4.1.1. Causality Diagram Analysis

The causal circuit diagram includes six systems, namely, external environment stage system, planning stage subsystem, procurement stage subsystem, manufacturing stage subsystem, transportation stage subsystem, and assembly stage subsystem; these six systems affect each other, interconnect, and ultimately affect the spread of risk in the entire prefabricated building supply chain. A causal analysis of the supply chain risk of prefabricated buildings is shown in Figure 3.

**Figure 3.** Causal analysis of the supply chain risk of prefabricated buildings.

#### 4.1.2. Result Tree Analysis

Set each risk factor as the current state and use the analysis tool uses tree to analyse the results brought by each risk factor. It is concluded that when the government policy changes, it has the widest impact on other stages. The result trees of other factors are not introduced here. The result tree of government policy changes is shown in Figure 4.

**Figure 4.** Result tree of government policy changes.

#### *4.2. Based on the Establishment of the Supply Chain Risk Propagation Model Considering the Recurrent SEAIR Model*

Through the above analysis, this paper concludes that changes in government policies have the greatest impact on the other stages of the supply chain of prefabricated buildings. Therefore, the government is regarded as the main body of the supply chain of prefabricated buildings, and it is introduced into the SEAIR model to explore the impact of relevant government policies on the supply chain of prefabricated buildings.

#### 4.2.1. Definition of the System Boundary

In the management and operation of the prefabricated building supply chain, one or more enterprises will be involved, which will influence each other. One of them will be affected by risks, and the whole supply chain may be affected. Under the supply chain of prefabricated buildings, the risk spread can be divided into unknown risk enterprises (susceptible to infection), latent risk enterprises (latent persons), risk transmission enterprises (symptomatic and asymptomatic infection), and infection rehabilitation enterprises (recovered persons). When the node enterprises in the assembled supply chain are disturbed by risks, they change from unknown risk enterprises to latent risk enterprises. Under the influence of a certain transfer rate, latent enterprises turn into risk transmission enterprises, and risk transmission enterprises turn into infection rehabilitation enterprises under the influence of the government. When the node enterprises become infection rehabilitation enterprises, they may lose their immunity to risks and then continue to become unknown risk enterprises. It is found that the system in this process includes six subjects: enterprises with unknown risks, enterprises with latent risks, enterprises with risk transmission, enterprises with infection rehabilitation, enterprises without risk immunity, and the government.

#### 4.2.2. Causality Analysis of Risk Communication

After determining the boundary of system research, through the analysis of the relationship between the internal factors of the boundary, the system causality diagram can be obtained. The risk communication system is no longer a single linear relationship but an intricate nonlinear system, which is a dynamic system under the action of many factors. Through the analysis of the risk propagation mechanism and the risk system of

the prefabricated building supply chain, the system causal loop diagram is constructed based on the SEAIR model considering recurrence, and the feedback analysis theory of system dynamics is applied to describe the system structure of the risk propagation of the prefabricated building supply chain by the feedback loop, as shown in Figure 5:

**Figure 5.** Causal circuit diagram of risk propagation.

The main circuits included in the figure are explained as follows:


rehabilitation enterprises. With an increase in the number of infection rehabilitation enterprises, to some extent, the number of enterprises that have lost their immunity increases; thus, the number of enterprises with latent new risks will increase, and the number of infection rehabilitation enterprises will be reduced to a certain degree.

### 4.2.3. Flow Chart Analysis of Risk Communication

According to the causality diagram, a complete system flow diagram is constructed by using the system dynamics Vensim software, as shown in Figure 6:

**Figure 6.** Flow chart of risk propagation.

As shown in Figure 6, the model contains four horizontal variables: enterprises with unknown risks, enterprises with latent risks, enterprises with risk transmission, and enterprises with infection rehabilitation. There are five rate variables: the number of unknown enterprises forming new risks, the number of infections, the number of transmissions, government support, and the number of enterprises losing immunity. There are five constants: infection rate, transmission rate, government financial support, government policy supervision, and the proportion of lost immunity. Through consultation with actual construction personnel and researchers in the field of prefabricated buildings, combined with the research literature in related fields [24,39], each constant is assigned to determine the parameter expression, as shown in Table 2:



#### *4.3. Analysis of Model Simulation Results*

As seen from Figure 5, the four main bodies involved in risk communication are risk-unknown enterprises, risk-latent enterprises, risk communication enterprises, and infection rehabilitation enterprises, and the number of the two main bodies of risk communication enterprises and infection rehabilitation enterprises directly reflects the intensity of risk communication. Among them, enterprises with unknown risks are affected by the number of infections, and the number of infections is determined by the infection rate. Latent enterprises are affected by the number of infections, the number of transmissions, and the number of latent enterprises forming new risks, and the number of transmissions is determined by the transmission rate. The number of risk communication enterprises

is affected by the amount of communication and government support, and government support is determined by financial support and policy supervision. The number of rehabilitation enterprises is affected by the number of enterprises that have lost their immunity and government support, while the number of enterprises that have lost their immunity is determined by the proportion of those that have lost their immunity. Therefore, in the process of risk spread, the infection rate, spread rate, government financial support, government policy supervision, and the value of the proportion of lost immunity play an important role. Through the analysis of the above factors, combined with the actual participants in the supply chain, the change in the number of risk-spreading enterprises in the component manufacturers and the change in the number of risk rehabilitation enterprises in the transporters are taken as examples to study. Vensim software was used to simulate this, and the influence of the infection rate, transmission rate, government financial support, government policy supervision, and the change in the proportion of losing immunity on risk transmission is explored.

#### 4.3.1. Impact of Change in Infection Rate on Risk Transmission

Set the initial infection rate at 10%, increase the infection rate by 5% and increase by 10%, and observe the change in the number of companies affected by risks. Figure 7 shows that, under the premise of infection rate as an influencing factor, the number of enterprises in the process of risk transmission shows significant changes.

**Figure 7.** *Cont*.

**Figure 7.** Impact of changes in infection rates on the number of enterprises in the process of risk transmission: (**a**) the impact of infection rates on businesses with unknown risks; (**b**) the impact of infection rates on businesses with latent risks; (**c**) the impact of infection rates on businesses where risk spreads; (**d**) impact of infection rate on infection recovery businesses.

With the increase in infection rate, the number of enterprises with unknown risks gradually increased, showing an overall increasing trend. The greater the initial infection rate, the smaller the number of businesses with unknown risk and the greater the number of businesses affected by the risk.

With the increase in infection rate, the number of risk-latent enterprises gradually increases, the infection rate is greater, and the number of risk-latent enterprises is greater; the greater the initial infection rate is, the greater the number of businesses with latent risk. On the thirtieth day, the number of risk-latent companies was as high as about 400.

The number of companies that spread the risk gradually increases with the increase in the infection rate, and the greater the infection rate, the greater the number of enterprises affected by the risk and the faster the growth rate. The number of enterprises showed a steady growth trend overall.

With the increase in infection rate, under the influence of risks, the number of infection rehabilitation enterprises gradually showed a slow growth trend from the fifth day, and the growth trend accelerated after that; in general, the greater the infection rate, the greater the infection, and the greater the number of rehabilitation enterprises. The study by Chen, J. et al. found a similar problem [23].

#### 4.3.2. Impact of Change in Transmission Rate on Risk Transmission

The initial transmission rate is set to 15%, and the change in the number of companies in the process of risk transmission is observed under the premise that the transmission rate is observed as an influencing factor by 5% in Figure 8.

**Figure 8.** *Cont*.

**Figure 8.** The impact of changes in transmission rate on the number of enterprises in the process of risk transmission: (**a**) the impact of transmission rates on businesses with unknown risks; (**b**) the impact of transmission rates on businesses with latent risks; (**c**) the impact of transmission rates on businesses where risk spreads; (**d**) impact of transmission rate on infection recovery businesses.

Under the influence of the transmission rate, the number of enterprises with unknown risk gradually increases, but a certain increase or decrease in the transmission rate of 15% will not affect the image transformation of enterprises with unknown risk. This is because in the context of considering relapse, infection rehabilitation enterprises become risk-latent enterprises after losing immunity to risks, and then continue to become risk transmission enterprises and infection rehabilitation enterprises with the spread of risks, and will not become risk-unknown enterprises. In this context of risk transmission, changes in transmission rate will have an impact on risk-latent enterprises, risk transmission enterprises, and infection recovery enterprises, and will not affect the change in the number of enterprises with unknown risks.

With the increase in transmission rate, the number of risk-latent enterprises has shown an increasing trend. Under different transmission rates, the number of latent enterprises increased in the first two days in line with the level of growth; the greater the transmission rate, the smaller the number of companies with latent risks; the smaller the transmission rate, the greater the number of companies with latent risks. Research by Subrata Paul et al. found a similar problem [40].

With the increase in the transmission rate, the number of risk communication companies showed an increasing trend from the fourth day. The greater the transmission rate, the greater the number of businesses affected by the risk; under the influence of different transmission rates, the initial difference in the number of risk transmission enterprises is small, and the number gap gradually increases over time.

With the increase in the transmission rate, the number of recovered enterprises showed an increasing trend from the sixth day. The transmission rate is proportional to the number of infected recovery enterprises, and the larger the transmission rate, the higher the number of infection rehabilitation enterprises; under the influence of different transmission rates, the initial difference in the number of risk transmission enterprises is small, and the quantitative gap gradually increases with the change in time.

#### 4.3.3. Impact of Changes in Government Financial Support on Risk Communication

The initial government financial support is set at 25%, and the probability of increasing or decreasing by 10% is based on this basis, and the number of companies in the process of risk transmission is changed by the government support obtained in Figure 9.

**Figure 9.** The impact of changes in government financial support on the number of enterprises in the process of risk propagation: (**a**) the impact of government financial support on enterprises with unknown risks; (**b**) the impact of government financial support on enterprises with latent risks; (**c**) the impact of government financial support on risk communication enterprises; (**d**) the impact of government financial support on enterprises recovering from infection.

Under the influence of government financial support, the number of enterprises with unknown risks gradually increases, but a certain increase or decrease in the ratio of 20% will not affect the image transformation of enterprises with unknown risks. This is because in the context of considering relapse, infection rehabilitation enterprises become risk-latent enterprises after losing immunity to risks, and then continue to become risk transmission enterprises and infection rehabilitation enterprises with the spread of risks and will not become risk-unknown enterprises. In the context of this risk transmission, changes in government financial support will have an impact on risk-latent enterprises, risk transmission enterprises, and infection recovery enterprises, and will not affect the change in the number of enterprises with unknown risks.

Under the change of government support, the number of enterprises with latent risks has shown an increasing trend. With different government support, the number of latent enterprises increased in the first 14 days in line with the level of growth; the greater the government support, the greater the number of companies with latent risks; the smaller the government support, the smaller the number of companies with latent risks.

Under the change in government support, the number of risk communication enterprises has shown an increasing trend. The financial support of the government is inversely proportional to the number of risk communication enterprises, and the greater the government support, the smaller the number of risk communication enterprises under the state of being affected by risk; with the passage of time, the initial difference in the number of risk-propagating enterprises under different government support is small, and the number gap gradually increases over time.

The degree of government support is directly proportional to the number of enterprises recovering from infection, and the number of rehabilitation enterprises has increased. With the increase in government financial support, the number of enterprises recovering from infection first showed a slow growth, and then increased the range of change.

#### 4.3.4. Impact of Changes in Government Policy Supervision on Risk Communication

The initial value of government policy supervision is set to 25%, and on this basis, a change of 15% is made, and Figure 10 shows the change in the number of enterprises in the process of risk transmission under government supervision.

Under the influence of government policies and supervision, the number of enterprises with unknown risks gradually increases, but a certain increase or decrease in the ratio of 15% will not affect the image transformation of enterprises with unknown risks. This is because in the context of considering relapse, infection rehabilitation enterprises become risk-latent enterprises after losing immunity to risks, and then continue to become risk transmission enterprises and infection rehabilitation enterprises with the spread of risks, and will not become risk-unknown enterprises. Under this background of risk transmission, changes in government policies and supervision will have an impact on risk-latent enterprises, risk transmission enterprises, and infection recovery enterprises, and will not affect the change in the number of enterprises with unknown risks.

The impact of government policies and supervision on the number of enterprises with latent risks is to increase slowly at first, and then increase the growth range. However, on the whole, the impact of changes in government supervision on the number of enterprises with latent risks has not changed much. Under different policies and supervision, the number of enterprises affected by risk all increased from the first 0, and then with the increase in supervision, the number of enterprises with latent risks gradually increased.

The stronger the government supervision, the greater the number of risk transmission enterprises and infection rehabilitation enterprises, but in general, the impact of government supervision on the number of risk transmission enterprises and rehabilitation enterprises gradually increases over time. Under the influence of government policies and supervision, the number of risk transmission enterprises and infection recovery enterprises gradually showed an upward trend since the previous days, and the number growth changed little, and then the quantitative gap gradually increased.

**Figure 10.** The impact of changes in government policy supervision on the number of enterprises in the process of risk propagation: (**a**) the impact of government policy support on enterprises with unknown risks; (**b**) the impact of government policy support on enterprises with latent risks; (**c**) the impact of government policy support on risk communication enterprises; (**d**) the impact of government policy support on enterprises recovering from infection.

4.3.5. Impact of Change in the Proportion of Lost Immunity on Risk Transmission

The initial immunity loss ratio is set to 20%, the increase is set to 25%, and the decrease is set to 15%, and the change in the number of companies in the process of risk transmission is obtained from Figure 11.

**Figure 11.** *Cont*.

**Figure 11.** The impact of changes in the proportion of lost immunity on the number of enterprises in the process of risk transmission: (**a**) the impact of the proportion of immunity loss on enterprises with unknown risk; (**b**) the impact of the proportion of loss of immunity on risk-latent enterprises; (**c**) the impact of the proportion of immunity loss on enterprises that spread risk; (**d**) impact of the proportion of lost immunity on enterprises recovering from infection.

Under the influence of government policies and supervision, the number of enterprises with unknown risks gradually increases, but a certain increase or decrease in the ratio of 20% will not affect the image transformation of enterprises with unknown risks. This is because in the context of considering relapse, infection rehabilitation enterprises become risk-latent enterprises after losing immunity to risks, and then continue to become risk transmission enterprises and infection rehabilitation enterprises with the spread of risks, and will not become risk-unknown enterprises. In the context of this risk transmission, the change in the proportion of loss of immunity will have an impact on risk-latent enterprises, risk transmission enterprises, and infection recovery enterprises, and will not affect the change in the number of risk-unknown enterprises.

Enterprises with lurking risks are generally showing a growth trend. The change in the proportion of loss of immunity has a direct impact on the number of risk-latent enterprises, and the larger the proportion of loss of immunity, the greater the number of risk-latent enterprises.

With the increase in the proportion of loss of immunity, the number of risk transmission enterprises gradually increases, which is directly proportional to the two; a lower number of recovered enterprises is inversely proportional to the two.

#### **5. Conclusions**

Based on the consideration of the SEAIR model, this paper established the risk propagation model of the prefabricated building supply chain and studied the impact of each influencing factor on the supply chain risk propagation by simulating each enterprise, increase and decrease in the virus transmission model, and used Vensim simulation software to set the initial value of related factors. Based on the above results, relevant suggestions are made:

1. With the increase in infection rate, the number of enterprises in the supply chain that are not affected by risk will be greatly reduced, and the number of risk transmission enterprises and the number of risk-latent enterprises will increase significantly. With the increase in transmission rate, the change trend of risk transmission enterprises, risk-latent enterprises, and infection recovery enterprises in the supply chain is roughly the same as the change in the number of enterprises brought about by the increase or decrease in infection rate, but the change in transmission rate will not affect the change in the number of enterprises with unknown risk. Through the above simulation, it can be seen that this is because, while considering the recurrence, some of the risk rehabilitation enterprises may continue to form new risk-latent enterprises,

and with the spread of risks, new risk-latent enterprises become risk transmission enterprises and infection rehabilitation enterprises, which will not affect the number of risk-unknown enterprises. In order to effectively control the number of enterprises affected by risks, it is necessary to take certain measures to reduce the infection rate, which requires enterprises to actively seek the cooperation of other manufacturers when producing products, find enterprises eroded by risks, avoid risks in time, and reduce infection from the root. The enterprise itself actively takes anti-risk measures, understands the enterprises it contacts to prevent itself from being infected, understands the potential risk factors of the department of the enterprise affected by the risk in the production process of the product, assesses its risk level, prepares emergency plans in advance, reduces the business dealings between the department affected by the risk and other departments that are not affected, and avoids the expansion of the risk infection rate.


enterprises and infection recovery enterprises. Therefore, future studies will improve on the basis of the SEAIR model and increase the time delay for analysis.

**Author Contributions:** Conceptualization, X.G. and R.S.; methodology, Y.W.; software, Y.W.; validation L.R. and Y.W.; formal analysis, L.L. and X.W.; investigation. L.R.; resources. Y.W.; data curation, L.R.; writing—original draft preparation, R.S.; writing—review and editing, X.G. and Y.W. visualization, L.R.; supervision L.L. and X.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the State Key Program of National Social Science Foundation of China (Grant no. 19AGL030) and Research Subject of Social Science Development of Hebei (Grant no. 20210201118).

**Data Availability Statement:** We declare that all data, models, and code generated or used during the study appear in the submitted article.

**Acknowledgments:** In this study, I would like to thank Wang Yingchen for his careful guidance and strong support and the students on the team for listening and exchanging ideas so that the research paper could be successfully published.

**Conflicts of Interest:** The authors declare no conflict of interest.
