Forecasting Demand for Emergency Material Classification Based on Casualty Population

Abstract

Accurately forecasting emergency material demand during the initial stages of disaster response is challenging due to communication disruptions and data scarcity. This study proposes a hybrid model integrating regression analysis and intelligent analysis to estimate casualties and predict emergency supply needs indirectly. A case study of five earthquake-affected villages validates the model, using building collapse rates and population data to calculate casualties and determine the demand for essential supplies, including food, water, medicine, and tents. The findings demonstrate that the proposed approach effectively addresses the “black box” condition by utilizing correction factors for population density, disaster preparedness, and emergency response capacity, providing a structured framework for rapid and accurate demand forecasting in disaster scenarios.

1. Introduction

Owing to the abrupt and unpredictable occurrence of natural disasters, coupled with challenges, such as road disruptions, communication network failures, reliance on singular disaster monitoring technologies, and the absence of advanced tools like multi-platform integration, disaster big data analysis, and intelligent prediction, the affected region becomes isolated, rendering its needs virtually inaccessible—a state commonly referred to as a “black box” [1]. In this scenario, the emergency command center faces difficulties in swiftly ascertaining the type and quantity of required emergency materials for effective disaster relief. Consequently, the center resorts to empirical models for rapid prediction and calculation, which often prove insufficient due to the lack of immediate information regarding the disaster area’s specifics, damage assessment, evolving disaster conditions, and the number of victims. This informational void in the disaster area impedes the expeditious and accurate execution of rescue operations.

The term “black box” in disaster management refers to a state in which vital information about the affected area is obscured or completely unknown to external responders [2]. This lack of visibility hinders the ability of emergency teams to assess the situation on the ground, including the scale of destruction, the number of people affected, and the specific needs for medical, food, and shelter resources [3]. The “black box” condition arises when conventional disaster monitoring tools—such as satellite imaging, ground sensors, and communication networks—are either unavailable or disrupted, leading to a significant delay in gathering real-time data [4]. Without access to this information, relief operations often rely on assumptions or outdated data, which can result in the misallocation of resources or delayed rescue efforts [5]. The failure to promptly break through the “black box” hampers decision-making, causing critical delays in the delivery of life-saving aid and services.

Post-disaster, it is imperative to promptly address and minimize the “black box” situation within the disaster area to enhance its inhabitants’ chances of survival [6]. Essential to this objective is the forecasting of demand, serving as the fundamental prerequisite for swift and accurate rescue efforts and forming the basis for all subsequent emergency response, management, and operations. Timely and accurate determination of the disaster area’s needs is paramount in mitigating the duration of the “black box” condition, thereby resolving the challenges associated with the inaccessible demand information post-disaster. Hence, this paper delves into the intricacies of demand forecasting, elucidating the requisites for effective disaster relief and, consequently, furnishing a foundation for the swift and precise execution of post-disaster rescue operations.

2. Literature Review

With the increasing frequency of disasters, disaster response has garnered significant attention. However, a systematic study of emergency response (ER) in disasters, particularly in predicting emergency material demand, has been largely neglected. This paper aims to bridge this gap by offering a comprehensive analysis of existing methodologies and proposing an innovative framework for demand forecasting during the critical initial phases of disaster relief. Based on a bibliometric analysis and visualization of 3678 ER-related journal articles (1970–2019) from the Web of Science, the current research landscape in the field has been examined, but key aspects, such as real-time demand forecasting, have not been fully explored [7]. Li et al. introduced a metabolic GM (1,1) model that emphasizes “removing old information and incorporating new information,” improving the traditional GM (1,1) model [8]. This was further expanded by Pradhananga, who applied the GM (1,1) model for processing emergency material data, addressing the difficulties in handling data fluctuations during disaster relief [9]. These grey models, while beneficial, depend heavily on early-stage data, which are often unavailable due to the “black box” nature of disaster areas. The “black box” phenomenon, where vital real-time information about the affected region is inaccessible due to communication breakdowns and road blockages, remains a major obstacle in emergency response. This lack of immediate data often forces emergency command centers to rely on empirical models, leading to inaccurate predictions of material demand and slower rescue operations. Several researchers have addressed this issue by using pre-disaster data or historical case bases for prediction. Wang tackled the lack of post-disaster information by utilizing pre-disaster cases to extract key characteristics related to emergency material demand through fuzzy set theory [10]. Similarly, Li Peng proposed a case-based reasoning model, employing similarity measurements to improve the selection of reference cases [11]. Despite these advances, accurately finding highly similar cases remains a challenge, limiting the precision of demand forecasting. Further refinements include Chen et al.’s reconstruction of the demand prediction model by incorporating time periods, embedding dimensions, and delay times, leading to improved accuracy [12]. Recognizing the difficulty of direct demand prediction due to the “black box” condition, researchers such as QianFenglin and Sun et al. have explored indirect approaches. These methods focus on predicting casualty numbers using BP neural networks and using these estimates to infer emergency material demand [13,14]. Similarly, Zhang Jie and Liu Jinlong have developed casualty-based prediction models derived from past earthquake data, offering valuable insights into disaster response logistics [15,16]. However, the accuracy of these models is highly dependent on casualty data, which is often incomplete or delayed during the early stages of a disaster. To address these shortcomings, Sheu proposed using data fusion technology to estimate casualties and material demand based on minimum individual requirements, although this method suffers from slow data processing speeds and the inconsistent reliability of early-stage data [17]. Meanwhile, Feng et al. advanced the field by proposing an XGBoost-based algorithm for predicting casualties during terrorist attacks, incorporating techniques such as random forest (RF), principal component analysis (PCA), and genetic algorithms to optimize prediction accuracy [18]. The introduction of an improved ant colony optimization algorithm (IACO) further enhances the efficiency of transport strategies in different scenarios [19].

The Federal Emergency Management Agency (FEMA) underscores the critical importance of supply chain resilience and demand forecasting in disaster response. By analyzing market trends and historical data while incorporating expert opinions, FEMA advocates for the formulation of accurate demand forecasts to mitigate unpredictable demand surges. For instance, during the spring of 2020, Campbell’s adeptly adjusted its production strategies in response to a surge in demand caused by the COVID-19 pandemic. The company strategically allocated resources to high-demand products, successfully meeting market needs. This case exemplifies how flexible supply chain management and real-time data analysis can effectively address the volatile demand for emergency supplies in the wake of sudden-onset disasters [20].

The United Nations Office for Disaster Risk Reduction (UNDRR) emphasizes in its 2022 Global Disaster Risk Assessment Report that traditional risk management frameworks must evolve to reflect the systemic nature of emerging risks. The report advocates for the integration of sustainable development principles and data-driven decision-making processes to enhance disaster response effectiveness [21].

The Sphere Association, through its Sphere Handbook, establishes minimum standards for humanitarian assistance, covering critical areas such as water, sanitation, nutrition, shelter, and health. The handbook stipulates that during emergencies, the timely and appropriate provision of essential supplies should align with the basic needs of affected populations. For instance, during crisis situations, the Sphere standards recommend ensuring access to at least 15 L of safe drinking water per person per day, along with sufficient food and basic healthcare services [22].

3. Prediction of Emergency Material Demand

After a natural disaster, the facilities in the affected area become non-operational, resulting in extensive damage. Communication with the outside world becomes challenging, making it difficult to report material demands promptly [23]. Obtaining timely disaster information poses a significant challenge, hindering the direct application of analogy analysis from previous rescue cases to determine material needs. Past rescue cases often lack comprehensive data on emergency material requirements, primarily providing statistics on casualties resulting from disasters.

This paper addresses these gaps by employing a sky–ground integrated monitoring system that combines satellite, UAV, and ground sensors to rapidly collect real-time casualty data. Using intelligent analysis methods, this system overcomes the “black box” issue, providing a clear picture of the disaster’s impact. The collected data are then fed into a regression analysis model to establish the relationship between casualties and emergency material demand. This indirect approach ensures that even in the absence of complete data, demand forecasting can still be conducted with greater accuracy and speed. The innovation and marginal contribution of this paper lie in the integration of real-time data collection technologies and intelligent prediction models, addressing the critical “black box” challenge and providing a more reliable foundation for early-stage disaster response. By combining advanced regression techniques with cutting-edge monitoring systems, this approach offers a new methodology for accurately predicting emergency material demand during the initial phase of disaster relief, thereby improving the overall efficiency and effectiveness of rescue operations.

It is evident that the number of casualties is closely linked to the demand for post-disaster relief materials [24]. By calculating the casualty count, it becomes possible to predict the demand for emergency materials indirectly. This paper adopts a two-step approach, initially predicting the number of casualties and subsequently deriving an indirect prediction of emergency supply needs based on the casualty count. It comprehensively considers factors significantly influencing casualty counts and categorizes the main contributors to streamline prediction, reduce complexity, minimize prediction time, and enhance accuracy. A critical step involves comparing existing prediction methods, selecting those aligned with practical scenarios, and refining methods through empirical testing to establish a casualty prediction model. This model, coupled with local foundational data, remote sensing satellite analyses, and disaster information, enables precise predictions of casualties in the affected area. The demand for emergency relief materials is intricately linked to the number of victims and the proportion of casualties [24]. For instance, the need for medical materials correlates directly with the number of injured individuals, while the demand for life relief materials depends on the total population in the disaster area. Thus, analyzing casualty figures and basic population data in the disaster area allows for the determination of emergency supply requirements. The research steps outlined in this chapter result from a systematic analysis of the emergency material demand prediction process, as illustrated in Figure 1.

As illustrated in Figure 1, the prediction of emergency material demand comprises two primary stages: the initial stage involves forecasting the number of casualties in the disaster area. This includes analyzing the factors influencing casualties and selecting an appropriate prediction model. The subsequent stage entails predicting emergency material demand based on the foundational data of casualties and the local population. This paper delineates the determination of both the casualty population prediction model and the construction of the emergency material demand model, focusing on the analysis of earthquakes, a common occurrence in natural disasters.

4. Casualty Forecast

The preceding analysis underscores the challenge of directly predicting the demand for emergency materials. Instead, an indirect approach is proposed, wherein the prediction of the casualty count in the disaster area serves as a prerequisite for estimating the demand for emergency materials. In this section, an optimized prediction model, aligned with the characteristics of post-disaster casualty prediction, is selected through an examination of influencing factors, a comparative analysis of existing prediction methods, and the consideration of expert recommendations.

4.1. Analysis of the Influencing Factors of Casualties

Based on the analysis of previous disaster cases and related literature about the factors influencing casualties, combined with the suggestions of rescue experts and prediction experts, and based on the disaster area for field research. Based on this comprehensive analysis and summary, it is concluded that the factors influencing casualties caused by natural disasters include disaster source, disaster-bearing body, and prevention and reduction measures [25].

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Disaster source

The disaster source, also known as the disaster-causing factor [26], encompasses events that jeopardize human life and property due to variations in natural phenomena in the human environment. Examples include earthquakes, floods, frost, and debris flow. The risk associated with the disaster source includes the type, level, intensity, and time of the disaster.

Disaster Types: Different disasters require distinct emergency materials. For instance, floods necessitate rubber boats and sandbags, while debris flows and landslides demand excavators. This paper primarily focuses on earthquakes, making other disaster types less relevant to the key factors under consideration.

Disaster Intensity: The magnitude of a natural disaster, represented by seismic measurements like the Richter scale for earthquakes, correlates with the level of destruction. Higher magnitudes signify greater energy release, resulting in increased casualties and losses. The Richter scale is employed in China, with each magnitude difference of 1.0 representing an approximately 30-fold difference in released energy.

Disaster Time: The timing of a disaster—day or night—significantly influences casualties. Generally, nighttime casualties tend to be higher due to the reduced chances of people escaping during sleep. Instances such as the 2016 Xingtai torrential rain and the 1976 Tangshan earthquake highlight the impact of disaster occurrence during nighttime, resulting in substantial casualties.

This comprehensive analysis of influencing factors provides a foundation for the subsequent selection and optimization of prediction models tailored to post-disaster casualty scenarios. In the following sections, the research proceeds to refine the casualty prediction model and construct an emergency material demand model.

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Disaster-bearing body

The disaster-bearing body, often referring to human society, encompasses various aspects. In this context, it comprises the disaster area, population density, and disaster resistance ability.

Disaster Area—Positive Relation with Casualties: The number of casualties is directly proportional to the size of the disaster area. Larger disaster areas result in more significant impacts and increased casualties. For instance, the Haiyuan earthquake affected expansive regions, causing substantial casualties. Similarly, the Wenchuan earthquake affected numerous counties, leading to a considerable loss of life.

Population Density—Influence on Casualties: Population density, representing the number of people in a unit area, significantly affects casualty rates. Densely populated areas experience more casualties during disasters. Urban areas, with higher population densities, tend to incur greater casualties compared to sparsely populated rural regions. Notably, the location of earthquakes in Xinjiang with lower population density resulted in fewer casualties [27].

Inverse Proportion with Casualties: The ability of a disaster area to resist natural disasters is inversely proportional to the number of casualties. Stronger disaster resistance reduces casualties. For example, Chile’s earthquake resilience, attributed to stringent building design standards, results in minimal casualties despite frequent high-magnitude earthquakes. Enhanced earthquake resistance, as seen in projects like the 1985 Valparaiso earthquake and the 6.7-magnitude earthquake in Aketao, Xinjiang, leads to fewer casualties.

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Prevention and reduction measures

Disaster prevention, mitigation, and relief measures encompass policies, methods, preparations, and actions taken in response to natural disasters. This includes pre-disaster preparation, prediction, and post-disaster emergency response capacity.

Key Components: Robust pre-disaster emergency material reserves, monitoring and prediction systems, emergency response plans, teams, and simulation exercises are crucial for effective disaster response. Well-prepared pre-disaster measures correlate with higher post-disaster emergency response capacity and increased satisfaction of the disaster area’s demands, resulting in fewer casualties.

Impact on Casualties: The level of pre-disaster prediction influences casualty numbers. Higher prediction accuracy and earlier prediction times correlate with reduced casualties. The 1976 Tangshan earthquake, lacking accurate prediction, resulted in significant casualties. Advances in earthquake warning technology, exemplified by the Japanese government’s one-minute warning for the 3.11 earthquake, provide crucial time for public evacuation, decreasing casualties.

Determining Factor: The emergency response capacity of the state, government, and society directly influences post-disaster rescue effectiveness. A robust emergency response reduces casualties. The critical “golden rescue time”—within 72 h after an earthquake—significantly impacts the number of casualties. Beyond this window, the efficiency of disaster relief diminishes, emphasizing the importance of prompt and effective post-disaster responses to mitigate casualties.

4.2. Selection of the Casualty Prediction Model

After comparing common prediction methods, a relatively reasonable method is selected for the prediction model of casualties [24]. Then, by comparing and analyzing existing scholars’ models under the prediction method, the more practical prediction model is selected, and the model is improved in combination with the factors influencing casualties.

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Comparative analysis of methods for predicting casualties

To facilitate rapid and accurate post-disaster rescue efforts, it is crucial to swiftly ascertain the needs of the disaster area [13]. The comparative analysis presented in

Table 1. Comparative analysis of prediction methods for disaster victims’ injury data.

Method	Implication	Advantages	Disadvantages
Time series smoothing prediction [31]	According to the relevant historical data, only the change rule with time is considered to predict the future time	Simple mathematical statistics prediction speed is faster	① Not suitable for complex data prediction ②The calculation process is complex and time-consuming ③ The history and data of dependent variables are needed as the basis of prediction
Regression analysis prediction [32]	Based on historical data, the causal and adjoint relationships between dependent and independent variables are established, and the unknown situation is predicted by analyzing the change of relevant factors	① Simple calculation and fast speed ② Applicable to short-term forecast	① Collect past historical data for correlation analysis and determine the prediction model ② There are some errors in the prediction
Neural network prediction [33]	By analyzing and determining the main factors affecting the casualties, and these factors as input neurons, casualties as output neurons, through network training and simulation, build a prediction model of casualties, and carry out dynamic prediction of casualties	① Applicable to prediction of nonlinearity and uncertainty ② Focus on input and output	① It needs to go through many drills and requires fast operation speed ② There are some errors in the prediction
Case-based reasoning prediction [34]	According to the analogy principle, through the analysis and summary of the past disasters, the rescue case database is established. When new disasters occur, the most similar cases are found by comparing against the case database to predict the emergency rescue demand	① Use short-term forecasts ② The prediction results are obtained directly through comparison, and the speed is relatively fast	① A large amount of case data need to be accumulated. Without data, there will be a lack of comparison objects, which will affect the accuracy of prediction ② It is difficult to find cases with high similarity, which affects the accuracy of prediction ③ It is possible to eliminate valuable information from other cases besides similar cases
Grey system model prediction [35]	According to the principle of inertia, through the correlation analysis of known and unknown information, the original data are processed, and the strong regular data series are generated by looking for the rules, and the future development trend is predicted by the differential equation model	Less forecast information required	① The speed of obtaining information about the disaster area determines the speed of prediction ② Prediction of time series limited to exponential form ③ Forecast must be based on previous data ④ Not applicable to the prediction of golden rescue period
Intelligent analysis and prediction [36]	Through the intelligent comparative analysis of the images before and after the disaster by computer, the disaster information of the disaster area can be obtained quickly, and the demand of emergency materials can be predicted according to the disaster information	① Direct comparison of image information of disaster area ② Fast operation speed	① The speed of obtaining information of disaster area determines the speed of prediction ② Higher requirements on the processing speed of the impact
Extrapolation [37]	It involves estimating future values based on existing data, assuming that current trends continue. Its implications include the risk of inaccuracy due to unforeseen changes, sensitivity to outliers, and the necessity for cautious interpretation and validation of results.	Fast analogy	① Only by collecting more data can we obtain the scatter diagram ②Low prediction accuracy

reveals that regression analysis prediction, case-based reasoning prediction, grey system model prediction, intelligent analysis prediction, and extrapolation prediction demonstrate faster speeds, aligning with the imperative for timely rescue operations. However, a more in-depth analysis is necessary. The grey system model prediction, reliant on correlating known and unknown information, encounters challenges when the demand information of the disaster area is in a “black box” state. As a result, predictions using this method may lack the desired accuracy [1]. Case-based reasoning, prediction, and extrapolation methods require comparisons with past rescue cases of similar disasters. Given substantial variations in the levels, population densities, and geological structures of earthquake disasters across different regions, finding truly similar cases is challenging [28]. Even cases in the same region at different times may not necessarily align. Consequently, these methods may fall short of meeting prediction requirements. Intelligent analysis and prediction, leveraging computer analysis of image data before and after the disaster, provide real-time data but may lack accuracy in material demand prediction [29]. Regression analysis, while simple and fast, fails to acquire real-time data from the disaster area. Combining regression analysis with intelligent analysis offers a promising solution. This paper proposes utilizing the Sky–Earth Integrated Information Monitoring System to capture real-time images of disaster areas [30]. By comparing pre- and post-disaster images and inputting the data into the regression analysis prediction model, a comprehensive approach is achieved. This hybrid method combines the simplicity, speed, and real-time capabilities of regression analysis and intelligent analysis, swiftly meeting the needs of the disaster area and aligning with the requirements of rapid rescue and early disposal.

Regression analysis, comprising both linear and non-linear regression analyses, is selected based on the correlation analysis of the factors influencing casualties presented in Section 4.1. Some relevant factors exhibit non-linear relationships with the number of casualties. For example, the time of earthquake occurrence is not entirely linearly related to casualties; earthquakes at night may result in more significant casualties than those during the day. The Tangshan earthquake, occurring at night, resulted in a substantial number of casualties. Therefore, non-linear regression analysis is deemed appropriate for this study.

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Selection of nonlinear regression model

Most casualties occur when individuals are affected by building collapses post-earthquake; it is evident that the destruction or collapse of houses is a crucial determinant of casualties [24]. The 1985 Valparaiso earthquake and the 1976 Tangshan earthquake, both magnitude 7.8, occurred in densely populated cities. Chile’s earthquake resilience prevented collapses, resulting in only 150 casualties. This underscores the significance of the collapse rate of houses as a primary factor influencing casualties. Furthermore, casualties and losses are higher during nighttime earthquakes due to reduced chances of escape while people are sleeping. The timing of an earthquake is a significant factor affecting casualties. Smaller-magnitude earthquakes generally do not cause casualties, with the magnitude and intensity of an earthquake being key factors. Earthquakes in densely populated cities lead to more significant casualties, such as the Tangshan earthquake, which occurred in an industrial city with a million people.

In summary, the collapse rate of houses, population density, earthquake timing, and intensity are identified as the main factors influencing casualties. Considering the desirable characteristics of prediction data, such as ease of obtainability, real-time nature, and the need for fast and accurate determination, this study selects models that align with these criteria for comparative analysis with existing prediction models by other scholars.

$${\mathit{l}\mathit{o}\mathit{g}}_{10}^{\mathit{R}\mathit{D}}=9.0 {\mathit{R}\mathit{B}}^{0.1}-10.07$$

(1)

$$\mathit{N}\mathit{D}={\mathit{f}}_{\mathit{p}}\times {\mathit{f}}_{\mathit{t}}\times \mathit{R}\mathit{D}$$

(2)

RD is the death rate of people; ND is the estimated death rate of people in a city or region; RB is the collapse rate of houses (the ratio of the number of collapsed rooms to the number of all rooms or the ratio of the area of collapsed buildings to the total building area in a region), and the number of people injured is generally three to five times the number of deaths [38]. ${\mathit{f}}_{\mathit{p}}$ is the population density correction coefficient of the region, and its value is shown in

Table 2. Population density correction coefficient in disaster areas.

Population density ρ (per/km3)	˂50	50–200	200–500	˃500
Correction coefficient ${\mathit{f}}_{\mathit{p}}$	0.8	1.0	1.1	1.2

[39]. f_t is the correction coefficient of earthquake occurrence time, which is related to earthquake intensity. See

Table 3. Time correction coefficient value after disaster.

Earthquake intensity	VI	VII	VIII	IX	X
Correction coefficient ${\mathit{f}}_{\mathit{t}}$ (night)	17	8	4	2	1.5

for its value [40].

4.3. Improvement of Casualty Prediction Model

The model considers four crucial factors: the collapse rate of houses, population density, earthquake occurrence time, and intensity. To enhance the model’s accuracy, this section delves into the correlation of additional factors and proposes improvements.

Buildings constructed at different times, with varying structures and seismic designs, exhibit differing seismic resistance capacities [41]. Assessing the seismic resilience of distinct buildings in the same area proves challenging. Therefore, the collapse rate of buildings serves as an indirect indicator of their disaster resistance capacity. Higher resistance levels compared to the natural disaster level prevent buildings from collapsing. The size of the affected area is determined by the territorial dimensions. In this context, the township is selected as the territory for predicting casualties. The impact of the disaster area on population fatalities is directly manifested in the population density of the selected territory. By incorporating these additional factors, the refined model strives to provide a more comprehensive understanding of the dynamics influencing casualty predictions. The expanded model aims to capture nuances in building characteristics and the size of the affected area, contributing to improved accuracy in forecasting population casualties.

It is predicted that the earlier the earthquake occurs, the more time will be available for the masses to transfer, thereby greatly reducing the number of casualties [37]. At present, many scholars think that the timing of an earthquake is unpredictable—even if it can be predicted, its timing usually lasts a few seconds, which does not play a role in reducing casualties. Therefore, this paper assumes that the earthquake is unpredictable, taking the situation in which there is no prediction before the occurrence of the earthquake as the cardinal number, that is, the correction coefficient ${\mathit{a}}_{\mathit{s}}$ of the unpredicted earthquake is taken as 1.

The more preparations that are made before a disaster, the faster the rescue speed is after it, and the fewer casualties there are [37]. Here, the emergency plan, emergency support, emergency team, simulation drill, and so on are taken as the factors for measuring the pre-disaster preparation, and the pre-disaster preparation work in a certain area is determined using expert evaluation and scoring. The more adequate the pre-disaster preparation, the fewer casualties there will be. As there is no research on the relationship between disaster preparedness and population death, it cannot be confirmed by cases. In this paper, we use this hypothesis to explain the influence of this factor on population casualties. We take the score of preparation before the earthquake as the base; that is, the correction coefficient of preparation score before the earthquake is taken as 1—by every 10 points it increases, the correction coefficient is reduced by 0.1, and by every 10 points it decreases, the correction coefficient is increased by 0.1. The correction coefficient of pre-disaster preparation is shown in

Table 4. Pre-disaster preparedness correction factor.

Score of pre-disaster preparation	0	10	20	30	40	50	60	70	80	90	100
Correction coefficient ${\mathit{a}}_{\mathit{u}}$	1.5	1.4	1.3	1.2	1.1	1	0.9	0.8	0.7	0.6	0.5

.

After an earthquake, most people are not hit and killed by buildings, but are temporarily buried under buildings awaiting rescue. The stronger the emergency response capability is, the fewer people there will be waiting for rescue. At present, China establishes the golden rescue time as 72 h. Within this timeframe, the number of deaths will be greatly reduced, but beyond this timeframe, the number of deaths will significantly increase. Therefore, this paper chooses 72 h as the rescue boundary; that is, the correction factor of 72 h is calculated as 1. Every 12 h ahead of schedule, the correction factor is reduced by 0.1. If it exceeds 72 h, the correction factor is calculated as 1. See

Table 5. Correction coefficient of emergency capacity after disaster.

Emergency capacity after disaster	0–12	12–24	24–36	36–48	48–60	60–72	>72 h
Correction coefficient ${\mathit{a}}_{\mathit{i}}$	0.4	0.5	0.6	0.7	0.8	0.9	1

for the correction coefficient of post-disaster emergency capacity.

To summarize, the prediction model of casualties is revised to:

$$\mathit{N}\mathit{D}={\mathit{f}}_{\mathit{p}}\times {\mathit{f}}_{\mathit{t}}\times \mathit{R}\mathit{D}{\times \mathit{M}\times \mathit{f}}_{\mathit{X}}\times {\mathit{f}}_{\mathit{Z}}\times {\mathit{f}}_{\mathit{n}}$$

(3)

${\mathit{f}}_{\mathit{x}}$ is the correction coefficient of earthquake prediction ability in this area, ${\mathit{f}}_{\mathit{z}}$ is the correction coefficient of pre-disaster preparation, and ${\mathit{f}}_{\mathit{n}}$ is the correction coefficient of emergency response capacity.

5. Construction of a Classified Demand Forecasting Model for Emergency Materials Based on Casualties

The foundation of emergency material forecasting is determining the number of casualties. This section focuses on establishing a demand forecasting model for emergency materials by analyzing the four main factors affecting the demand forecast, as discussed in Section 4.2.

5.1. Analysis of the Influencing Factors of Emergency Material Demand Forecast

The key factors influencing the prediction of emergency material demand encompass casualties, classification of emergency materials, seasonal demand, and regional differences.

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Number of casualties

The number of casualties emerges as the most influential factor in forecasting emergency material demand [23]. It is directly related to the need for various emergency materials and living essentials, such as drinking water, food, tents, and clothing. The demand for these materials is directly proportional to the number of people affected by the disaster. Additionally, the demand for emergency supplies like drugs and rescue equipment correlates directly with the number of injured individuals. Predicting the number of victims, deaths, and injuries in the disaster area facilitates the prediction of demand for emergency materials.

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Classification of emergency materials

Emergency materials can be classified based on the prediction basis, leading to two categories: prediction based on the disaster area and prediction based on the victims [42].

Prediction Based on the Disaster Area: This category includes materials like infrastructure restoration items, road rescue equipment, and disinfection materials directly related to the disaster area. For example, disinfection materials are predicted based on the area of the disaster, and road rescue equipment can be forecasted according to the extent of road damage in the disaster area.

Prediction Based on the Victims: This category encompasses life-saving supplies and daily necessities. Life-saving supplies pertain to emergency items for rescuing and treating the injured, such as drugs and rescue equipment. Daily necessities refer to emergency supplies meeting the basic needs of the victims, including tents, drinking water, and food. Both life-saving supplies and daily necessities involve one-time demand and cyclic demand. One-time demand materials, like tents and rescue equipment, are necessary only once, while cyclic demand materials, such as food and medicine, are continuously needed and depend on the number of people affected and the rescue time.

This classification provides a nuanced understanding of the diverse demands arising from different aspects of a disaster, as illustrated in Figure 2.

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Seasonal demand

The demand for emergency supplies experiences seasonal variations following natural disasters [43]. The season in which the disaster occurs impacts the types of emergency supplies needed. For instance, in hot summers, the demand for items such as drinking water, anti-inflammatory drugs, and disinfectants tends to be higher than in winter. Conversely, during cold winters, the demand for supplies like quilts, tents, and warm clothing may surpass that in summer. Therefore, when forecasting the demand for emergency materials in a disaster area, seasonal factors are converted into corresponding coefficients for different seasons based on previous disaster rescue data.

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Regional disparity

The characteristics of different disaster areas influence the demand for emergency materials [44]. Large cities, with dense buildings and complex structures, may have higher requirements for rescue equipment and a greater overall demand. Additionally, high population density in urban areas can increase the risk of infectious diseases, leading to a larger demand for disinfectants. This paper acknowledges the impact of regional differences on the type of emergency materials required but does not directly consider the impact on the quantity of emergency materials [45]. The focus is on the calculation of the number of emergency materials required, recognizing that emergency supplies are often sourced locally and tailored to the specific needs of each region.

5.2. Forecast Model of Classified Demand for Emergency Materials

Different categories of emergency materials exhibit distinct demand patterns. Determining the types and quantities of emergency materials in a disaster area involves considering the classification of emergency materials, along with factors such as casualties, seasonal variations, and regional differences.

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Life-saving supplies demand

Life-saving supplies are essential for treating the wounded, and their demand is directly linked to the number of injured individuals in the disaster area [46]. The prediction for life-saving supplies necessitates determining the number of injured people. By considering the unit demand for life-saving supplies per injured person and incorporating factors like the disaster area and season, area coefficients and season coefficients are derived. This category is further divided into one-time demand and cyclic demand, allowing for the calculation of the demand for life-saving supplies and cyclic emergency materials. One-time emergency material demand for life is calculated as follows:

$${\mathit{D}}_{\mathit{j}\mathit{k}}={\mathit{Q}}_{\mathit{k} \mathit{u}\mathit{r}\mathit{g}\mathit{e}\mathit{n}\mathit{c}\mathit{y}}\times \mathit{S}\mathit{S}\times {\mathit{G}}_{\mathit{k}}\times {\mathit{Z}}_{\mathit{k}}$$

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• ${\mathit{D}}_{\mathit{j}\mathit{k}}$ refers to the demand for the k-th material at the j-th disaster site;
• ${\mathit{Q}}_{\mathit{k} \mathit{urgency}}$ refers to the unit demand for primary life-saving supplies for a single injured population;
• ${\mathit{G}}_{\mathit{k}}$ refers to the seasonal coefficient of the emergency supplies;
• ${\mathit{Z}}_{\mathit{k}}$ refers to the regional coefficient of the emergency supplies; and
• SS refers to the number of injured in the disaster area.

Life cycle emergency material demand is calculated as follows:

$${\mathit{D}}_{\mathit{j}\mathit{k}}={\mathit{Q}\mathit{V}}_{\mathit{k} \mathit{u}\mathit{r}\mathit{g}\mathit{e}\mathit{n}\mathit{c}\mathit{y}}\times \mathit{S}\mathit{S}\times \mathit{T}\times {\mathit{G}}_{\mathit{k}}\times {\mathit{Z}}_{\mathit{k}}$$

(5)

$\mathit{Q}{\mathit{V}}_{\mathit{k} \mathit{urgency}}$ refers to the unit demand for life cycle materials of a single injured population, and T refers to time of emergency material demand.

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Daily necessities demand

Daily necessities are mainly used to meet the needs of the disaster victims [47]. The demand for emergency materials is directly related to the total number of survivors (excluding the number of dead in the disaster area). According to the unit demand of the number of survivors and the number of single survivors for emergency materials, combined with the seasonal coefficient of the disaster, it is divided into one-time demand and cycle demand, and the first-time emergency materials are calculated as material demand and life cycle emergency material demand.

One-time emergency material demand is calculated as follows:

$${\mathit{D}}_{\mathit{j}\mathit{k}}={\mathit{Q}}_{\mathit{k} \mathit{d}\mathit{a}\mathit{i}\mathit{l}\mathit{y}}\times (\mathit{Z}\mathit{S}-\mathit{S}\mathit{W})\times \mathit{T}\times {\mathit{G}}_{\mathit{k}}$$

(6)

• ${\mathit{Q}}_{\mathit{k} \mathit{daily}}$ refers to the unit demand for primary daily necessities of a single living population;
• ZS is the total number of people in the disaster area; and
• SW is the number of deaths in the disaster area.

Demand for life cycle emergency materials is calculated as follows:

$${\mathit{D}}_{\mathit{j}\mathit{k}}={\mathit{Q}\mathit{V}}_{\mathit{k} \mathit{d}\mathit{a}\mathit{i}\mathit{l}\mathit{y}}\times (\mathit{Z}\mathit{S}-\mathit{S}\mathit{W})\times \mathit{T}\times {\mathit{G}}_{\mathit{k}}$$

(7)

${\mathit{Q}}_{\mathit{k} \mathit{daily}}$ represents the unit demand of living cycle materials for a single living population.

To summarize, the prediction model of emergency material demand based on the classification of casualties and emergency materials can be obtained as follows:

$$D_{jk}=\left\{\begin{array}{c}{D}_{jk}=Q_{k urgency}\times SS\times G_k\times Z_k, \mathrm{Primary} \mathrm{demand} \mathrm{materials} \mathrm{for} \mathrm{life}\\ D_{jk}={QV}_{k urgency}\times SS\times T\times G_k\times Z_k, \mathrm{Life} \mathrm{cycle} \mathrm{demand} \mathrm{materials}\\ D_{jk}=Q_{k daily}\times (ZS-SW)\times T\times G_k, \mathrm{Primary} \mathrm{demand} \mathrm{materials} \mathrm{for} \mathrm{living}\\ D_{jk}={QV}_{k daily}\times (ZS-SW)\times T\times G_k, \mathrm{Life} \mathrm{cycle} \mathrm{materials}\end{array}\right.$$

• ${\mathit{Q}}_{\mathit{k} \mathit{urgency}}$ refers to the unit demand for primary life-saving supplies for a single injured population;
• ${\mathit{QV}}_{\mathit{k} \mathit{urgency}}$ refers to the unit demand for life cycle materials of a single injured population;
• ${\mathit{Q}}_{\mathit{k} \mathit{daily}}$ refers to the unit demand for primary daily necessities of a single living population;
• ${\mathit{Q}}_{\mathit{k} \mathit{daily}}$ represents the unit demand of living cycle materials for a single living population;
• ${\mathit{D}}_{\mathit{j}\mathit{k}}$ refers to the demand for the k-th material at the j-th disaster site;
• ${\mathit{G}}_{\mathit{k}}$ refers to the seasonal coefficient of the emergency supplies;
• ${\mathit{Z}}_{\mathit{k}}$ refers to the regional coefficient of the emergency supplies;
• T refers to time of emergency material demand;
• SW is the number of deaths in the disaster area;
• SS refers to the number of injured in the disaster area; and
• ZS is the total number of people in the disaster area.

6. Case Analysis

In the aftermath of a sudden earthquake disaster within a specific region, all municipalities have incurred varying degrees of damage. Notably, YX town, characterized by a complex terrain environment, has emerged as the epicenter of the devastation. Within the affected area of YX Township, five villages (referred to as affected areas n1, n2, n3, n4, and n5) have lost communication links with the external world. In response to this crisis, the territorial government promptly initiated measures to retrieve pre-disaster satellite images of the affected villages, leveraging data acquired by satellites before the seismic event. Furthermore, post-disaster satellite images of the impacted villages were procured utilizing a virtual satellite constellation. Subsequent to a meticulous comparative analysis of these satellite images, the collapse rates are graphically depicted in Figure 3 and Figure 4, See Supplementary Materials for additional figures.

The collapse rate of the five affected villages is shown in

Table 6. Collapse rate of affected villages.

Village	N1	N2	N3	N4	N5
Collapse rate (%)	0.4	0.5	0.4	0.65	0.6

.

To improve the accuracy and timeliness of casualty estimation and emergency supply demand forecasting after the earthquake, this study adopts a hybrid analytical method that combines regression analysis with intelligent image analysis. The approach consists of the following components:

(1)

Intelligent Analysis Based on Satellite Imagery

To assess building damage in the five affected villages, pre- and post-earthquake satellite images were analyzed using intelligent image processing techniques. Python 3.10.9 scripts were developed, utilizing the OpenCV library to perform preprocessing, grayscale conversion, image differencing, and binarization to automatically extract collapsed building areas and compute the building collapse rate (RB). The basic workflow is illustrated as Figure 5.

This procedure is used to automatically calculate the collapse rates for each of the five affected villages, providing critical input to the subsequent regression model.

(2)

Statistical Regression Model Using the Least Squares Method

RD represents the personnel mortality rate, ND denotes the estimated number of deaths in a city or region, and RB signifies the collapse rate of buildings, measured as the ratio of the number of collapsed rooms or the area of collapsed buildings to the total building count or area in a specified region. This paper employs the least squares statistical regression method to comprehensively analyze factors such as house collapse rate, personnel density, earthquake onset time, and intensity, proposing a human casualty estimation formula based on these considerations. Include the collapse rate in the formula ${\mathit{log}}_{10}^{\mathit{RD}}=9.0{\mathit{R}\mathit{B}}^{0.1}-10.07$ to obtain the death rate of the five affected villages, as shown in

Table 7. Mortality rate of affected villages.

Village	N1	N2	N3	N4	N5
Population mortality (%)	0.0139	0.0212	0.0139	0.0355	0.0303

.

According to the statistics of the civil affairs department before the disaster, the population density and the total population can be obtained; the correction coefficient fp can be obtained from the population density correction coefficient; the correction coefficient fz can be obtained from an assessment of the disaster preparedness; the correction coefficient fn can be obtained from the emergency response capacity after the disaster, as shown in

Table 8. Population density and total population of affected villages.

Village	N1	N2	N3	N4	N5
Total population	750	860	1100	820	730
Population density (per/km3)	40	50	36	30	60
Correction coefficient fp	0.8	1	0.8	0.8	1

,

Table 9. Correction coefficient of disaster preparedness of affected villages.

Village	N1	N2	N3	N4	N5
Pre disaster preparation score	30	80	20	50	90
Correction coefficient fz	1.2	0.7	1.3	1	0.6

and

Table 10. Correction coefficient of emergency response capacity of affected villages.

Village	N1	N2	N3	N4	N5
Post disaster emergency capacity	0–12	0–12	0–12	0–12	0–12
Correction coefficient fn	0.4	0.4	0.4	0.4	0.4

.

After the disaster, according to the intensity statistics of the five affected villages from the Seismological Bureau, combined with the earthquake’s occurrence at night, the time correction coefficient of the five affected villages is determined, as shown in

Table 11. Earthquake intensity and time correction coefficient of affected villages.

Village	N1	N2	N3	N4	N5
Earthquake intensity	X	X	IX	X	IX
Correction coefficient ft (night)	1.5	1.5	2	1.5	2

.

With the population density correction coefficient fp, earthquake intensity correction coefficient ft, population mortality, and the total population in $\mathit{N}\mathit{D}=\mathit{f}\mathit{p} \ast \mathit{f}\mathit{t} \ast \mathit{R}\mathit{D} \ast \mathit{M} \ast \mathit{f}\mathit{z} \ast \mathit{f}\mathit{n}$, the number of deaths in the five affected villages is obtained. According to the fact that the number of injured is generally 3–5 times of the number of deaths, this calculation example selects three times to analyze and calculate the number of injured in the five villages; and according to the total of five villages minus the number of deaths, the number of victims in the five villages is obtained. The number of casualties in the affected villages is shown in

Table 12. Number of casualties in the affected villages.

Village	N1	N2	N3	N4	N5
Death toll (person)	6	8	13	14	11
Number of injured	30	38	63	70	53
Number of victims	744	852	1087	806	719

.

According to the above analysis, emergency supplies are divided into two categories: daily life and life cycle. In this example, four kinds of emergency supplies are selected: food, medicine, water, and tents. Among them, food, medicine, and water belong to the materials for life cycle. Generally, it is assumed that each person needs four bottles of mineral water (12 bottles of mineral water per unit package), four packages of food (ten packages of food per unit package), and five packages of medicine (ten packages of medicine per unit package). Tents belong to the primary demand materials for daily life. Generally, it is assumed that two people live in one tent; that is, each person’s demand for a tent is 1/2 (if less than two people, it is calculated as one tent). After calculation, the demand for emergency supplies (selected in this example) of the five affected villages is obtained, as shown in

Table 13. Emergency materials demand of affected villages (unit: PCS).

	Disaster Point1	Disaster Point2	Disaster Point3	Disaster Point4	Disaster Point5
Food	298	341	435	322	288
Medicine	15	19	32	35	27
Water	248	284	362	269	240
Tent	372	426	544	403	360

.

(3)

Integration and Advantages of the Hybrid Method

This hybrid method leverages intelligent image analysis to efficiently and objectively extract key disaster indicators, while regression modeling provides a statistically grounded and interpretable means to estimate human casualties. The integration of these two approaches compensates for the limitations of using either method in isolation, improving both the accuracy and reliability of post-disaster prediction, which forms the basis for subsequent emergency resource allocation decisions. Through a comparative analysis of the estimated population casualties resulting from seismic events, such as the Tangshan earthquake in Hebei Province, the Lijiang earthquake in Yunnan Province, and the Wenchuan earthquake in Sichuan Province, juxtaposed with verified statistical data, it becomes evident that the collapse rate is the predominant influencing factor. By taking into account variables such as the seismic event’s occurrence timeframe and population density, the predicted outcomes closely align with the empirically derived statistical results, as visually represented in Figure 6.

7. Conclusions

This study presents a comprehensive analysis of the key factors influencing casualty rates in disaster scenarios, emphasizing the importance of accurately predicting emergency material demand to enhance disaster response efficiency. By comparing various prediction methodologies—including time series smooth prediction, linear regression, non-linear regression, neural networks, case-based reasoning, grey system models, and intelligent analysis techniques—this study has identified a hybrid approach combining regression and intelligent analysis as the most effective model for estimating casualties. To address the inherent challenges associated with data scarcity during the initial phases of a disaster, this study proposes a “Sky–Earth Integrated Monitoring System.” By leveraging satellite imagery, unmanned aerial vehicles (UAVs), and ground sensors, the system facilitates real-time data acquisition from disaster-affected areas, effectively mitigating the “black box” phenomenon where critical information is inaccessible due to communication disruptions and logistical barriers. Integrating the collected data into the predictive model establishes a robust correlation between casualty numbers and emergency material demand, thereby enhancing the accuracy and timeliness of demand forecasting in post-disaster scenarios. While the proposed methodology significantly improves the efficiency of disaster response by ensuring that essential supplies are accurately forecasted and rapidly delivered to affected populations, several potential limitations warrant further exploration.

First, the generalizability of the model to various disaster types, geographic regions, and demographic conditions remains uncertain. Future research should seek to refine this model to account for diverse disaster profiles, such as floods, hurricanes, or landslides, and integrate local variations in infrastructure resilience, cultural response behaviors, and social vulnerability. Second, the model’s reliance on collapse rates and casualty estimations might oversimplify the complex interactions between disaster impacts and human responses. Integrating additional variables, such as transportation network infrastructure damage and social behavior in the face of disasters, could provide a more nuanced understanding of emergency needs. Third, ethical considerations surrounding casualty predictions and resource allocation are essential but not fully addressed in this study. Predictive models, while useful for optimizing rescue operations, can raise ethical concerns related to data privacy, the accuracy of estimates, and the prioritization of resources.

Additionally, the study’s primary focus on short-term emergency material demand underscores the need for a more holistic perspective that extends to longer-term recovery phases. Future research could explore evolving community needs as they transition from immediate rescue to recovery and rebuilding, thus enabling more adaptive and sustainable disaster response strategies that effectively balance immediate relief efforts with longer-term resilience building.

By incorporating international standards and best practices from organizations such as FEMA, UNDRR, and Sphere, the proposed methodology not only enhances operational relevance but also aligns with broader disaster management frameworks. This alignment fosters a standardized, data-driven approach to emergency logistics decision-making, contributing to a more robust and comprehensive disaster response system capable of mitigating the impacts of large-scale disasters while supporting the recovery of affected communities.