This study gave a research framework for “the integration of JPCM coordination and emergency collaborative modularization” to evaluate the experience of cross-organizational networks to COVID emergencies and address theoretical research concerns. The following were the primary components of the research framework:

The emergency organizations participating in COVID cross-organizational emergency networks were organized by collecting and sorting data according to international, national, provincial and municipal, cross-regional, residential, third sector, and cyber jurisdiction criteria. Among these groups of emergency organizations, the World Health Organization, which monitored risks to global public health and coordinated responses to a wide range of health emergencies, was an example of an international emergency organization. National emergency organizations were a collection of central government agencies and departments. Some examples of national emergency departments included the National Health Commission, the Ministry of Emergency Management, and the Ministry of Public Security. Provincial and municipal emergency organizations were the collection of provincial and municipal agencies and departments that had jurisdiction over the location where the emergency occurred. Some examples of provincial and municipal emergency organizations included the Provincial JPCM, the Municipal JPCM, the Provincial Health Commission, and the Municipal Health Commission. Cross-regional emergency organizations, such as Disaster Medical Assistance Teams (DMATs), provide rapid-response medical rescue when public health and medical emergencies overwhelm the resources available in a region. Residential emergency organizations included the area’s streets (townships), communities (villages), and hospitals. Third-sector emergency groups pursued specific goals, frequently associated with particular social and political perspectives. In this study, one such association was the China Welfare Institute, which served as an example of one that can participate in the production and livelihood aid of people whose lives have been disrupted due to major natural disasters or severe public accidents. Cyber emergency organizations referred to the Network Resiliency Platform, where ICT regulators, policymakers, and other interested parties can share information. They viewed what initiatives and measures have been implemented to ensure that communities and individuals remained connected during the COVID-19 crisis.

The study considered emergency organizations participating in COVID cross-organizational emergency collaboration as network actors. It used the links between actors to represent the collaborative relationships between emergency organizations. After that, the networks for COVID emergency collaboration can be mapped. To obtain a comprehensive enumeration of the organizations participating in COVID emergency response and their corresponding abbreviations, please refer to Supplementary Appendix.

Network density ( D ) is the ratio of the actual number of node connections to the theoretical maximum number of connections (23, 31). Equation (1) can calculate D values for a network with n nodes and m lines connecting them.(1) D = 2 m n n − 1 where n and m are the numbers of nodes and connections between nodes in the network, respectively.

Network diameter ( N D ) and average path length ( A P L ) measure the communication distance between emergency organizations in the emergency response coordination network and indicate the network’s overall connection. The network diameter measures the distance between the most distant emergency response groups that are collaborating. The average path length equals the average collaboration distance between all emergency organizations (23). The expressions for N D and A P L can be found in the following Equations (2) and (3).(2) N D = L max (3) A P L = ∑ i = 1 n L i n where L max denotes the maximum distance between nodes; L i represents the distance between each pair of nodes; and n is the number of nodes in the network.

Network centralization ( C ) indicates the degree to which a network tends to cluster around its central node, whose values are computed using Equation (4). There are three types of network centralization: degree centralization, betweenness centralization, and closeness centralization (23, 32). This study employs degree centralization to determine whether the emergency response coordination network has a central emergency organization.(4) C = ∑ i = 1 n C max − C i max ∑ i = 1 n C max − C i where C max for the highest possible centrality value at each network node; C i for the centrality of node i .

The clustering coefficient ( C C ) is a metric to assess how well organizations in an emergency response coordination network are developing stable collaborative or modular organizational relationships (32). Equations (5) and (6) presents the density coefficient of node n 1 ( D C n 1 ) and the C C of the network.(5) D C n 1 = 2 u k k − 1 (6) C C = ∑ i = 1 n D C n 1 n where n is the number of network nodes, D C n 1 is node n 1 ’ s density coefficient, k is the number of nodes immediately surrounding node n 1 , and u is the total number of connections between nodes immediately surrounding node n 1 .

As depicted in Figure 1, the overall network of JPCM was drawn to illustrate the panoramic framework. Where nodes represented the sectors or agencies participating in the network, lines reflected the collaboration between the joint prevention and control group nodes. Meanwhile, the larger the size of the JPCM node, the more nodes were connected to it. In Figure 1, the JPCM of the State Council (JPCM), the JPCMs of provincial and municipal governments (exJPCMs), medical facilities (exHospitals), departments at provincial and municipal levels (exHCs, exMCAs, exMHSs, exMOTs, exMPSs, exMOEs, exCAAs, exNRAs, exMCTs, exMFAs, exMIIs, exAMRs, etc.), the Disaster Medical Assistance Team (exDMAT), and street (township) and community (village) (exCMTYs) were represented by purple, orange, blue, and green nodes.

As indicated in Table 1, the network structure indicators were calculated here for each module and the overall JPCM network. The overall network size of the JPCM was 85, indicating that there were a total of 85 departments or agencies participating in the joint control mechanism for the response to the COVID outbreak. Different types of member departments performed different duties in the JPCM and occupy different positions in the collaborative governance network. This study examined the characteristics of different functional working modules. The Interrupt Spread module, Manage Supply module, Medical Rescue module, Restore Work and Production module, and Implement Responsibility module were depicted in Figures 2A–E. As in Figure 1, nodes and lines indicated the participating departments and collaborative relationships. The sectors involved in the Interrupt Spread network are mainly transportation departments, the State Council’s JPCM, and provincial and municipal governments’ exJPCMs. Meanwhile, the exJPCMs of provincial and municipal governments, industry and information technology departments, market regulation departments, and health departments of provincial and municipal governments constituted the fundamental structure of the Manage Supply network. In addition, the health departments, civil affairs departments, and JPCMs of the State Council, as well as these departments at provincial and municipal levels, made up the majority of the departments and agencies in the Medical Rescue network. The representative nodes of the Medical Rescue network also included associations and social organizations for healthcare provision. The representative nodes of the network for the restoration work and production network were the JPCMs and market regulation departments at the State Council and provincial and municipal government levels. Finally, the implementation responsibility network had participating entities such as JPCMs, the State Council’s health departments, emergency management departments, human resources and social insurance departments, and the provincial and municipal governments. The key nodes of the Implement Responsibility network also included market regulation, development and reform, industry and information technology, customs, border inspection, public security, transport, education, and culture and tourism departments of the provincial and municipal governments.

The network structure indicators of each module were calculated in Table 1. In the collaborative governance for the COVID pandemic, the Interrupt Spread network, the Manage Supply network, the Medical Rescue network, the Restore Work and Production network, and the Implement Responsibility network had 73, 55, 60, 47, and 66 member departments and agencies, respectively. There were 78, 62, 127, 46, and 286 collaboration partnerships among the member departments and agencies. There was a significant increase in the scale and quantity of the Implement Responsibility module compared to other functional networks. This phenomenon was related to the diversity and complexity of emergency departments and agencies that in the Implement Responsibility functional network. The network densities of the Interrupt Spread, Manage Supply, Medical Rescue, Restore Work and Production, and Implement Responsibility modules were 3.0, 4.2, 7.1, 4.3, and 17.2%, respectively. The Implement Responsibility and Medical Rescue modules had a higher network density, whereas the Interrupt Spread, Manage Supply, and Restore Work and Production modules had relatively lower network densities. This demonstrated that the departments and agencies in the Implement Responsibility and Medical Rescue modules collaborated frequently and had the closest synergistic links. The Interrupt Spread, Manage Supply, and Restore Work and Production modules primarily had collaborative relationships with a relatively low number of departments and agencies; therefore, the overall collaboration density among the departments and agencies was relatively low. Overall, the Implement Responsibility module had a higher network density and network cohesion than the overall JPCM emergency coordination network, indicating a higher degree of sharing among the same emergency response departments and agencies in the Implement Responsibility module network.

The network centralization of the Interrupt Spread, Manage Supply, Medical Rescue, Restore Work and Production, and Implement Responsibility modules was 11.72, 23.46, 11.04, 18.48, and 11.76%, respectively, indicating the presence of prominent core emergency response in the Manage Supply module. Similarly, in the Restore Work and Production network, there was a clear tendency for the network to cluster toward the core emergency response agencies, with a relative concentration of network power. However, in the Interrupt Spread, Medical Rescue, and Implement Responsibility modules, the position of different emergency response departments and agencies was generally balanced, as was the distribution of power among emergency response departments and agencies. The collaboration networks of the Interrupt Spread, Medical Rescue, and Implement Responsibility modules typically exhibited the characteristics of a homogeneous structure.

The network diameters of the Interrupt Spread, Manage Supply, Medical Rescue, Restore Work and Production, and Implement Responsibility modules were correspondingly 2, 3, 2, 2, and 3. Correspondingly, the network average path lengths of the Interrupt Spread, Manage Supply, Medical Rescue, Restore Work and Production, and Implement Responsibility modules were 1.97, 1.99, 1.93, 1.96, and 1.93, which indicated that the Manage Supply module had the best collaboration network connectivity, the collaboration and communication distance between the departments and agencies was the shortest, and collaboration between the departments and agencies was more consistent. Despite having a network diameter of 3, the Implement Responsibility module’s average path length was also low. This indicated that the implemented responsibility collaboration network had convenient connectivity and that communication between the emergency agencies was efficient and smooth.

The clustering coefficients for the modules of Interrupt Spread, Manage Supply, Medical Rescue, Restore Work and Production, and Implement Responsibility were 0.762, 0.286, 0.537, 0.000, and 0.459, respectively. Therefore, the emergency departments and agencies involved in the Interrupt Spread and Medical Rescue modules had established a number of stable and cooperative links. The emergency departments and agencies with a cooperating connection had higher agglomeration levels. Additionally, the clustering coefficients of the Interrupt Spread and Medical Rescue modules were higher than those of the overall JPCM network, illustrating that the JPCM network had not yet established a stable clustering organization model. However, due to the high degree of heterogeneity among the emergency departments and agencies in the network, all of them were more likely to have access to heterogeneous emergency resources and had higher emergency resource transfer efficiency.

The E–I index was introduced to explore the resource flow and faction structure among departments and agencies in the emergency response network. To assess the E-I index’s effectiveness and determine whether each network’s E-I index is random, we performed 5,000 random permutations of the same nodes and relational links. According to Table 2, the overall JPCM and Implement Responsibility networks passed with a value of p < 0.001, while the Manage Supply and Medical Rescue networks passed the significance test with p < 0.05. Therefore, the E-I index observations for the four networks were statistically significant.

According to Table 2, the E–I index for the Medical Rescue and Implement Responsibility networks were 0.122 and 0.147, respectively. The finding suggested that there were more external relationships than internal ones. Cross-group emergency response coordination was at a higher level. In addition, it was found that within the Medical Rescue and Implement Responsibility networks, different departments and agencies had a stronger sense of identity and were better able to respond to emergencies. In contrast, the E–I indexes for the overall JPCM and Manage Supply networks were − 0.192 and − 0.452, respectively. This showed that each group of departments and agencies in these networks was likelier to engage in intra-group than inter-group collaboration.

Further, the external and internal links were calculated for each group of departments and agencies. Drawing chord diagrams of the relationships between groups of departments and agencies (see Figures 3A–F) allowed us to discuss the collaborative relationships, frequency of interactions, and resource transfers between groups of departments and agencies in the overall JPCM network and in the different emergency response modules. The E-I indices for each group of departments and agencies in the overall JPCM network and the Interrupt Spread, Manage Supply, Medical Rescue, Restore Work and Production, and Implement Responsibility modules were given in Tables 3–6 (networks with statistically significant E-I indices).

Table 3 displayed the external and internal links and E–I index for several groupings within the overall JPCM network. The E-I index for the international group was 1. International cooperation within the JPCM network referred to the link with the World Health Organization (WHO), which notified the epidemic and, in January 2020, established a support team to respond to the early outbreak. Therefore, the international group’s partnership with the JPCM network was an external link. The national, provincial and municipal E-I indexes are −0.172 and −0.197, respectively. This suggested that although the national group issued orders to the provincial and municipal groups, and the provincial and municipal groups were then required to receive and execute those orders, there were slightly more collaborative relationships within the same jurisdiction than between the external emergency response agencies of these groups. The E-I indices for the cross-regional, residential, and third-sector groups were −0.333, −0.429, and −0.478, respectively. This indicated that the departments and agencies within these groupings were more inclined to collaborate internally and provide resources. In the JPCM network, the cross-regional groups mainly referred to the Disaster Medical Assistance Team (Emergency Medical Teams (EMTs) as classified by WHO), which was dispatched to the center of a pandemic to assist in health emergencies. Residential groups consisted of local hospitals, communities, and neighborhoods. After receiving direction and resources from external relationships, the residential group primarily engaged in emergency response coordination through internal operations. Moreover, this also occurred in the third sector group. In addition, the cyber group mainly coordinated with external offline emergency response organizations.

Table 4 demonstrated the external/internal links and E–I index for each group in the Manage Supply module. The E-I index of the national group was −0.452, indicating that national emergency response organizations were more inclined to engage in internal collaboration and resource provision in the Manage Supply module. The E-I index of provincial and municipal organizations was −0.091, indicating that their synergistic relationship with external emergency organizations was almost random. In the Manage Supply module, the E-I index for the residential and the third sector group was 1, suggesting that residential and online departments and agencies relied exclusively on external collaboration and resource provision.

Table 5 presented the external/internal links and E–I index for each group in the Medical Rescue network. The E–I index of a national group was 0.255, which can improve the coordination and direction of heterogeneous nodes in the Medical Rescue collaborative network. The E–I index of the provincial and municipal group was −0.182, indicating that provincial and municipal emergency agencies preferred internal collaboration and resource provision for Medical Rescue tasks. Furthermore, the E-I indexes of the cross-regional and third sector were − 0.333 and − 0.130, respectively, indicating that when it came to Medical Rescue tasks, information and resources flew more within the cross-regional and third sector groups. In addition, the E–I indexes for the residential and cyber groups were 0.143 and 0.333, respectively. This indicated that the residential and cyber agencies were connected to external nodes for obtaining resources and carrying out rescue activities.

The external/internal links and E–I indices of the groups in the implement responsibilities network were shown in Table 6. The E-I index of the national group was 0.222, and that of the provincial group was 0.019. This was because the activities of receiving administrative instructions and creating a connection between the diverse nodes in the implement responsibilities module were primarily moved from higher-level to lower-level departments. The E-I index for the residential group was −0.333, indicating that more internal nodes were responsible for improving the implementation of emergency management at the residential level. The E-I index for both the third sector and cyber groups was 1. The collaborative relationships between the third sector and cyber participants in the implement responsibilities module were provided exclusively by external entities of administrative power.

The JPCM emergency response coordination model was diverse and had complex tasks, including interrupting the spread of the epidemic, managing the logistics and supply of emergency supplies, providing medical care for infected people, safeguarding economic stability and the order of work and production, and reinforcing the implementation of instructions in all segments. The emergency coordination model consisted of several emergency function modules, which affected the construction and development of JPCM’s overall emergency coordination network. For this reason, QAP analysis was applied to study each emergency response functional module in JPCM emergency response coordination to elucidate each module’s driving mechanism and influence on the construction of overall emergency response coordination.