# Risk Causal Analysis of Traffic-Intensive Waters Based on Infectious Disease Dynamics
## 3 Empirical Case Analysis
### Evolution of Risk Factor Nodes over Time  
According to the above-mentioned ranking of risk factors of ship navigation, the risk causal propagation process of the infectious disease dynamics model was simulated to verify the influence of key nodes. Through the screening of key risk factors, onboard officer duties and officer skill were summarized as human error; Beaufort wind scale of greater than or equal to 6 and visibility were summarized as bad weather. In the case where the model parameter coefficient \(\alpha\) is set as 10, the above risk causal analysis model was used to describe the risk propagation of nodes, such as ship traffic flow density, tide, human error, and bad weather. According to the characteristics of the selected key influencing factors, combined with the principle of SEIR, the susceptible node (\(S\)) was expressed as the most vulnerable factor to receive the risk mutation, which can be mapped to the ship traffic flow density in this paper. The exposed node (\(E\)) was expressed as a risk factor which can receive a sudden change in risk but not transmit the risk. Due to the fact that the traffic control will be made by the maritime department under the large tidal range in the Yangtze River estuary, the exposed node can be  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cloud Parameter** & \(\mathbf{E_{x}}\)1  & \(\mathbf{E_{u}}\)2  \\ \hline Beaufort wind scale is greater than 6 & 0.0365 & 0.0584 & 0.0325 \\ Visibility & 0.0400 & 0.0955 & 0.1528 \\ Wave level & 0.0013 & 0.0024 & 0.0009 \\ Flow state & 0.0224 & 0.0439 & 0.0117 \\ Tidal & 0.3079 & 0.3157 & 0.1843 \\ Flow & 0.0168 & 0.0297 & 0.0144 \\ Channel water depth & 0.0026 & 0.0065 & 0.0145 \\ Speed & 0.0016 & 0.0039 & 0.0100 \\ Route complexity & 0.0012 & 0.0030 & 0.0075 \\ Navigational regulation rationality & 0.0304 & 0.0515 & 0.0268 \\ VTS coordination degree & 0.0010 & 0.0026 & 0.0077 \\ Early warning and emergency reliability & 0.0028 & 0.0063 & 0.0064 \\ Onboard officer duties & 0.0559 & 0.0775 & 0.0462 \\ Onboard officer skill & 0.1831 & 0.2594 & 0.1538 \\ Ship navigation performance & 0.0185 & 0.0377 & 0.0075 \\ Ship age & 0.0169 & 0.0366 & 0.0221 \\ Ship traffic flow density & 0.4375 & 0.3597 & 0.1894 \\ Ship front and rear spacing & 0.0090 & 0.0213 & 0.0298 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Cloud parameters of risk factors of ship navigation in traffic-intensive waters.  
Figure 4: Evaluation of risk factors based on the cloud model.  
mapped to the tide. The infective node (\(I\)) was expressed as a risk factor that transmits the risk, which can be mapped to the bad weather in this paper. The removal node (\(R\)) was expressed as the risk factor, which can receive risk and stop transmitting risk. Due to the fact that the removal node has a large subjective initiative, it can be mapped as human errors.  
The traffic flow in the south and north waterways of the Yangtze River Estuary was 161, 459 ships in 2015 and 181, 812 ships in 2016, respectively. Thus, the growth rate of traffic flow was 0.1261. The traffic flow in the south and north waterways of the Yangtze River Estuary in 2016 is set as \(N\), so \(N=1.8\) (million). Assume that at the initial time, the ratio of key influencing factors is \(S_{o}=0.5219\), \(E_{o}=0.4163\), \(I_{o}=0.0502\), \(R_{o}=0.0116\). Besides, assume \(P_{se}=0.6\), the value of \(P_{sr}\), \(P_{er}\), \(P_{ei}\), and \(P_{ir}\) is obtained in turn according to Formula (10), meaning \(P_{sr}=0.4\), \(P_{er}=P_{ei}=0.3\), \(P_{ir}=0.3\). Based on the above data, the risk factor nodes are simulated, and then the key nodes of risk factors are analyzed.  
During the propagation of risk factor nodes over time, the corresponding propagation law was simulated by the propagation step size. The impact of key node density, traffic flow, bad weather, tides, and human error on the risk propagation process was described, respectively.