Evaluation Model of Urban Resilience in the Face of Public Health Emergencies: A Case Study of Xi’an

Abstract

In recent years, there have been frequent outbreaks of public health emergencies worldwide, especially resulting from the COVID-19 pandemic, which has seriously affected social and economic development and people’s production and life. In order to avoid or minimize the harm caused by these emergencies to society and the public, this article constructs a resilience indicator system for urban emergency response capabilities based on resistance, adaptation, and recovery. We establish a dynamic model of urban emergency response resilience, select the infectious disease dynamics method as the index weight calculation method, analyze the correlations among various indicators and parameters of the urban emergency response resilience system, and conduct sensitivity analysis on the model parameters to determine the importance sequence of each model parameter. Combined with the fuzzy hierarchy analysis method, we evaluate the model and use the 2021 year-end epidemic in Xi’an as an example to evaluate the urban emergency response resilience level using the evaluation model. According to the maximum membership degree principle, the results show that the emergency resilience levels of Xi’an were “moderately strong”, “moderately strong”, and “strong” in the first, second, and third stages of the epidemic, respectively. The results demonstrate that the method proposed in this article can objectively reflect the current level of urban emergency resilience and provide some references and guidance for improving the resilience of urban emergency response to public health emergencies.

1. Introduction

In the 21st century, frequent public safety incidents have triggered chain reactions in many regions, and global public events have gradually become an uncertain factor affecting international social stability. Among them, the most serious damage to human security and development, the widest range of impact, and the most rapid spread are infectious disease outbreaks. In recent years, infectious disease alarms, such as those for H1N1 influenza, H7N9 avian influenza, Zika virus, Ebola hemorrhagic fever, and Middle East respiratory syndrome (MERS), have been frequently sounded, exposing the insufficient emergency management capabilities of various countries. The emergency response capability of governments in the face of public emergencies has become an important factor in evaluating their governance capacity.

Scholars from various countries have actively established emergency systems for research purposes: POSID et al. defined public health emergencies from the perspectives of operation and management and public health, considering the national perspective [1]. Ignacio Mastroleo pointed out that if a complete set of emergency measures is established before a public emergency occurs, corresponding measures can be taken in emergency management during the emergency to better resolve the crisis [2]. The research by Passi D found that governments can only quickly and accurately deal with public health emergencies if they establish an emergency management system with high-quality emergency measures in advance [3].

Scholars have conducted extensive research on different recommended measures to improve emergency response capabilities: Carlos et al. explained the government’s handling of public health emergencies based on civic value theory, emphasizing that ensuring the value of citizens’ lives is a basic principle, forming a positive interaction with citizens and jointly constructing an emergency warning system to reduce losses caused by crises [4]. John proposed that establishing a comprehensive mechanism for government and public collaborative prevention and control, and precise and detailed end-system information can make the emergency warning system for public health emergencies more timely and effective [5]. Daniela (2013), based on the perspective of system theory, designed a command decision-making system that can mobilize the organization’s emergency response capabilities on the basis of fully considering the advantages of relevant emergency professional disposal teams [6]. Jan et al. (2020) conducted research on the prevention and control of the new coronavirus pneumonia epidemic based on investigation and research, constructed a more efficient medical and health system, and studied the epidemic prevention and control strategies of multiple countries and regions worldwide [7]. Susan proposed that, in the future, we need to break the information silo, integrate training and practice, strengthen local emergency and public health preparation planning and emergency response, and ultimately build stronger community health, people’s livelihood, and administrative resilience [8]. Feng C. C. et al. [9] based on a large number of surveys and studies, ultimately confirmed that social media is a new trend for publishing emergency information. Through social media, the value of emergency information can be maximized.

The study of emergency systems often employs the approach of establishing indicator systems: Lu et al. [10] used the external data envelopment analysis method to establish a comprehensive evaluation index system for urban emergency capabilities. Pfefferbaum R L et al. [11] investigated the emergency resilience of five poor communities by using the Communities Advancing Resilience Toolkit (CART) and evaluated the community’s emergency resilience based on the information collected from the community, guiding the construction of the community’s emergency resilience. Wood P. B. [12] established a city disaster emergency capacity evaluation model based on the Capability Maturity Model Integration (CMMI) viewpoint.

Evaluation of the emergency capacity currently employs subjective, objective, and combined weighting methods. Among them, subjective weighting methods, such as expert scoring and the Analytic Hierarchy Process (AHP) [13] exhibit noticeable subjectivity and arbitrariness. Objective weighting methods, such as Principal Component Analysis (PCA) and the Entropy Weight Method (EWM) [14] require high data completeness, and the determination of the weight of existing evaluation indicators has a low correlation with public health emergencies. This paper establishes a comprehensive SEIR-FAHP urban emergency resilience evaluation model based on the construction of a city emergency resilience evaluation index system. Taking the Xi’an epidemic situation at the end of 2021 as an example, the proposed model was applied to evaluate the epidemic prevention and control process in Xi’an, and thus, urban emergency resilience enhancement strategies are put forward.

2. Concept and Connotation

2.1. Resilience Curve

The “resilience curve” is a curve that characterizes the resilience level of a system based on time as the horizontal axis and the system functionality level as the vertical axis. This is shown in Figure 1. When describing system resilience as a process, it is necessary to measure the dynamic process of the system’s response to disturbances. The usual method is to measure the system resilience by constructing a resilience curve. This study constructed a resilience curve that changes over time to scientifically and reasonably measure the resilience level of a city’s emergency response capability.

The horizontal axis represents time, and the vertical axis represents the system’s safety state. At time t₀, the system experiences a certain disaster or emergency event, causing its safety state to decline from the initial state to a certain extent (t₀–t₁). The post-disaster recovery and reconstruction efforts will restore the system from the accident state to the initial safe state within a certain period (t₁–t₃). As shown in Figure 1, curve A is the original toughness curve, and it is expected to improve the toughness level through various measures, as shown in curves B, C, and D.

2.2. SEIR Model

There are various infectious disease models, such as the SI model, SIR model, SIS model, SIRS model [15], and SEIR model [16]. The most common models are the SIS and SIR models, but the SEIR model has the best fit and can better reflect the actual situation. The SEIR model is based on the SIR model, but adds an exposed population (E). It divides the population into susceptible, exposed, infected, and removed groups and establishes differential equations based on different transmission mechanisms among the groups to reveal the transmission pattern of the infectious disease. In the SEIR model, Susceptible refers to the healthy population without antibodies against the infectious disease, which is most of the population; Exposed refers to those in the latent period of the disease; Infected refers to those who have been diagnosed and can transmit the virus to susceptible people; and Removed refers to those who have been cured or died from the infection. Their relationships are shown in Figure 2.

Given the transition process shown in Figure 2, the state transitions of the four population groups in the SEIR model are shown in

Table 1. Transitions of population states in SEIR Model.

Number	Transition Status	Transition Rate
①	$\left(\mathrm{S},\mathrm{E}\right)\to \left(\mathrm{S}-1,\mathrm{E}+1\right)$	$\mathsf{\beta }\mathrm{SI}/\mathrm{N}$
②	$\left(\mathrm{E},\mathrm{I}\right)\to \left(\mathrm{E}-1,\mathrm{I}+1\right)$	$1/\mathsf{\alpha }$
③	$\left(\mathrm{I},\mathrm{R}\right)\to \left(\mathrm{I}-1,\mathrm{R}+1\right)$	γ I

.

The symbol β in the figure represents the infection rate of infected individuals (I), I/N represents the probability of contact with infected individuals, 1/α represents the average incubation period of latent individuals (E) to become infected individuals (I), and 1/γ represents the average period for infected individuals (I) to be removed from the population (R).

3. Indicator System and Research Methods

3.1. Indicator System Framework

Combining the three important characteristics of the resilience system, namely “resistance, recovery, and adaptation”, and based on the “National Emergency Plan for Public Health Emergencies”, “Law of the People’s Republic of China on the Prevention and Control of Infectious Diseases”, “Emergency Response Law of the People’s Republic of China”, and the Capability Assessment for Readiness (C.A.R) [17] for Emergency Management in the United States, and by analyzing previous relevant research [18,19,20,21,22,23,24,25,26,27,28,29], grasping the connotation and characteristics of urban resilience, a comprehensive evaluation index system reflecting the emergency response capabilities of cities when facing public health emergencies was constructed. The evaluation indicators for urban emergency resilience are divided into two levels: criterion-level indicators, which include resistance, recovery, and adaptation capabilities, and indicator-level indicators, which are factors that reflect the criterion-level indicators, totaling 22 items as shown in

Table 2. Indicator system for evaluating urban emergency resilience capacity.

Target Level	Criterion Level	Indicator Level	Indicator Description
Resistance (A1)	Monitoring and Early Warning Capability (B1)	Information dissemination capability (C1)	Fixed broadband internet access users
		Warning speed (C2)	Size of transmission chain
	Personnel Earthquake Resistance Ability (B2)	Population size (C3)	Urban population density (people/km2)
		Disaster prevention awareness of residents (C4)	Health and hygiene education
	Physical Facility Earthquake Resistance Ability (B3)	Transportation system security capability (C5)	Road network density
		Water supply system security capability (C6)	Length of water supply pipe network per capita (m/person)
		Medical system security capability (C7)	Medical insurance coverage rate (%)
		Electric power system security capability (C8)	Per capita electricity consumption (kW·h/person)
		Gas supply system security capability (C9)	Gas penetration rate (%)
Adaptability (A2)	Self-help and Mutual Assistance Ability (B4)	Age structure (C10)	Proportion of population aged 15–64 in urban areas (%)
		Educational level (C11)	Proportion of illiterate population aged 15 and above (%)
	Emergency Rescue Ability (B5)	Emergency management capability (C12)	Per capita public safety expenditure (RMB/person)
		Emergency rescue experience (C13)	Number of epidemic prevention efforts
		Social rescue capability (C14)	Density of social organizations (number/10,000 people)
		Shelter size (C15)	Per capita shelter area (square meters/person)
Recovery Ability (A3)	Medical Service Capability (B6)	Medical level (C16)	Health expenditure as a percentage of GDP (%)
		Medical service personnel (C17)	Number of health technical personnel per 1000 people
		Medical security capability (C18)	Number of hospital beds per 1000 people
	Physical Facility Recovery Capability (B7)	Government financial strength (C19)	Per capita GDP (10,000 RMB/person)
		Scale of related talents (C20)	Number of doctors per 10,000 people
		Living security capability (C21)	Per capita resident savings balance in urban and rural areas
		Economic stability (C22)	Employment rate (%)

.

Resistance refers to the ability of a system to withstand disaster shocks and reduce system losses. The city’s resistance mainly depends on the anti-interference ability of the city’s physical facilities and personnel to public health emergencies. In addition, monitoring and early warning capabilities can also effectively reduce the damage caused by public health emergencies to urban systems.

Adaptability refers to the ability of a system to learn and adjust to cope with the next disaster. It is reflected in the rescue and shelter stages after the occurrence of public health emergencies, including self-help and mutual aid capabilities and emergency rescue capabilities.

Recovery refers to the ability of a system to internally repair and restore normal system functions. The restoration of the damage caused by disturbance and the restoration of normal social order are mainly related to the level of medical and health care, while the restoration of physical systems requires a lot of financial and human resources.

The dependency and constraint relationships between the emergency resilience level of a city and various indicators in the urban emergency resilience evaluation system were sorted out, and the topological map was analyzed, as shown in Figure 3.

This article presents quantitative and qualitative descriptions of each evaluation index, and based on the evaluation objectives, the hierarchical standards for each index were formulated. The evaluation set was a language that expresses the evaluation of urban resilience. Following reference [30], this article divides the resilience levels into four categories (Level I: strong resilience; Level II: relatively strong resilience; Level III: moderate resilience; Level IV: weak resilience), and we constructed a fuzzy evaluation system for urban emergency resilience. The hierarchical standards and scoring values for each evaluation index are listed in

Table 3. Evaluation criteria for urban emergency resilience.

Indicator	Level Division of Indicators
	I (Strong Resilience)	II (Relatively Strong Resilience)	III (Average Resilience)	IV (Weak Resilience)
	≥90	75~90	60~75	<60
Information dissemination capability (C1)	>900	600~900	300~600	<300
Warning speed (C2)	1	2	3	4
Population size (C3)	>9000	6000~9000	3000~6000	<3000
Disaster prevention awareness of residents (C4)	Strong	Relatively strong	General	Weak
Transportation system security capability (C5)	>9	6~9	3~6	<3
Water supply system security capability (C6)	>15,000	12,000~15,000	9000~12,000	<9000
Medical system security capability (C7)	0.75~1	0.5~0.75	0.25~0.5	0~0.25
Electric power system security capability (C8)	>150	120~150	90~120	<90
Gas supply system security capability (C9)	0.75~1	0.5~0.75	0.25~0.5	0~0.25
Age structure (C10)	0.75~1	0.5~0.75	0.25~0.5	0~0.25
Educational level (C11)	0~0.01	0.01~0.05	0.05~0.1	>0.1
Emergency management capability (C12)	>2500	2000~2500	1500~2000	<1500
Emergency rescue experience (C13)	>5	3~5	1~3	<1
Social rescue capability (C14)	Strong	Relatively strong	General	Weak
Shelter size (C15)	1.5~2	1~1.5	0.5~1	0~0. 5
Medical level (C16)	1.5~2	1~1.5	0.5~1	0~0. 5
Medical service personnel (C17)	>30	15~30	10~15	<10
Medical security capability (C18)	>60	40~60	20~40	<20
Government financial strength (C19)	>200,000	150,000~100,000	50,000~100,000	<50,000
Scale of related talents (C20)	>50	40~50	30~40	<30
Living security capability (C21)	>15,000	10,000~15,000	5000~10,000	<5000
Economic stability (C22)	0.75~1	0.5~0.75	0.25~0.5	0~0.25
Linguistic membership	0.75~1	>0. 5~0.75	>0.25~0.5	>0~0.25

.

3.2. Research Method

The authors of this article used the method by [31] of differences to obtain the exact solution:

$$\left\{\begin{array}{l}\mathrm{S}(\mathrm{i}+1)=\mathrm{S}(\mathrm{i})-\mathrm{r}\beta \mathrm{S}(\mathrm{i})\mathrm{I}(\mathrm{i})/\mathrm{N}-{\mathrm{r}}_2{\beta }_2\mathrm{S}(\mathrm{i})\mathrm{E}(\mathrm{i})/\mathrm{N}\\ \mathrm{E}\left(\mathrm{i}+1\right)=\mathrm{E}\left(\mathrm{i}\right)+\mathrm{r}\beta \mathrm{S}\left(\mathrm{i}\right)\mathrm{I}\left(\mathrm{i}\right)/\mathrm{N}+{\mathrm{r}}_2{\beta }_2\mathrm{S}\left(\mathrm{i}\right)\mathrm{E}\left(\mathrm{i}\right)/\mathrm{N}-\mathrm{aE}\left(\mathrm{i}\right)\\ \mathrm{I}\left(\mathrm{i}+1\right)=\mathrm{I}\left(\mathrm{i}\right)+\mathrm{aE}\left(\mathrm{i}\right)-\gamma \mathrm{I}\left(\mathrm{i}\right)\\ R\left(\mathrm{i}+1\right)=R\left(\mathrm{i}\right)+\gamma I\left(\mathrm{i}\right)\end{array}\right.$$

(1)

In the above formula, β₂ represents the probability of susceptible individuals being infected by contacting latent individuals, and r₂ represents the number of susceptible individuals contacted by one latent individual per unit of time.

The authors of this article used MATLAB software to fit the above model.

The accuracy of safety evaluation results mainly depends on the objective selection of the evaluation indicators and the weight assignment [32]. Existing evaluation models for epidemic impact, regardless of the evaluation methods employed, generally still rely on subjective evaluation such as “expert assessment” in their key evaluation steps, which limits the applicability and objectivity of the methods.

In this paper, government public data were used as the information source, and the SEIR epidemiological model of the evaluated city was taken as the basis. Through sensitivity analysis of the model parameters and using the cumulative number of infected people as the standard, the importance sequence of each model parameter was determined, which served as the basis for selecting the evaluation indicators and assigning weights in the evaluation model. The concept of sensitivity analysis was introduced to the application of parameter importance ranking, where sensitivity analysis was used to determine which parameters had a greater impact on the system or model, thereby providing a basis for selecting the model’s evaluation indicators. Secondly, through the sensitivity value of each parameter, the degree of influence of the parameters on the model system was analyzed, which served as the basis for the weight assignment.

In general, evaluation models can be represented in the form of a multivariate mathematical function:

$$y=f\left(x_1,x_2,x_3,\dots ,x_n\right)$$

(2)

where y represents the evaluation result, and x_n represents the n-th parameter in the evaluation model, which can also be referred to as the nth evaluation index.

In general, the contribution of each evaluation index x_n to the evaluation result y in the evaluation model is not the same. Therefore, selecting appropriate evaluation factors and their weight coefficients is a prerequisite for model parameter estimation and model effectiveness verification. In the process of constructing a mathematical model, the contribution of parameters is often directly related to their sensitivity, which cannot be ignored. If the evaluators can master the contribution of each evaluation index to the evaluation result, then they can directly choose the evaluation index and allocate weights based on these contributions.

Using mathematical partial differentiation, the sensitivity S_i of the i-th parameter x_i can be solved:

$$s_i=\partial f/\partial x_i$$

(3)

Due to the complexity of the function form, it is often difficult to obtain the exact solution of the partial differentiation directly. Therefore, the authors of this article used the differential decomposition approximation method to replace the exact solution of partial differentiation:

$$s_i=\partial f/\partial x_i\approx \Delta f/{\Delta x}_i$$

(4)

Since the SEIR model is suitable for a short-term simulation of virus transmission, sensitivity analysis of the parameters is mainly focused on a specific city within a certain time period. If the parameter values change due to control measures and virus mutations, the results will also change. Therefore, when simulating an outbreak that has already occurred, a segmented and comprehensive analysis must be conducted to ensure the accuracy and reliability of the results. Many scholars have used the above modeling methods, but they have ignored the influence of important factors, such as the stage and duration of the epidemic, which has led to significant errors in the mathematical models they built.

Therefore, the authors of this article studied the parameter values for a specific time period in a certain city and used the control variable method for iteration to establish the sensitivity curve of the parameter, with the x-axis representing the variable, and the y-axis representing the cumulative number of infected individuals. Meanwhile, the factors that affect the speed and degree of the epidemic are considered, and the corresponding weight coefficients are calculated based on these factors. Using this method, the population in other time periods or regions can be predicted. The variable is plotted on the x-axis and the peak number of existing infected individuals is plotted on the y-axis to help with analysis.

The contribution of each evaluation index to the evaluation model obtained from the sensitivity analysis of the parameters also needs to be transformed into an evaluation matrix table through the concept of a safety system method in order to establish the evaluation model. The authors of this article drew from the operation of the fuzzy consistent judgment matrix in the fuzzy hierarchy analysis method (FAHP), directly transforming the parameter sensitivity into an evaluation matrix that can be directly analyzed by the evaluation model, and finally realized the comprehensive SEIR-FAHP evaluation model of the urban epidemic prevention and control system. The evaluation process is shown in Figure 4.

When using the fuzzy analytic hierarchy process, after determining the system hierarchy and its elements, it is necessary to establish a fuzzy judgment matrix R:

$$\mathit{R}=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1j}\\ r_{21}& r_{22}& \cdots & r_{2j}\\ ⋮& ⋮& & ⋮\\ r_{i1}& r_{i2}& \cdots & r_{ij}\end{array}\right]$$

(5)

The relationship between r_ij and the weight in the fuzzy judgment matrix is:

$$r_{ij}=a\left(w_i-w_j\right)+0.5,a\ge \frac{n-1}{2}$$

(6)

The expression for calculating the weight value of each factor using the least-squares method is:

$$W_i=\frac{{{\displaystyle \sum }}_{j=1}^n{a}_{ij}+\frac{n}{2}-1}{n\left(n-1\right)}$$

(7)

4. Results and Discussions

4.1. Research Object

Xi’an is a core city in the northwest region of China and an economic and cultural center. Its regional location is shown in Figure 5, and it faces more emergencies than other cities in China. Xi’an has basic characteristics such as high building density, high population density, and high population mobility. The impact of emergencies on the city’s development also shows characteristics such as high impact, long duration, and complex management methods. Based on this, Xi’an was chosen as the study area for this research, and the resilience level of urban emergency management in Xi’an was studied as an example.

As shown in Figure 6, Xi’an City has experienced multiple outbreaks of COVID-19, with each district conducting nucleic acid tests for its entire population more than a hundred times. However, in terms of the number of confirmed cases, duration, and impact, the outbreak that occurred in Xi’an at the end of 2021 was the most severe. This outbreak has a certain typical representative significance from the perspective of a large-scale outbreak. It occurred near the end of the year when the weather was cold, and there was a large influx of people. The gathering density of various social and economic organizations was high. At the same time, people tend to stay indoors in enclosed spaces, which promoted the transmission of respiratory infectious diseases. Therefore, it is necessary to conduct research and analysis from the perspective of epidemic prevention and control in Xi’an during this outbreak to summarize experiences and lessons learned.

The current epidemic in Xi’an has reported a total of 2053 local confirmed cases, and its development trend is shown in Figure 7. The epidemic development is divided into three stages: The first time point is 19 December 2021, which was when the first round of city-wide nucleic acid testing occurred after a relatively loose management stage compared to the later period. The second time point is 31 December 2021, when Xi’an implemented stricter epidemic prevention and control measures, marking the beginning of the second stage.

4.2. Evaluation Results

At the early stage of the epidemic, taking the evaluation unit as an example, due to the strict preventive measures at that time, the contact rate should have been reduced compared to the early outbreak of the epidemic in Wuhan, Hubei. However, the long-term and recurrent existence of the epidemic made people’s attention to the epidemic decrease. Therefore, according to the actual situation, the contact rate r was adjusted to 10. The average incubation period of the Delta variant was 4.4 days, that is, α = 1/4.4. At the same time, due to the strong concealment of the virus at the early stage of the epidemic, patients in the incubation period could not be detected in time, so α was set to 1/7 in this stage. Based on the actual situation and the literature [33,34], and by iterating the parameter values around the fixed parameter values to obtain the sensitivity of each parameter, the sensitivity analysis result of parameter α is shown in Figure 4. The sensitivity of each parameter can be obtained through the differential Formula (1), as shown in

Table 4. Summary table of parameters in the first stage.

Parameters	Definition	Initial Value
N	Total number of individuals (people)	12,000,000
I	Number of infected individuals (people)	S = N − I − R
E	Number of latent individuals (people)	0
R	Number of recovered individuals (people)	1
S	Number of susceptible individuals (people)	0
β	Probability of an susceptible individual being infected after contact with an infected individual	0.68
β2	Probability of an susceptible individual being infected after contact with a latent individual	0.7
r	Number of susceptible individuals that an infected individual comes into contact with per unit of time	10
r2	Number of susceptible individuals that a latent individual comes into contact with per unit of time	10
ɑ	Transition rate from latent to infected, which is the reciprocal of the latent period	0.62
γ	Recovery rate of infected individuals per unit of time	0.003

.

To obtain the sensitivity of the various parameters mentioned above, the authors of this paper iterated the range of values around the fixed parameter values. Sensitivity analysis was performed on parameter α, and the results can be found in Figure 8.

Similar to the sensitivity analysis process for parameter α, other parameter sensitivity analysis results were obtained in the same way. The quantified results are shown in

Table 5. Sensitivity analysis summary table of the main epidemic parameters.

	Parameters	Stage One	Stage Two	Stage Three
Sensitivity	β	0.415 × 105	0.615 × 105	0.779 × 105
	β2	0.495 × 105	0.725 × 105	0.953 × 105
	r	0.00371 × 105	0.00551 × 105	0.00731 × 105
	r2	0.00495 × 105	0.00705 × 105	0.00998 × 105
	α	0.14 × 105	0.25 × 105	0.29 × 105
	γ	0.115 × 105	0.207 × 105	0.215 × 105
Sensitivity Ratio	β	0.353595	0.339862	0.345563
	β2	0.421758	0.40065	0.42275
	r	0.003161	0.003045	0.003243
	r2	0.004218	0.003896	0.004427
	α	0.119285	0.138155	0.128644
	γ	0.097984	0.114392	0.095374

, showing that the sensitivity ratio β₂ and the proportion of β were the largest, while r and r₂ had the smallest proportions.

Based on the above results, it can be seen that small changes in the four parameters of the number of contacts of the latent and infected individuals (r, r₂) and the transmission rates (β, β₂) can lead to a sharp change in the cumulative number of infections. Therefore, the model parameters for the three stages of the Xi’an epidemic were different. Although the sensitivity values for the three stages differed greatly, there was no significant change in the sensitivity ratio among the parameters for each stage.

According to the evaluation process of the Analytic Hierarchy Process, the relationships between each indicator and the model parameters in each established indicator system are shown in Figure 9. The sensitivity ratio of each indicator in the SEIR model is divided into each evaluation indicator, i.e., the sensitivity ratio of each indicator, as shown in Table 4. For example, C1 is related to five parameters: β, β₂, r, r₂, and γ. Let X be the sensitivity ratio, then:

$${\mathrm{X}}_{\mathrm{C}1}=\frac{{\mathrm{X}}_{\mathsf{\beta }}}{22}+\frac{{\mathrm{X}}_{{\mathsf{\beta }}_2}}{22}+\frac{{\mathrm{X}}_{\mathrm{r}}}{22}+\frac{{\mathrm{X}}_{{\mathrm{r}}_2}}{22}+\frac{{\mathrm{X}}_{\mathsf{\gamma }}}{4}$$

(8)

Based on the fuzzy judgment matrix scale and the sensitivity ratio values of the evaluation indicators shown in

Table 6. Sensitivity ratio of evaluation indicators in the first stage.

Indicator Layer	Sensitivity Ratio in the First Stage
Information dissemination capacity (C1)	0.060074727
Warning speed (C2)	0.060074727
Population size (C3)	0.035578727
Disaster prevention awareness of the population (C4)	0.035578727
Transportation system security capacity (C5)	0.055459561
Water supply system security capacity (C6)	0.035578727
Medical system security capacity (C7)	0.079955561
Electric power system security capacity (C8)	0.035578727
Gas supply system security capacity (C9)	0.035578727
Age structure (C10)	0.060074727
Education level (C11)	0.055459561
Emergency management capacity (C12)	0.079955561
Emergency rescue capacity (C13)	0.079955561
Social rescue capacity (C14)	0.035578727
Size of shelter facilities (C15)	0.055459561
Medical level (C16)	0.079955561
Medical service personnel (C17)	0.060074727
Medical security capacity (C18)	0.060074727
Government financial strength (C19)	0.035578727
Scale of relevant talents (C20)	0.060074727
Life security capacity (C21)	0.035578727
Economic stability (C22)	0.055459561

, the fuzzy judgment matrix is established, and the results of the division are shown in Figure 10.

The fuzzy judgment matrix meets the conditions of a fuzzy consistent matrix, and the fuzzy judgment matrix T is consistent with the fuzzy consistent matrix A, i.e., CI = 0, which satisfies consistency.

According to the method mentioned earlier, the element weights during the first stage in Xi’an are shown in Figure 11. The final weights ranked as follows: physical facilities emergency capacity (B3), emergency rescue capability (B5), medical service capability (B6), physical facilities recovery capability (B7), monitoring and early warning capability (B1), and personnel emergency capability (B2). It can be seen that the indicators with higher weights mainly focus on the middle and later stages of urban response to public health emergencies, which are also important stages for urban adaptation and recovery.

The data of relevant indicators in this paper were obtained by referring to materials such as the China City Statistical Yearbook (2021), the Xi’an Statistical Yearbook (2021), and the Shaanxi Provincial Center for Disease Control and Prevention (sxcdc.com). The specific values and resilience evaluation scores are shown in

Table 7. Evaluation indicators for Xi’an City.

Indicator Layer	Indicator Value/Description	Indicator Evaluation Score	Membership Vector R
Information dissemination capacity (C1)	615.87	75	(0,0.5,0.5,0)
Warning speed (C2)	4	50	(0,0,0,1)
Population size (C3)	6767	75	(0,0.5,0.5,0)
Disaster prevention awareness of the population (C4)	Relatively strong	79	(0,0.77,0.23,0)
Transportation system security capacity (C5)	5.58	70	(0,0.37,0.63,0)
Water supply system security capacity (C6)	12,534.7	75	(0,0.5,0.5,0)
Medical system security capacity (C7)	0.45	70	(0,0.37,0.63,0)
Electric power system security capacity (C8)	1,153,784	75	(0,0.5,0.5,0)
Gas supply system security capacity (C9)	0.74	88	(0.73,0.27,0,0)
Age structure (C10)	0.69	83	(0. 07,0.93,0,0)
Education level (C11)	0.008	90	(1,0,0,0)
Emergency management capacity (C12)	2193	85	(0.33,0.67,0,0)
Emergency rescue capacity (C13)	7	90	(1,0,0,0)
Social rescue capacity (C14)	General	50	(0,0,0,1)
Size of shelter facilities (C15)	1.5	90	(1,0,0,0)
Medical level (C16)	1.2	86	(0.47,0.53,0,0)
Medical service personnel (C17)	15	79	(0,0.77,0.23,0)
Medical security capacity (C18)	59.9	88	(0.73,0.27,0,0)
Government financial strength (C19)	92,256	75	(0,0.5,0.5,0)
Scale of relevant talents (C20)	49.56	88	(0.73,0.27,0,0)
Life security capacity (C21)	11,996	79	(0,0.77,0.23,0)
Economic stability (C22)	0.66	86	(0.47,0.53,0,0)

.

Based on the evaluation weight vector and membership degree vector, the fuzzy comprehensive evaluation model B = W·R was applied to calculate the fuzzy evaluation results of urban emergency resilience.

$${\mathrm{B}}_1=\left(0.0200\hspace{1em}0.0779\hspace{1em}0.3937\hspace{1em}0.1364\right)$$

According to the principle of maximum membership degree, the resilience evaluation result of the first stage in Xi’an was level II, indicating strong resilience.

Similarly, the evaluation results for the middle and late stages of the epidemic in Xi’an were as follows:

$${\mathrm{B}}_2=\left(\begin{array}{ccccc}0.0437& 0.3075& 0.4088& 0.2248& 0.0152\end{array}\right)$$

$${\mathrm{B}}_3=(0.1995 0.4987 0.2992 0.0026 0)$$

According to the principle of maximum membership degree, the resilience evaluation result of the second stage in Xi’an was Level II, indicating relatively strong resilience, while the resilience evaluation result of the third stage was Level I, indicating strong resilience.

Based on the analysis in Section 2.2, the curve of the emergency resilience of Xi’an City during the current epidemic was calculated from 2 December 2021 to 17 January 2022, as shown in Figure 12. Although the emergency resilience level of Xi’an City decreased after the outbreak of the COVID-19 epidemic, it began to rise steadily and quickly. In the middle and later stages of the epidemic, Xi’an actively improved its medical services and expanded its medical treatment facilities. After the epidemic, the emergency resilience level of Xi’an was higher than the initial resilience level before the outbreak. The emergency resilience of Xi’an City has been improved after experiencing this emergency event.

On 9 December 2021, Xi’an began experiencing the COVID-19 outbreak, and the city’s emergency resilience level rapidly declined. Due to the slow warning in Xi’an, the first city-wide nucleic acid testing was not carried out until 19 December 2021, with nucleic acid testing previously limited to areas where cases were detected, such as the Yanta District. Until the end of the first phase, Xi’an did not implement strict measures for comprehensive control, which led to the emergence of the super-spreader chain of Chang’an University and the expansion of the infectious area to various districts and even areas outside the urban area. Starting 19 December, the city’s emergency resilience level began to slowly rise, and Xi’an initiated the second round of city-wide nucleic acid testing on 21 December and implemented closed management in all communities on 22 December. The number of cases detected in community nucleic acid screening was relatively high compared to the confirmed cases. Relationships among confirmed cases also existed, until the risk control level was raised again, prohibiting people from going out except for nucleic acid testing, and the number of new cases began to decrease and were all in the quarantine control area.

Although the emergency resilience level slowly recovered in the later stages of the disaster, Xi’an’s strong self-help and mutual assistance capabilities, as well as rich experience in epidemic prevention and control, allowed the city to adjust its prevention and control measures and increase social rescue forces in a short period of time when the epidemic prevention and control measures network failed. Additionally, Xi’an’s medical service capacity and related financial investments increased during the later stages of the COVID-19 outbreak. As a result, the city’s emergency resilience level was higher than before the outbreak, better preparing it for the next public health emergency.

5. Conclusions

(1) This paper proposes a city system resilience evaluation and analysis framework based on the three major characteristics of resilience, namely resistance, adaptation, and recovery, and establishes a city emergency resilience evaluation index system containing three dimensions, seven domain layers, and 22 indicators based on this framework.

(2) Infectious disease dynamic methods were used to analyze the relationship between the indicators and parameters in the city emergency resilience system, to determine the weight of the indicators, and to study the changes in the city’s emergency resilience level in response to public health emergencies. This provides support and reference for urban research.

(3) Based on the evaluation results, this paper proposes the establishment of a proactive approach to public health emergency management, emphasizing proactive planning and early deployment. Scientific prevention and control should be prioritized, and effective preventive management should be carried out. Risks and losses under extreme conditions should be anticipated and assessed. Based on this, comprehensive public health risk plans should be developed, and targeted preventive and control measures should be implemented to prevent the escalation of situations and the occurrence of chain reactions, thereby shifting the focus of public health security from a “treatment-oriented” approach to a “prevention-oriented” approach. Furthermore, it is essential to improve the urban planning system and establish a framework for enhancing urban emergency resilience and disaster reduction. The urban planning system should be refined based on resilience indicators, taking into account the fast and wide spread of public health incidents. Measures should be taken to control urban scale and population density, regulate building density, maintain open spaces, and prioritize the development of specialized teams. The size and specialization level of relevant personnel directly affect the effectiveness of emergency responses.

The proposed model in this paper can objectively and effectively evaluate urban epidemic prevention and control systems, predict the trend of epidemic development, and assess the effectiveness of prevention and control measures and the timing of interventions. This method has great potential for application in the field of public safety and can provide valuable insights for governments in formulating further policies. The SEIR model used in this study is a basic infectious disease model with few parameter variables. In future research, additional reasonable parameters can be supplemented based on the actual situation. Due to data availability issues, an emergency resilience assessment was only conducted for Xi’an City. In the next step of the research, we can explore the differences among different regions and identify the weaknesses in emergency resilience construction among different cities.