A Malware Propagation Model Considering Conformity Psychology in Social Networks
Abstract
:1. Introduction
2. Assumptions and Model Formulation
3. Stability Analysis of the Equilibria
3.1. Local Stability of the Equilibria
3.2. Existence and Local Stability of Endemic Equilibrium
3.3. Global Stability of the Malware-Free Equilibrium
4. Numerical Simulations
5. Experimental Analysis
Algorithm 1: The state transformation of computers on the Internet |
Input: Input the network G = (v,e) which is given by the set of data and the original number of nodes per state |
Output: Output the number of nodes in each state at time ${t}^{\ast}$ |
6. Sensitivity Analysis
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Initial Value | Source |
---|---|---|---|
$\alpha $ | Rate of exposed computers becoming infected computers. | 0.008 | [26] |
$\beta $ | Rate of susceptible computers becoming exposed computers. | 0.053 | [26] |
$\varphi $ | Rate of infected computers being quarantined. | 0.05 | [26] |
$\gamma $ | Rate of susceptible computers becoming exposed computers. | 0.02 | - |
$\eta $ | Recovery rate for the exposed computers. | 0.0008 | [26] |
$\epsilon $ | Rate of quarantined computers becoming susceptible computers. | 0.005 | [26] |
$\mu $ | Recruitment and mortality rate. | 0.001 | - |
${m}_{E},{m}_{I},{m}_{Q}$ | The impact of social networks corresponding to $E,I,Q$. | 0.2, 0.3, 0.3 | - |
Parameter | $\mathit{\alpha}$ | $\mathit{\beta}$ | $\mathit{\gamma}$ | $\mathit{\varphi}$ | $\mathit{\eta}$ | $\mathit{\epsilon}$ | $\mathit{\mu}$ | ${\mathit{m}}_{\mathit{E}}$ | ${\mathit{m}}_{\mathit{I}}$ | ${\mathit{m}}_{\mathit{Q}}$ |
---|---|---|---|---|---|---|---|---|---|---|
Value | 0.1 | 0.1 | 0.2 | 0.05 | 0.0008 | 0.005 | 0.001 | 0.2 | 0.3 | 0.3 |
Parameter | $\mathit{\beta}$ | $\mathit{\alpha}$ | $\mathit{\eta}$ | $\mathit{\mu}$ | $\mathit{\varphi}$ |
---|---|---|---|---|---|
Group 1 | 0.1 | 0.24 | 0.5 | 0.7 | 0.8 |
Group 2 | 0.3 | 0.45 | 0.6 | 0.9 | 0.1 |
Group 3 | 0.5 | 0.75 | 0.9 | 0.15 | 0.28 |
Group 4 | 0.7 | 0.8 | 0.28 | 0.4 | 0.53 |
Group 5 | 0.9 | 0.22 | 0.29 | 0.5 | 0.75 |
Parameter | $\mathit{\beta}$ | $\mathit{\alpha}$ | $\mathit{\eta}$ | $\mathit{\mu}$ | $\mathit{\varphi}$ |
---|---|---|---|---|---|
Case 1 | +1.0000 | +0.8333 | −0.3472 | −0.9528 | −0.5333 |
Case 2 | +1.0000 | +0.7692 | −0.3077 | −1.3615 | −0.1000 |
Case 3 | +1.0000 | +0.5833 | −0.5000 | −0.4322 | −0.6512 |
Case 4 | +1.0000 | +0.4595 | −0.1892 | −0.7004 | −0.5699 |
Case 5 | +1.0000 | +0.7822 | −0.2871 | −0.8950 | −0.6000 |
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Zhu, Q.; Liu, Y.; Luo, X.; Cheng, K. A Malware Propagation Model Considering Conformity Psychology in Social Networks. Axioms 2022, 11, 632. https://doi.org/10.3390/axioms11110632
Zhu Q, Liu Y, Luo X, Cheng K. A Malware Propagation Model Considering Conformity Psychology in Social Networks. Axioms. 2022; 11(11):632. https://doi.org/10.3390/axioms11110632
Chicago/Turabian StyleZhu, Qingyi, Yuhang Liu, Xuhang Luo, and Kefei Cheng. 2022. "A Malware Propagation Model Considering Conformity Psychology in Social Networks" Axioms 11, no. 11: 632. https://doi.org/10.3390/axioms11110632