\sigma_1^*$

Figure 6.  Case of $\sigma_1^*<\sigma_1<1$

Figure 7.  The successor function is monotonically decreasing

Figure 8.  ${S_1},{S_2},\cdots ,{S_{k+1}},{S_{k + 2}},\cdots$ are the subsequent points of ${S_0},{S_1},\cdots ,{S_k},{S_{k + 1}},\cdots$ respectively

Figure 9.  Establish coordinate system $(s,n)$ on point $A$

Figure 10.  Subplot (a) is the trajectory of system (1) and (b) and (c) are time series of $S$ and $I$ respectively

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