# Study on the Evolution of Risk Contagion in Urban River Ecological Management Projects Based on SEIRS

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## Abstract

**:**

## 1. Introduction

## 2. Complex Network of Risks

#### 2.1. Risk Identification

- (1)
- (2)
- The list of common problems in the inspection of water conservancy project construction management (2020, Ministry of Water Resources).
- (3)
- Accident investigation report of the safety production management platform of construction units.

#### 2.2. Complex Network Construction and Characterization

#### 2.2.1. Construction of Risk Networks

#### 2.2.2. Network Characteristics and Network Visualization

#### 2.3. Analysis of Risk Propagation and Delay Effects

#### 2.3.1. Propagation Effects

#### 2.3.2. Delay Effects

## 3. SEIRS-Based Risk Contagion Model for Urban River Ecological Management

#### 3.1. Model Assumptions

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

**Hypothesis**

**4.**

#### 3.2. Construction Based on the SEIRS Model

#### 3.3. Immunization Strategy Construction

_{c}and the steady-state density of infected nodes I

_{1}of the immunized network are as follows:

## 4. Numerical Simulation

#### 4.1. Initial Model Parameter Setting

#### 4.2. Model Dynamics Simulation

#### 4.3. Dynamic Simulation Analysis of the SEIRS Model

#### 4.3.1. Effect of Delay Time and Network Size on Propagation Thresholds

#### 4.3.2. Effect of Delay Time on Steady-State Density

#### 4.3.3. Infection Rate Effects on Steady-State Density

_{1}in the model leads to an increase in the steady-state densities of the infected node and latent node, indicating that more individuals are infected or in a latent state in the system.

#### 4.3.4. Sensitivity Analysis

#### 4.4. Immunization Strategy

_{1}and T when $a=0,0.2,0.4,0.6,0.8,1$. This study normalized the immune density of the infected nodes after immunization to ensure a convincing analysis. I in the figure indicates the steady-state density of the infected nodes before immunization, i.e., the maximum value of the steady-state density of the infected nodes, and the results of the analysis are shown in Figure 14.

## 5. Discussion

## 6. Conclusions

_{1}and h

_{2}) and the delay times. The simulation results indicate that in a scale-free network of project risks, the presence of risk is persistent, and the delay in risk propagation leads to a lower risk propagation threshold within the network, thereby accelerating the spread of the risk. Additionally, the decrease in the risk transmission threshold within the network, caused by the delay in risk propagation, facilitates the diffusion of network risks and the emergence of a balanced state of risk outbreak within the network. Furthermore, the steady-state densities of both the infected nodes (I) and latent nodes € in the risk network increase with higher effective transmission rates and longer propagation delay times. Moreover, the transmission rate of the latent nodes has a greater impact on the steady-state density of the risk nodes. According to the simulations involving the immunization of the susceptible risk nodes in the network, strengthening the immunity of the susceptible nodes can effectively control risks in the urban river ecological management network.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Equilibrium Point Stability and Steady-State Density Analysis

#### Appendix A.1.1. Equilibrium Point and Stability of the Model

#### Risk Aversion Balance Point and Stability

#### Risk Outbreak Equilibrium and Stability Analysis

#### Appendix A.2. Steady-State Density Analysis of the Model

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**Figure 6.**Dynamic evolution of the network model over time: (

**a**) Dynamic evolution of the risk network for N = 1500. (

**b**) Dynamic evolution of the risk network for N = 50. (

**c**) Dynamic evolution of the risk network for N = 10.

**Figure 7.**Propagation threshold λ

_{c}Relationship between, T, and N. (

**a**) A function of delay time for the contagion threshold; (

**b**) Contagion threshold as a function of network size.

**Figure 8.**The variation pattern of effective transmission rate $\lambda $ with ${h}_{1}$ and ${h}_{2}$.

**Figure 9.**Variation of steady-state density with delay time $T$. (

**a**) ${h}_{1}=0.01,{h}_{2}=0.03$ Variation of steady-state density with delay time $T$; (

**b**) ${h}_{1}=0.1,{h}_{2}=0.3$ Variation of steady-state density with delay time $T$.

**Figure 10.**The relationship between infection node, latent node and ${h}_{1}$, ${h}_{2}$. (

**a**) Steady-state density of infected nodes as a function of ${h}_{1}$ and ${h}_{2}$; (

**b**) Steady-state density of latent nodes as a function of ${h}_{1}$ and ${h}_{2}$.

**Figure 11.**Steady-state density of infected and latent nodes with h

_{2}for ${h}_{1}=0.01$. (

**a**) The law of steady-state density of infected nodes changing with ${h}_{2};$(

**b**) The law of steady-state density of Latent Nodes changing with ${h}_{2}$.

**Figure 12.**Steady-state density of infected and latent nodes with h

_{1}for h

_{2}= 0.03. (

**a**) The law of steady-state density of infected nodes changing with ${h}_{1};$(

**b**) The law of steady-state density of Latent Nodes changing with ${h}_{1}$.

**Figure 13.**The sensitivity of model parameters and model states. (

**a**) Non-normalized sensitivity; (

**b**) Normalized sensitivity.

**Figure 14.**Relationship between relative steady-state density of risk infection nodes and immune probability and delay time. (

**a**) Relative value of steady-state density of risk-infected nodes versus probability of immunity; (

**b**) Relative value of steady-state density of risk-infected nodes versus delay time.

Stage | Risk 1 Level | Risk 2 Level |
---|---|---|

1 Project concept stage | 1 Political Risk | A1 Policy risk |

A2 Legal and regulatory risks | ||

2 Economic Risks | A3 Inflation risks | |

A4 Risk of interest rate changes | ||

A5 Financing risk | ||

3 Natural environmental risks | A6 Hydrological and geological risks | |

A7 Risk of meteorological conditions | ||

A8 Ecological environment risk | ||

4 Social Risks | A9 Sociocultural risk | |

A10 Resident negotiated land acquisition risk | ||

A11 Social security situation | ||

A12 Public opinion | ||

2 Project decision stage | 5 Project decision risk | A13 Project approval risk |

A14 Basic acceptance risk before implementation | ||

A15 Risk of decision-making error | ||

A16 Risk of land change | ||

A17 Risk of incomplete collection of basic data | ||

3 Project preparation phase | 6 Bidding risks | A18 Risk of document loss |

A19 Risk of improper competition | ||

A20 Information leakage risk | ||

A21 Bid evaluation risk | ||

A22 Normative risk of bidding process | ||

7 Plan and design risks | A23 Risk of qualification of design unit | |

A24 design schedule lag | ||

A25 There are defects, errors, omissions, and frequent changes in the design plan | ||

A26 Survey accuracy risk | ||

8 Prepare for risks before construction | A27 Construction site layout and technical preparation risk | |

A28 Project contract risks | ||

A29 Risk of insufficient supply of substances (materials) and materials | ||

A30 Risk of illegal start | ||

4 Project implementation phase | 9 Construction personnel risk | A31 Technical water risk |

A32 Weak security awareness | ||

A33 Employee qualification risk | ||

A34 Risk of construction personnel slowing down | ||

10 Construction technical risks | A35 (construction) drawings improper design risk | |

A36 Engineering and technical risks | ||

A37 Construction machinery and equipment condition risk | ||

A38 Cross operation condition risk | ||

A39 Risk of construction accidents | ||

11 Construction management risks | A40 Safety management risks | |

A41 Coordination risks of participating parties (including technical disclosure) | ||

A42 Rationality of construction organization design | ||

A43 Plan Adjustment and engineering change risk | ||

A44 Contract management and enforcement risks | ||

A45 Risk of organizational structure setup confusion | ||

A46 Manage permission risk | ||

12 Construction duration factor risk | A47 Certification period | |

A48 Construction period | ||

A49 Risk of construction delay | ||

13 Completion acceptance risk | A50 Risk of file transfer not in place | |

A51 Quality assessment risk | ||

A52 Audit risk | ||

A53 Risk of cost overruns |

A1 | A2 | A3 | A4 | A5 | A6 | A7 | … | A47 | A48 | A49 | A50 | A51 | A52 | A53 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

A1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A3 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

A4 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

A5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | 0 | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ |

A47 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A48 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 1 | 0 | 1 | 0 | 0 | 0 | 0 |

A49 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 1 | 0 | 0 | 0 | 0 | 0 | 1 |

A50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A51 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A52 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

A53 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | … | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Parameter Name | Overall Network | Parameter Names | Overall Network |
---|---|---|---|

Number of nodes | 53 | Network diameter | 7 |

Number of network edges | 255 | Network average aggregation coefficient | 0.2977 |

Network density | 0.0925 | Intermediation centrality | 0.0331 |

Network average path | 2.5287 | Approach centrality | 0.3015 |

Network average | 9.6226 | Global network efficiency | 0.5281 |

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## Share and Cite

**MDPI and ACS Style**

Xu, J.; Zhu, J.; Xie, J.
Study on the Evolution of Risk Contagion in Urban River Ecological Management Projects Based on SEIRS. *Water* **2023**, *15*, 2622.
https://doi.org/10.3390/w15142622

**AMA Style**

Xu J, Zhu J, Xie J.
Study on the Evolution of Risk Contagion in Urban River Ecological Management Projects Based on SEIRS. *Water*. 2023; 15(14):2622.
https://doi.org/10.3390/w15142622

**Chicago/Turabian Style**

Xu, Junke, Jiwei Zhu, and Jiancang Xie.
2023. "Study on the Evolution of Risk Contagion in Urban River Ecological Management Projects Based on SEIRS" *Water* 15, no. 14: 2622.
https://doi.org/10.3390/w15142622