# Supply Chain Risk Diffusion Model Considering Multi-Factor Influences under Hypernetwork Vision

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## Abstract

**:**

## 1. Introduction

- (1)
- A two-layer dynamic evolution network model under the vision of a hypernetwork is constructed;
- (2)
- We consider the impacts of the herd mentality, self-vigilance, talent recruitment, and enterprise management on risk diffusion;
- (3)
- A theoretical analysis is carried out with a Microscopic Markov Chain Approach (MMCA), and a Monte Carlo (MC) simulation is used to verify the correctness of the MMCA.

## 2. Model Description

#### 2.1. Two-Layer Dynamic Evolution Network Model

#### Activity-Driven Network

- (1)
- At each discrete time step $t$, the network ${G}_{t}$ consists of $N$ isolated nodes;
- (2)
- Each node $i$ becomes active with probability ${b}_{i}(t)$, and it forms $m$ hyperedges with $d$ nodes selected by Equation (2). The inactive nodes can also receive connections.$${\omega}_{j}(t)=\frac{{\vartheta}_{j}(t)+1}{{\displaystyle \sum _{j}\left({\vartheta}_{j}(t)+1\right)}},$$
- (3)
- At the next time step $t+\u25b3t$, all hyperedges in network ${G}_{t}$ are removed. Therefore, the continuous action time $\u25b3t$ between nodes is constant.

#### 2.2. Coupled UAU–SIRS Compartment Model

#### 2.2.1. UAU Compartment Model

#### 2.2.2. SIRS Compartment Model

## 3. Theoretical Analysis

## 4. Numerical Simulation

#### 4.1. Scale

#### 4.2. Threshold

## 5. Discussion and Conclusions

- (1)
- The risk diffusion scale is negatively correlated with the herd mentality, self-vigilance, talent recruitment, and enterprise management;
- (2)
- The risk diffusion threshold is positively correlated with the herd mentality, self-vigilance, talent recruitment, and enterprise management;
- (3)
- The indirect influence is not as good as the direct influence; talent recruitment and enterprise management in the cooperation layer are more effective than the alertness-raising of the consciousness layer for restraining the diffusion of risks.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**The impact of parameters $\delta $ and ${\alpha}_{0}$ on ${P}^{I}$. The color represents the risk diffusion scale ${P}^{I}$ under steady state.

**Figure 12.**The impact of parameters $\delta $ and ${\alpha}_{0}$ on ${\lambda}_{0}^{*}$. The color represents the risk outbreak threshold ${\lambda}_{0}^{*}$ under steady state.

Parameter | Description |
---|---|

$N$ | Total number of nodes |

${b}_{i}(t)$ | $\mathrm{The}\text{}\mathrm{activity}\text{}\mathrm{rate}\text{}\mathrm{of}\text{}\mathrm{node}\text{}i$$\text{}\mathrm{at}\text{}\mathrm{time}\text{}t$ |

${d}_{1}$ | Number of nodes selected in the upper layer |

${d}_{2}$ | Number of nodes selected in the lower layer |

${m}_{1}$ | Number of hyperedges formed by an active node in the upper layer |

${m}_{2}$ | Number of hyperedges formed by an active U node in the lower layer |

${M}_{2}$ | Number of hyperedges formed by an active A node in the lower layer |

${\mathsf{\Theta}}_{i}(t)$ | $\mathrm{Probability}\text{}\mathrm{that}\text{}\mathrm{node}\text{}i$$\text{}\mathrm{is}\text{}\mathrm{not}\text{}\mathrm{infected}\text{}\mathrm{by}\text{}\mathrm{risk}\text{}\mathrm{at}\text{}\mathrm{time}\text{}t$ |

$\tau $ | Risk immunity failure rate |

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**MDPI and ACS Style**

Yu, P.; Wang, P.; Wang, Z.; Wang, J.
Supply Chain Risk Diffusion Model Considering Multi-Factor Influences under Hypernetwork Vision. *Sustainability* **2022**, *14*, 8420.
https://doi.org/10.3390/su14148420

**AMA Style**

Yu P, Wang P, Wang Z, Wang J.
Supply Chain Risk Diffusion Model Considering Multi-Factor Influences under Hypernetwork Vision. *Sustainability*. 2022; 14(14):8420.
https://doi.org/10.3390/su14148420

**Chicago/Turabian Style**

Yu, Ping, Peiwen Wang, Zhiping Wang, and Jia Wang.
2022. "Supply Chain Risk Diffusion Model Considering Multi-Factor Influences under Hypernetwork Vision" *Sustainability* 14, no. 14: 8420.
https://doi.org/10.3390/su14148420