Dynamic Analysis of the Effectiveness of Emergency Collaboration Networks for Public Health Emergencies from a Systems Thinking Perspective

Abstract

In recent years, public health emergencies have become frequent worldwide. In response to these complex and evolving emergencies, the organizations involved are increasingly collaborating with each other. From a systems thinking perspective, greater attention should be given to the long-term development and continuous operation of emergency collaboration systems. By time slicing the development of the COVID-19 epidemic in Wuhan, the different phases of emergency collaboration networks can be respectively established. A new method for identifying key organization nodes and different network attack strategies is proposed, assessing network effectiveness from two dimensions: efficiency and resilience. The results indicate that, compared to random attack strategies, the efficiency and resilience of these networks are significantly affected by deliberate attack strategies, underscoring the network’s sensitivity to high-importance nodes. Based on the variations in network efficiency and resilience, the effectiveness of different forms of networks are classified into four types. The pre-emergency network is categorized as resilience-focused, the mid-emergency network as efficiency-oriented, the post-emergency network as efficient-resilient, and the overall emergency network as inefficient-fragile. Analyzing forms of network effectiveness at different phases offers a deeper understanding of the operational characteristics, dynamic changes, and existing issues within emergency collaboration networks. This study provides a vital theoretical basis and practical guidance for emergency management departments and decision-makers on how to effectively improve collaboration mechanisms between different organizations.

1. Introduction

In recent years, the frequent occurrence of emergencies has heightened uncertainty, presenting significant challenges for effective disaster response [1,2]. Public health emergencies, a type of sudden event, often trigger cascading effects where risks can intertwine and evolve across regions, sectors, and time, necessitating interdepartmental collaboration for effective emergency management [3,4,5]. Additionally, these emergencies often persist and cause substantial damage, spanning the entire emergency management process, from onset to outbreak and routine control, and encompassing the pre-, mid-, and post-emergency phases [6,7]. Both the evolution of these situations and their response mechanisms require analysis from a comprehensive, systemic perspective [8]. The global spread of COVID-19 undoubtedly sounded a critical alarm. Building on experience from managing SARS, H1N1, and Ebola, countries have continued to innovate and develop response systems and models tailored to their public health emergencies [8,9,10,11]. However, certain issues warrant further exploration. For instance, during the early stages of the COVID-19 pandemic, disorder and confusion frequently arose with disorganized and fragmented participation from social forces [12,13]. As more organizations became involved, unclear boundaries and poor communication led to dilemmas regarding participation for some [14,15].

Cross-organizational emergency collaboration has emerged as a viable strategy for responding to the uncertainty and complexity of disaster events [16,17,18]. This dynamic process, characterized by multi-party participation and interconnected action, gradually shapes complex and adaptive emergency collaboration networks [19,20]. As disaster scenarios grow more complex, traditional, single-type emergency response functions are inadequate for addressing the challenges posed by these disasters [21,22]. These collaboration networks integrate various emergency functions, including command and dispatch, search and rescue, medical treatment, and security, thereby forming a comprehensive and multifaceted response system [23,24,25,26]. A critical issue for discussion is how the networks’ structural characteristics influence collaborative behavior and affect their overall effectiveness.

Indicators such as network density, centrality, cohesion, clustering coefficients, and average path lengths are commonly used to study the structural characteristics of these networks [27,28,29]. Additionally, network connectivity is evaluated by measuring clustering trends and the dependence on core nodes [30,31,32,33,34]. Clarifying these concepts is essential when studying network effectiveness. Effectiveness differs from efficiency; the latter typically refers to the amount of work completed in a specific timeframe, suggesting optimal resource utilization [35]. In contrast, effectiveness emphasizes the degree of goal achievement, encompassing the concept of efficiency [36]. Studying network effectiveness requires consideration of networks’ inherent attributes and their ability to withstand and adapt to adverse external conditions. Resilience is a prominent topic in crisis management [37,38]. Nonetheless, it remains unclear how emergency networks can maintain resilience while maximizing efficiency [39]. Comfort and Kapucu suggests that resilience and collaboration are vital for ensuring rapid crisis response while minimizing societal impacts [40,41]. Resodihardjo’s study on Dutch safety regions (SRs) indicates that their national strategic agenda explicitly emphasizes the importance of resilient action [39,42]. Liu et al. assert that effectively utilizing inter-organizational relationships is crucial for enhancing network efficiency [43]. Inter-organizational collaboration optimizes resource sharing and information transfer processes, enhancing efficiency, significantly improving the overall emergency response speed, and reducing rescue costs [44]. By analyzing the response networks among stakeholders during hurricane Harvey, network robustness was measured through natural connectivity to provide theoretical guidance for optimizing the robustness of U.S. urban emergency management networks [45].

However, empirical research on the collaborative processes within networks remains insufficient [46]. This paper first summarizes and reviews the literature on cross-organizational emergency collaboration networks, as well as resilience and efficiency in public health emergencies. It combines actual cases from China’s response to COVID-19 and employs a systems theory perspective to establish four networks: pre-emergency, mid-emergency, post-emergency, and overall networks, exploring the formation and effectiveness of these collaboration networks. Secondly, we propose an innovative method for identifying key nodes in emergency collaboration networks, designing two types of attack modes, random attacks and deliberate attacks, based on node importance. Network efficiency is measured using the average shortest path, while network resilience is assessed through connectivity. We classify four levels of network effectiveness: efficient-resilient, efficiency-oriented, resilience-focused, and inefficient-fragile. The aim is to strengthen both network resilience and efficiency, ensuring that emergency operations can continue even when some organizational nodes fail. This study aims to provide theoretical support and practical guidance for the establishment of more systematic and effective emergency management systems.

The remainder of this paper is organized as follows. Section 2 introduces the research framework, the identification method for key nodes of emergency collaboration networks, and the measurement of network effectiveness. Section 3 evaluates the effectiveness of emergency collaboration networks through case analysis. Section 4 discusses the findings obtained from the analysis. Section 5 provides conclusions and some recommendations.

2. Research Design and Methods

2.1. Research Framework

Public health emergencies trigger cross-disciplinary chain reactions, leading multiple organizations to form emergency collaboration networks. Firstly, networks will evolve over time and with events. Using time slicing, they are divided into three phases: pre-, mid-, and post-emergency. Therefore, several phased sub-networks and an overall emergency network covering the whole process are constructed. Secondly, we design key node identification and attack strategies to evaluate the effectiveness of a network from a systems thinking perspective. Thirdly, the effectiveness of the network is measured from two aspects: network efficiency and resilience. Finally, by conducting a two-dimensional analysis of network efficiency (high/low) and resilience (strong/weak), we classify the effectiveness of emergency collaboration networks and provide forms of network effectiveness in different stages. These are helpful to understand the operational characteristics, dynamic changes, and challenges of emergency collaboration networks. The research analysis framework is shown in Figure 1.

2.2. Evaluation Method of Node Importance

Key organization nodes have a significant impact on maintaining the efficiency and resilience of an emergency collaboration network, so a new method for evaluating node importance is proposed. To address the problem of a single index being inadequate for evaluating the importance of nodes [47], the degree of centrality, betweenness centrality, closeness centrality, and eigenvector centrality of nodes were selected as the four indicators to measure the importance of nodes. The importance of the nodes is re-determined by assigning corresponding weights to the indexes.

For the graph G = (V,E) with n nodes, the degree centrality of nodes refers to the total number of nodes connected to other nodes. Degree centrality in directed networks can be divided into in-degree centrality and out-degree centrality. The high degree centrality of the emergency organization indicates that the organization is centrally located in the network and is more active in establishing collaborative relationships with other emergency organizations. Standardization of degree centrality is necessary when comparing different networks, as presented in Equation (1).

$$C_d(v_i)=\sum _{i=1,i\ne j}^n{d}_{ij}^{in/out},{C^{\prime }}_d(v_i)={\displaystyle \frac{C_d(v_i)}{n-1}},$$

(1)

where $C_d(v_i)$ is the degree centrality of node i, ${C^{\prime }}_d(v_i)$ is the standardized degree centrality, $D_{ij}$ is the number of in-degree and out-degree, and n is the total number of nodes.

Betweenness centrality measures the frequency at which a node as a bridge to the shortest path between other nodes, reflecting the degree of control of network resources by the nodes. The higher the betweenness centrality of an emergency organization, the more important its brokerage role is in the network. The role of brokerage makes the emergency organization node closer to the network center and has stronger control over other nodes. The calculation process is shown in Equation (2).

$$C_B\left(v_i\right)=\sum _{i\ne v\ne j\in V}{\displaystyle \frac{{\sigma }_{ij}\left(v\right)}{{\sigma }_{ij}}},{C^{\prime }}_B\left(v_i\right)={\displaystyle \frac{2C_B\left(v_i\right)}{(n-1)(n-2)}},$$

(2)

where $C_B\left(v_i\right)$ is the betweenness centrality of node i, ${C^{\prime }}_B\left(v_i\right)$ is the standardized betweenness centrality, ${\sigma }_{ij}\left(v_i\right)$ is the number of shortest paths from s to t passing through node v, and ${\sigma }_{ij}$ is the number of shortest paths from point i to j.

Closeness centrality measures the reciprocal of the average shortest path length from one node to the other nodes. If an emergency organization needs to be selected as the core transit organization in an emergency collaboration network, and its connection distance to other organizations is generally close, the emergency organization with the highest closeness centrality will be selected. The closeness centrality is computed using Equation (3).

$${C^{\prime }}_C\left(\begin{array}{c}{v}_i\end{array}\right)={\displaystyle \frac{1}{d_i}}={\displaystyle \frac{n-1}{{\displaystyle \sum _{j\ne i}}{d}_{ij}}},$$

(3)

where ${C^{\prime }}_C\left(\begin{array}{c}{v}_i\end{array}\right)$ is the standardized closeness centrality of node i, and $d_{ij}$ is the shortest path length from node i to node j.

Eigenvector centrality is an index to measure the importance of adjacent nodes to nodes. The higher the eigenvector centrality of a node, the higher the degree centrality of its adjacent nodes. Specifically, high-quality connectivity means having more powerful partners closer to the core organization. Eigenvector centrality not only analyses the connection quantity, but also the connection quality of emergency organization nodes. The calculation formula is shown in Equation (4).

$${E^{\prime }}_C\left(\begin{array}{c}{v}_i\end{array}\right)=x_i=c\sum _{j=1}^n{a}_{ij}{x}_j,$$

(4)

where ${E^{\prime }}_C\left(\begin{array}{c}{v}_i\end{array}\right)$ is the standardization eigenvector centrality of node i, $a_{ij}$ is the adjacency matrix of the network, and c is the eigenvalue of the eigenvector.

The importance degree of nodes (NID) is calculated comprehensively by combining the above four indexes, in which each index is weighted according to the analytic hierarchy process. The formula for computing the NID index in this study is given in Equation (5).

$$NI{D}_i={\omega }_1{C^{\prime }}_d(v_i)+{\omega }_2{C^{\prime }}_B\left(v_i\right)+{\omega }_3{C^{\prime }}_C\left(\begin{array}{c}{v}_i\end{array}\right)+{\omega }_4{E^{\prime }}_C\left(\begin{array}{c}{v}_i\end{array}\right),$$

(5)

where $NID(v_i)$ is the importance degree of node i, and ω is the weight of each index.

2.3. Network Attack Strategy

To evaluate the effectiveness of emergency collaboration networks, different types of attack strategies have been designed to simulate potential interference and failure scenarios in the network. On the one hand, we consider the possibility of random failure of the nodes. Because of the uncertainty of emergencies, a series of uncertain events will occur immediately. Such as in the COVID-19 epidemic, a number of organizational nodes collapsed due to the constant spread of the virus. Thus, the failure mode of random attack is designed to simulate the random failure of nodes in the network. In this case, a certain proportion of nodes are randomly selected and regarded as failed nodes to evaluate the effectiveness of the emergency collaboration network in the face of random node failures, and to test its vulnerability and stability when subjected to stochastic destruction. On the other hand, we consider the possibility of failure of a specific node. For example, when medical and health institutions are hit hard, we evaluate the robustness and fault tolerance of the network in the face of uncertainty and potential danger. Therefore, a deliberate attack strategy is designed to simulate the failure of a specific node. According to the importance of nodes, a certain proportion of nodes are deleted from the initial state of emergency cooperation networks in order to evaluate the sustainability of the response abilities of emergency cooperation networks in the face of targeted damage.

2.4. Index of Network Effectiveness

In this paper, network efficiency and resilience are used to measure the effectiveness of emergency collaboration networks.

For the measurement of network efficiency, the network efficiency index represents the abilities in information sharing, resource allocation, and decision-making coordination among organizations through direct or indirect channels in the emergency collaborative network. Higher network efficiency means that when dealing with public health emergencies, resources can quickly reach the places where they are needed, reducing the risks caused by poor communication or delay. The calculation of network efficiency is based on the concept of the average shortest path in graph theory, and the average value of the shortest path between each pair of nodes in the network. The shorter the distance between two nodes, the higher the efficiency of information and resource transmission, so the contribution of this node is greater. The greater the total contribution of all node pairs in the network, the higher the efficiency of the whole network, as shown in Equation (6).

$$E(G)={\displaystyle \frac{1}{N(N-1)}}\sum _{i\ne j}^n{\displaystyle \frac{1}{d_{ij}}},$$

(6)

The proportion of the number of nodes in the largest connected subgraph to the total number of nodes in the network is used as an index to measure the network resilience. When a network is subjected to an attack, it will be divided into several sub-networks that are not interconnected. The sub-network containing the most nodes is referred to as the largest connected subgraph, which is generally used to measure the overall connectivity of the network, as shown in Equation (7).

$$R(G)={\displaystyle \frac{N^{\prime }}{N}},$$

(7)

where N’ is the number of nodes in the largest connected subgraph, N is the total number of nodes in the emergency collaboration network, and G is the resilience of the emergency collaboration network. The larger the value of G, the more connected nodes there are in the emergency collaboration network, indicating stronger resilience. Conversely, a smaller G value indicates weaker resilience.

The efficiency and resilience of a network actually reflects the persistence and resistance of the network in the face of external interference or internal node failure, representing the effectiveness of an emergency collaboration network to the greatest extent.

3. Case Analysis

3.1. Case Selection

Public health emergencies, especially the spread of infectious diseases, cause great distress to residents in different areas. At the end of 2019, the concentrated outbreak of COVID-19 epidemic attracted global attention, and Wuhan, China was the main area suffering from it. Given that the region’s response to the COVID-19 pandemic has a clear narrative and background information, featuring a pattern of centralized treatment and multi-party support in its event development, it was chosen as a typical case for this study. From beginning to end, it involves the whole process of emergency. The story line is as follows. On 31 December 2019, an unexplained pneumonia was first reported domestically, leading up to the lockdown of Wuhan city on 23 January 2020, which represents the pre-emergency period (pre-emergency). After 76 days of struggle, the control of departure passage was lifted and the foreign traffic was resumed on April 8. This period is considered the intensive control phase of the epidemic, that is, the mid-emergency phase. After that, on 26 April a number of hospitalized COVID-19 patients in this city were cleared for the first time and the whole city entered the stage of normalized infectious disease control, which was determined as the post-emergency phase.

3.2. Construction of Emergency Collaboration Networks

The data of emergency collaboration network were collected by a multi-source information collection method. The collaboration relationship between emergency organizations was determined by extracting key information from policy documents, official notices, and authoritative news reports. The data mainly come from the official websites and blogs of governments and relevant departments, as well as non-government official websites such as the Chinese Red Cross, Wuhan Charity Federation, the Wuhan branch of the Chinese Red Cross, and news articles on Xinhua Net and People’s Daily Online. The data related to emergency plans primarily come from the textual materials of national and local public health emergency response plans, including but not limited to the National Public Health Emergency Response Plan, the Hubei Province Public Health Emergency Response Plan, and the National Public Health Emergency Medical Rescue Emergency Response Plan. Finally, three phased emergency collaboration networks and an overall emergency collaboration network were constructed, as shown in Figure 2. The nodes represent emergency organizations and the lines represent collaboration relationships.

The structural characteristics of each network are summarized in

Table 1. Characteristic indexes of emergency collaboration networks.

Emergency Collaboration Network	Size (Nodes)	Cooperation Relations (Edges)	Average Degree	Average Clustering Coefficient	Density
Overall	72	359	4.9	0.296	0.066
Pre-emergency	34	111	3.3	0.239	0.099
Mid-emergency	56	242	4.3	0.309	0.079
Post-emergency	21	65	3.1	0.282	0.155

. The scale of the overall network and the number of network connections are 72 and 359, respectively, and 359 collaboration relationships have been established among 72 emergency organizations. The average degree is 4.9 and the average clustering coefficient is 0.296, which are large enough to consider that there are stronger ties or collaborative relationships in the overall network. The network density is only 0.066, which may lead to inefficient resource sharing and information transmission, thus affecting the sustainability of emergency response. Compared with an overall network, phased emergency collaboration networks involve less organizations and collaborative relationships, but their structural characteristics are better than the overall network. The average degrees of the pre-, mid- and post-emergency collaboration networks are 3.3, 4.3, and 3.1, respectively; the average clustering coefficients are 0.239, 0.309, and 0.282, respectively, and the network densities are 0.099, 0.079, and 0.155, respectively, indicating that the resource and information interactions among emergency organizations are frequent and close. Therefore, it can be preliminarily concluded that the efficiency of the phased networks is better than that of the overall network.

3.3. Analysis of Node Importance in Emergency Collaboration Network

To evaluate the important organization nodes in each emergency collaboration network, the indexes of degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality for each node were calculated. The order of the nodes’ importance in the emergency collaboration network was calculated by Equation (5). The partial orders are listed in

Table 2. Importance ranking of nodes in emergency collaboration networks.

Emergency Collaboration Network	Rank	Organization	Degree Centrality	Betweenness Centrality	Closeness Centrality	Eigenvector Centrality	NID
Overall	1	HPCPCH	1.095	0.164	0.525	0.302	0.577
	2	HPG	1.041	0.176	0.534	0.236	0.550
	3	HPCDPC	0.838	0.138	0.474	0.322	0.479
	4	HPTD	0.527	0.196	0.321	0.843	0.468
	5	CRC	0.649	0.110	0.354	0.700	0.463
Pre-emergency	1	HPG	0.588	0.417	0.650	0.825	0.608
	2	SCPRC	0.265	0.269	0.426	1.000	0.454
	3	HPCDPC	0.353	0.166	0.542	0.689	0.416
	4	HPPSD	0.412	0.027	1.000	0.286	0.411
	5	CCDPC	0.294	0.116	0.382	0.931	0.402
Mid-emergency	1	HPCDPC	0.509	0.146	0.519	0.706	0.462
	2	HPTD	0.309	0.151	0.643	0.873	0.457
	3	HPSSACA	0.364	0.055	0.514	0.892	0.429
	4	HPHC	0.455	0.091	0.662	0.507	0.418
	5	HPPSD	0.345	0.064	0.514	0.654	0.375
Post-emergency	1	HPPHC	0.65	0.058	1	0.85	0.617
	2	ORNGO	0.55	0.011	1	0.849	0.572
	3	CRC	0.55	0.011	1	0.849	0.572
	4	OCW	0.55	0.011	1	0.849	0.572
	5	RCSCHB	0.55	0.011	1	0.849	0.572

. It was observed that the order of node importance differs from that of its four centrality characteristics; there are significant differences, which further indicate that the nodes’ importance cannot be comprehensively evaluated only by a single characteristic index of nodes. This defect is improved by the comprehensive calculation of node importance.

The Hubei Province COVID-19 Prevention and Control Headquarters (HPCPCH), Hubei Province Government (HPG), and the Hubei Province Center for Disease Prevention and Control (HPCDPC) rank in the top three in the overall emergency collaboration network. The HPG, State Council of the People’s Republic of China (SCPRC), and the HPCDPC rank in the top three in the pre-emergency collaboration network. The HPCDPC, Hubei Province Transportation Department (HPTD), and the Hubei Province Safety Supervision Administration of Civil Aviation (HPSSACA) rank in the top three in the mid-emergency collaboration network. Hubei Province Psychology Hospitals and Clinics (HPPHC), other relevant non-government organizations (ORNGNs), and the community residents committees (CRCs) rank in the top three in the post-emergency collaboration network. Emergency organizations may play different roles in each network, such as key organizers, executors, or coordinators. For example, the HPCPCH serves as the pivotal core in the overall network and is crucial for collaboration. Through its close connections to local governments, rescue teams, and suppliers, it serves as a bridge for inter-organizational collaboration to facilitate rapid resource and information transmission. In addition, the connection between the HPCPCH and influential organizations endows it with significant influence and decision-making power. Therefore, the HPCPCH is an executor, coordinator, and influencer, with the highest comprehensive importance.

3.4. Analysis of Network Effectiveness Under Different Attack Strategies

Based on the overall and phased emergency collaboration networks, the effectiveness of the networks under the two strategies of random attack and deliberate attack are compared and analyzed by Pycharm.

3.4.1. Analysis of Emergency Collaboration Network Efficiency

Figure 3 illustrates the variations in the network efficiency of emergency collaboration networks under two different attack strategies. The horizontal axis indicates the proportion of removed nodes, while the vertical axis reflects network efficiency, evaluating both the phased and overall networks at various node removal rates.

As shown in Figure 3a, under the random attack strategy, network efficiency steadily decreases with increasing node removal proportions. Specifically, the pre-emergency network and the overall network exhibit a more pronounced decline, with efficiency halving when 50% of the nodes are removed. In contrast, the mid-emergency and post-emergency networks show slower declines, particularly in the post-emergency network, where efficiency remains relatively high despite a large proportion of node removal. This indicates that the mid-emergency and post-emergency networks demonstrate higher robustness under random node removal, whereas the pre-emergency network is more vulnerable. Additionally, the overall network experiences the steepest decline in efficiency with node removal, demonstrating that random attacks substantially affect the overall network performance. Under the deliberate attack strategy (Figure 3b), nodes are removed based on their importance, leading to a much sharper decline in network efficiency. Particularly at lower removal proportions, the network efficiency in the pre-emergency and overall networks drops sharply, highlighting the critical role of high-importance nodes in network performance during these phases. Meanwhile, the post-network exhibits strong attack resistance, maintaining relatively high network efficiency even with significant node removal. In general, as the node removal increases, the rate of network efficiency decline is much faster under the deliberate attack strategy compared to the random attack strategy. This further validates the effectiveness of the proposed key node identification method.

3.4.2. Analysis of Emergency Collaboration Network Resilience

Similarly, the results of the resilience assessment for the emergency collaboration networks are presented in Figure 4.

As shown in Figure 4a, network resilience gradually decreases with an increasing proportion of removed nodes. The pre-emergency and post-emergency networks exhibit slow declines, maintaining relatively strong resilience, with the post-emergency network demonstrating the highest resilience. In contrast, the mid-emergency and overall networks display weaker resilience, particularly in the overall network, where resilience declines the most sharply as the node removal increases. In general, under random attack, network resilience declines across all phases, with the mid-emergency network showing the strongest resilience and the overall network the weakest. Under deliberate attack (Figure 4b), network resilience declines more rapidly and sharply. When the proportion of node removal reaches approximately 20%, the resilience in the mid-emergency network drops sharply, indicating a high dependence on key nodes during this phase. In the overall network, resilience drops steeply when the node removal proportion reaches 30–40%, remaining at a low level afterward. The resilience variation in the pre-emergency network is similar to that observed under random attack. The post-emergency network similarly demonstrates strong resilience under deliberate attack. In general, under deliberate attack, the decline in network resilience is significantly faster than under random attack, highlighting the network’s sensitivity to high-importance nodes.

In summary, network efficiency and resilience decrease under both random and deliberate attacks, with the decline being more pronounced under deliberate attacks, particularly when high-importance nodes are removed. The post-emergency network consistently exhibits high efficiency and strong resilience, regardless of whether the attack is random or deliberate. These findings highlight the critical role of protecting high-importance nodes to maintain network efficiency and resilience, particularly in the early phases when the network is most vulnerable to targeted attacks.

3.5. Comparative Analysis of Emergency Collaboration Network Effectiveness

To better understand the effectiveness of emergency collaboration networks, a comparative analysis of network efficiency and resilience across different phases was performed. Results from the deliberate attack strategy were selected, as shown in Figure 5. The horizontal axis shows the proportion of removed nodes, while the left and right vertical axes represent network efficiency and resilience, respectively. The blue line represents the changes in network efficiency, while the orange line reflects changes in resilience.

Figure 5a illustrates the overall emergency collaboration network, showing that both network efficiency and resilience decrease as more nodes are removed. Network efficiency drops rapidly after about 10% of the nodes are removed, following an almost linear trend towards zero. Network resilience follows a similar downward trend. This suggests that the overall network’s efficiency and resilience are highly dependent on key nodes, leading to vulnerability and inefficiency. Figure 5b illustrates the pre-emergency collaboration network. As more nodes are removed, both network efficiency and resilience gradually decrease in a relatively steady manner. However, after 30% of the nodes are removed, the efficiency declines sharply while resilience remains stable. This suggests that the pre-emergency collaboration network is more sensitive to node removal, particularly in terms of efficiency. Figure 5c illustrates the mid-emergency collaboration network, where resilience is more affected by node removal than efficiency. The resilience declines sharply after around 20% of the nodes are removed, while efficiency remains relatively high, showing a steady downward trend. Although the mid-emergency network can maintain efficiency to some degree, it struggles to retain its resilience. Figure 5d illustrates the post-emergency collaboration network, which shows the highest efficiency and resilience compared to other phases. Although both efficiency and resilience decline after 50% of the nodes are removed, the reduction is slow and not significant. This suggests that the post-emergency network maintains high efficiency and structural resilience even with node failures.

Based on the analysis results, the effectiveness of the emergency collaboration networks is categorized into four types based on changes in efficiency and resilience. These types are efficient-resilient, efficiency-oriented, resilience-focused, and inefficient-fragile. The corresponding network forms for each phase of the emergency collaboration network are discussed, as shown in Figure 6. The post-emergency network shows minimal decline in both efficiency and resilience, exhibiting high performance, and is classified as efficient-resilient. The mid-emergency network maintains stable efficiency, but its resilience is significantly impacted, classifying it as efficiency-oriented. Unlike the mid-emergency network, the pre-emergency network shows strong resilience but is more sensitive to efficiency changes, making it resilience-focused. The overall emergency network experiences the greatest decline in performance, classifying it as inefficient-fragile.

4. Discussion

4.1. Key Organizations in Emergency Collaboration Network

In emergency collaboration networks, organizational roles and functions are interdependent. An organization’s role may shift as its functions change, and the reverse is also true. Consequently, roles with distinct functions, such as supervisor, coordinator, and actor, have emerged [48]. Given this correlation, it is impossible to evaluate key organizations based on a single index, as each index serves a different purpose. Each index carries different implications. For instance, high degree centrality indicates more direct connections, while high betweenness centrality reflects a node’s role as a “bridge”. However, a node’s importance within the overall emergency network is not solely tied to its role or function. With societal advancement and technological development, roles and functions expand and require more comprehensive assessments of node importance. Relying on a single measurement—whether degree, betweenness, closeness, or eigenvector centrality—to determine key organizations is overly simplistic. In this paper, these four indexes are combined, with their importance ranked through a comprehensive weighting system. An attack strategy targeting key nodes was developed and network effectiveness was evaluated through simulated attacks. The results show that considering multiple centrality measures has a greater impact on network effectiveness than relying on a single index. The effectiveness of using multiple centrality measures to assess node importance is thus demonstrated. Therefore, a more comprehensive and dynamic approach to assessing node importance is essential for adapting to the evolving environment of emergency collaboration networks. This approach not only enhances network efficiency and responsiveness, but also aids in understanding their complexity [49].

Evaluating key nodes in both overall and phased networks helps identify global and local core organizations. Variations in network attributes result in different core organizations. The nodes can be classified into two categories. The first category includes hubs of information and resources [50], which accelerate information dissemination and enhance connectivity and efficiency. However, these nodes can also introduce vulnerability in the network, as their failure can negatively impact the network structure and function. The second category reflects power structures and social capital distribution within the network [51]. These nodes significantly influence network behavior and overall functionality. For example, the HPCPCH is a core node in the overall emergency collaboration network, responsible for policy-making, command decisions, and resource coordination [52]. Local emergency response forces act as a “bridge” between national and community levels and their rapid, professional actions minimize disaster impacts [53]. Therefore, identifying and understanding key nodes is essential for optimizing network design, improving performance, and formulating effective management strategies. This ensures efficient resource allocation, improves decision-making quality and speed, and clarifies organizational roles, contributing to more adaptable and sustainable emergency collaboration networks.

4.2. Effectiveness of Emergency Collaborative Network

An important finding is that the overall emergency collaboration network performs poorly, with its efficiency and resilience significantly impacted by node failures. The overall network, covering pre-, mid-, and post-emergency activities, involves numerous organizations, complex information flows, and diverse collaborations. Differences in organizational roles and priorities lead to poor coordination of information transmission and decision-making, lowering the overall network efficiency. Due to the insufficient understanding of the new coronavirus, delays occurred in information sharing and the implementation of response measures across various sectors and organizations. The failure to promptly synchronize communication and process outbreak information among the healthcare system, public health agencies, and the government hindered the effectiveness of outbreak control [54]. Furthermore, extensive connections between the. organizational nodes mean that key node failures can quickly disrupt the entire collaboration, increasing a network’s vulnerability. During the epidemic, the healthcare system in Wuhan faced immense pressure. Overloaded hospitals, caused by a surge in patients, led to the failure of critical healthcare service nodes [13] and disruptions to supply chain nodes for medical supplies and necessities, which rapidly propagated throughout the network [55]. Additionally, participation by government organizations, enterprises, non-profits, and social groups in the emergency network leads to a relative decentralization of power. The increased distance in resource sharing and information transmission further decentralizes the network. In situations with limited resources and time constraints, deviations and delays in policy execution cause inconsistencies in the blockade measures, such as in Wuhan, undermining the overall effectiveness of epidemic prevention and control [56]. Therefore, the overall network’s effectiveness requires further improvement.

The pre-emergency collaboration network, classified as resilience-focused, demonstrates low efficiency but high resilience linked to organizational preparation and defensive strategies during the pre-emergency phase. In this phase, many organizations focus on information preparation and resource reserves. Though collaboration is not fully underway, contingency plans and protective measures offer a degree of resilience. Moreover, the swift activation of higher-level emergency response measures in Wuhan and Hubei Province enhanced the network’s resilience [33]. Thus, even if some nodes fail, the network maintains high resilience. However, as pre-emergency collaboration is largely preparatory, actions and resource allocation are limited, reducing network efficiency. The gaps between the public’s demand for outbreak information and the government’s disclosure undermine the public protective awareness and behavior, reducing the network’s collaboration efficiency [57]. In other words, the pre-emergency network excels at maintaining stability and resilience but lacks coordination efficiency during actual emergencies.

The mid-emergency collaboration network, classified as efficiency-oriented, demonstrates high efficiency but low resilience, explained by the nature of the emergency responses in this phase. In this phase, organizations swiftly initiate responses, accelerating information flow and resource allocation, thereby enhancing collaboration efficiency. The government rapidly mobilized national resources to support Wuhan, exemplifying strong collaboration and efficiency [4,17]. This efficiency arises from close collaboration under high-pressure conditions, with key nodes (such as government agencies or medical institutions) leading rapid response efforts. Other key nodes, including supply chains and transport systems, faced a heightened risk of failure due to the rapid spread of the epidemic [55,58]. However, over-reliance on a few key nodes weakens the network’s resilience. If these nodes fail, the network may collapse, revealing that while the mid-emergency network efficiently handles specific crises, it is vulnerable to multiple failures or cascading effects.

The post-emergency collaboration network, classified as efficient-resilient, shows both high efficiency and strong resilience. After the mid-emergency response, collaboration between organizations becomes more mature and adaptable. In the post-emergency phase, lessons from past experiences stabilize information sharing and resource allocation mechanisms, reducing barriers and maintaining strong network efficiency. In particular, volunteer organizations, non-governmental organizations (NGOs), and government agencies strengthen their collaboration to facilitate community recovery and reconstruction [59]. Furthermore, the adoption of emerging technologies, including health codes, trave cards, and online medical platforms significantly improves the efficiency of post-disaster epidemic control and recovery [60,61]. Additionally, the post-disaster recovery phase typically involves long-term planning and multi-party participation, with clearer roles and responsibilities, leading to a network with greater adaptability and resilience. Therefore, the post-emergency network maintains high resilience. Through the above discussion, the main proposals of this article are compared with other related works, as shown in Table 3.

In summary, the differences in the efficiency and resilience of emergency collaboration networks across phases stem from the complexity of organizational cooperation, information flow barriers, and reliance on key nodes in each phase. This study, along with prior research, confirms that the emergency collaboration system is complex, involving multiple levels, actors, and sectors [36,62]. Multi-level coordination involves various management tiers, from central to local, and from macro to micro levels. Multi-actor participation includes government, enterprises, NGOs, and the public. Cross-sectoral integration spans various fields, such as healthcare, rescue, transportation, and communication. Inefficient communication or decision delays between levels may hinder the timeliness of emergency collaboration. Lack of coordination between actors, conflicting actions, or unsynchronized efforts may cause resource competition or shortages. Professional differences across sectors may result in the misalignment of understanding and execution [63]. From a systems thinking, holistic, and sustainable perspective, it is crucial to optimize communication processes across levels, introduce efficient tools and mechanisms, and ensure the rapid transmission of critical information to all tiers. Standardized processes and protocols can be established between actors to strengthen coordination, using a unified communication platform to ensure consistent information. The key to cross-sectoral integration is establishing an emergency collaboration framework based on specific inter-sector connections, reducing unnecessary friction and misunderstandings [64].

Table 3. The comparison of main proposals with other related works.

Related Works		This Article
Key organization nodes identification
Measurements	Main proposals	Measurements	Main proposals
Degree centrality [30,31]	Identify the number of node connections and obtain the key organizational nodes	The comprehensive importance degree of node	Through the integration of degree centrality, betweenness centrality, closeness centrality and eigenvector centrality, the comprehensive importance of the nodes was solved and key organizational nodes were identified
Node centrality; Betweenness centrality [34,35,65]	The dynamic characteristics of the communication network among emergency organizations are measured to obtain the core organizations of the emergency collaboration network
Betweenness centrality [40,66]	Find out the “bridge” of the emergency plan’s organization system
Eigenvector centrality [56]	Focus on identifying organizations connected to other important nodes
Network effectiveness measurement
Measurements	Main proposals	Measurements	Main proposals
Network robustness [5,45]	The robustness of stakeholder collaboration evolves over time, promoting inter-organizational collaboration	Measured by two dimensions: network efficiency and resilience	Analysis of the effectiveness of phased emergency collaboration networks, to correspondingly improve emergency cooperation ability
Network efficiency [27,33]	An effective collaboration network can significantly improve emergency cooperation ability

Table 3. The comparison of main proposals with other related works.

Related Works		This Article
Key organization nodes identification
Measurements	Main proposals	Measurements	Main proposals
Degree centrality [30,31]	Identify the number of node connections and obtain the key organizational nodes	The comprehensive importance degree of node	Through the integration of degree centrality, betweenness centrality, closeness centrality and eigenvector centrality, the comprehensive importance of the nodes was solved and key organizational nodes were identified
Node centrality; Betweenness centrality [34,35,65]	The dynamic characteristics of the communication network among emergency organizations are measured to obtain the core organizations of the emergency collaboration network
Betweenness centrality [40,66]	Find out the “bridge” of the emergency plan’s organization system
Eigenvector centrality [56]	Focus on identifying organizations connected to other important nodes
Network effectiveness measurement
Measurements	Main proposals	Measurements	Main proposals
Network robustness [5,45]	The robustness of stakeholder collaboration evolves over time, promoting inter-organizational collaboration	Measured by two dimensions: network efficiency and resilience	Analysis of the effectiveness of phased emergency collaboration networks, to correspondingly improve emergency cooperation ability
Network efficiency [27,33]	An effective collaboration network can significantly improve emergency cooperation ability

5. Conclusions

This paper uses the COVID-19 outbreak in Wuhan, Hubei, as a case study to empirically assess the effectiveness of emergency collaboration networks at different phases, focusing on efficiency and resilience, to reveal the network’s sustainability and resistance. Firstly, a new key node identification method was proposed, using network analysis to assess the importance of the key nodes. Secondly, based on their importance, a deliberate attack model was developed to test the impact of various attack strategies on the emergency collaboration network’s effectiveness. The results indicate that the effectiveness of the overall emergency coordination network is poor and the change degree of network efficiency and network toughness is the most significantly affected by node failure. The information transmission and sharing and response measures between different departments and organizations were delayed. The failure of a node with extensive connections leads to the dilution or even disintegration of the whole cooperative relationship, and the network becomes more fragile. As more and more organizations participate in emergency coordination, the overall network structure becomes more dispersed, which affects the network’s efficiency. Compared with random attacks, deliberate attack strategies lead to more significant changes in network efficiency and resilience, highlighting the network’s sensitivity to key nodes. Moreover, the network’s effectiveness was classified into four types based on changes in efficiency and resilience. The pre-emergency network was categorized as resilience-focused, the mid-emergency network as efficiency-oriented, the post-emergency network as efficient-resilient, and the overall emergency network as inefficient-fragile. Based on the findings, the following recommendations are proposed to optimize the effectiveness and management of emergency collaboration networks.

(1)

In emergency practice, organizations that are critical to the network should be prioritized for identification and protection, ensuring resource sharing and information flow to prevent cascading failures caused by disruptions. Alternative mechanisms to strengthen the risk resilience of key nodes should be developed;

(2)

Enhance early preparedness by requiring emergency management agencies to strengthen their regular resource reserves and information-sharing mechanisms, establishing an efficient coordination system for more agile and forward-looking preparations;

(3)

Increase resilience during the emergency phase by requiring all sectors to be flexible and capable of maintaining and enhancing autonomous adaptability, self-organization, rapid feedback, and effectively mitigating external shocks, ensuring strong inter-sectoral connections to neutralize external threats;

(4)

Strengthen post-emergency recovery capabilities. To maintain network continuity, use emerging technology and dynamic resource allocation to strengthen capabilities and further enhance network effectiveness.

This paper comprehensively evaluates the effectiveness of emergency collaboration networks during public health emergencies from a systems thinking perspective, integrating network analysis with effectiveness assessment. It expands the depth and breadth of emergency collaboration research, enriching the methodology for assessing node importance, and provides theoretical and methodological support for optimizing collaboration structures and enhancing effectiveness. However, this paper has certain limitations. Due to data collection constraints, this study focuses on a single case, but the study is not confined to specific incidents. Future research aims to broaden its scope and case data, transitioning from a single type of disaster to multiple types, thereby increasing the case diversity and enhancing the reliability. Additionally, the dimensions of effectiveness evaluation could be expanded to encompass fairness, adaptability, and other factors, providing a more comprehensive assessment of network performance.