Abstract

In the context of an aging population and the "Healthy China" strategy, the rational allocation of urban medical facilities is crucial for enhancing the health and well-being of the elderly. Based on multi-source data including the Seventh National Population Census, points of interest (POI) for medical facilities, and route planning data, this study employs methods such as average nearest neighbor analysis, an improved two-step floating catchment area method, and bivariate local spatial autocorrelation to investigate the accessibility of medical care for the elderly and the degree of supply-demand matching in Lanzhou City in 2020. The results reveal the following: (1) The spatial distribution of the elderly population in Lanzhou is uneven, with both elderly population density and aging rate exhibiting a "dual-core" structure. (2) The spatial clustering characteristics vary across the three levels of medical facilities. City-level facilities display a "single-center" structure, district-level facilities follow a "one main, multiple secondary" distribution pattern, and street-level facilities adopt a "multi-center" distribution pattern. (3) Significant spatial disparities exist in accessibility across different levels of medical facilities. City-level and district-level facilities show pronounced unevenness in accessibility distribution, while street-level facilities have the broadest distribution of high-accessibility areas, though some streets still exhibit low-accessibility "blind spots." (4) Due to the uneven spatial distribution of medical facilities, mismatches between the elderly population and medical facilities exist to varying degrees at the city, district, and street scales. These findings can provide a scientific basis for the rational allocation of urban medical facilities and the development of healthy cities.

Keywords: elderly population; medical facilities; accessibility; matching degree; Lanzhou City

Introduction

During this unique period of rapid population aging, socio-economic transformation, and urban-rural spatial restructuring, China's aging phenomenon is becoming increasingly complex. According to the Seventh National Population Census, the population aged 65 and above reached 190.64 million, accounting for 13.50% of the total population, an increase of 4.63 percentage points compared to the Sixth National Population Census. Due to the growing elderly population and increased health risks, demand for medical facilities among older adults is rising. To actively respond to population aging, the "Healthy China 2030" Planning Outline proposes advancing the construction of elderly healthcare service systems and extending medical and health services to communities and households. With gradual improvements in economic development and ongoing medical system reforms, China's healthcare sector has developed rapidly, and residents' health levels have improved significantly. However, the problem of "difficulty in accessing medical care" remains prominent, making the rational allocation of regional medical resources crucial for safeguarding the health of the elderly and comprehensively promoting healthy city development.

Accessibility to medical facilities can be understood as the convenience with which residents can obtain medical resources. International research on medical facility accessibility primarily analyzes spatial disparities in healthcare access for different groups based on residents' diverse travel modes and their medical needs and usage patterns. For instance, Sibley and Weiner evaluated access to healthcare services along the rural-urban continuum in Canada, finding that urban residents had better access to specialist physicians than rural residents. Guida et al. analyzed accessibility differences among different age groups of elderly people in Milan, discovering that those aged 65-69 had higher healthcare accessibility compared to those aged 70 and above. Donald and Hoenig examined healthcare accessibility for disabled elderly populations in the United States, finding that residential areas lacked walkable medical facilities, leading to reliance on home healthcare services. In recent years, with the comprehensive advancement of healthy city construction, domestic research has increasingly focused on healthcare accessibility from the perspective of different groups, including vulnerable populations such as the elderly, affordable housing residents, and floating populations. Methodologies commonly employed include the nearest distance method and potential model approach. For example, Xu et al. used the nearest distance method to comprehensively evaluate public service facility accessibility for vulnerable groups in Beijing, revealing a gradual decrease in comprehensive accessibility from the inner ring outward along east-west and north-south axes. Zhang et al. applied the potential model to examine healthcare accessibility for affordable housing residents in Beijing, finding that newer affordable housing developments had poorer accessibility. Tao et al. compared healthcare accessibility differences between floating and registered populations in Shanghai using the potential model, revealing that registered populations enjoyed better accessibility.

In summary, spatial disparities in healthcare accessibility across different groups have received widespread attention. The prevalence of chronic diseases among the elderly increases with age, making them a key population requiring medical attention. However, existing research has insufficiently addressed accessibility differences between elderly populations and different levels of medical facilities, particularly primary healthcare facilities such as clinics and pharmacies that serve daily medical needs. Methodologically, compared to the nearest distance method and potential model, the two-step floating catchment area method and its improved variants better account for both supply-demand conditions and distance factors, making them more suitable for complex scenarios. In terms of data, most studies have focused on developed eastern cities, with less attention paid to inland cities in northwestern China. Given this context, this study takes Lanzhou as a case study, utilizing multi-source data including the Seventh National Population Census, medical facility POI data, and route planning data. Through average nearest neighbor analysis, an improved two-step floating catchment area method, and bivariate local spatial autocorrelation analysis, this paper examines street-scale healthcare accessibility and supply-demand matching for the elderly population, aiming to provide a basis for rational urban medical facility allocation and healthy city construction.

1.1 Study Area Overview

Lanzhou, the capital of Gansu Province, governs five districts (Chengguan, Qilihe, Anning, Xigu, and Honggu) and three counties (Yongdeng, Gaolan, and Yuzhong). The city is situated in a typical valley setting, with mountains flanking the north and south and the Yellow River flowing eastward through the city. The main urban area serves as the primary concentration of economic activity and population. Administratively, it comprises Chengguan, Qilihe, Anning, and Xigu districts, including 53 streets and two high-tech development zones. In 2020, the main urban area had a permanent population of 2.9059 million, with 471,300 elderly people aged 65 and above, accounting for 65.27% of Lanzhou's total elderly population. The aging rate in the main urban area reached 16.22% in 2020, an increase of 4.05 percentage points from 2015. With the continuous growth of the elderly population and deepening aging rates, demand for medical facilities continues to rise, highlighting increasingly prominent supply-demand structural contradictions. Therefore, this study focuses on Lanzhou's main urban area as the research region, encompassing 55 study units.

1.2 Data Sources

The research data includes elderly population data, administrative division data, medical facility data, and route planning data for Lanzhou's main urban area. Specifically: (1) Elderly population data: Obtained from the Seventh National Population Census, including total population and population aged 65 and above for each street. (2) Administrative division data: Derived from basic geographic information spatial data obtained from Google remote sensing imagery. For accessibility analysis, considering that elderly populations have limited activity ranges and are relatively immobile, the geometric centroid of each street polygon was used as the spatial distribution center for the elderly population. (3) Medical facility data: Collected through Python programming using the Amap API to crawl medical facility point data for Lanzhou's main urban area in 2020, including name, address, type, and latitude/longitude information. Facilities such as obstetrics and gynecology hospitals, children's hospitals, and cosmetic surgery hospitals unrelated to this study were excluded, resulting in 1,242 medical facility points (Table 1). Considering service capacity differences across facility levels, medical facilities were categorized into city-level, district-level, and street-level based on the "Guiding Principles for Medical Institution Planning (2021-2025)" and existing research. City-level facility service capacity was characterized by bed numbers collected from hospital official websites, while district-level and street-level facility bed numbers were set according to the "Gansu Provincial Health and Health Development Statistical Bulletin" and other sources. (4) Route planning data: Travel time between supply and demand points based on real-time traffic conditions was obtained using the Amap API multiple-route planning interface (https://lbs.amap.com/product/path). Considering that elderly travel primarily occurs during non-commuting hours, the API was called during non-commuting periods to calculate travel times.

1.3 Methodology

1.3.1 Aging Rate

The aging rate refers to the percentage of the population aged 65 and above relative to the total population. When this ratio exceeds 7%, the region is considered an aging society; when it reaches 14%, the region has entered a later stage of aging.

1.3.2 Average Nearest Neighbor Analysis

Average nearest neighbor analysis is used to determine the degree of spatial clustering of point features, providing an overall measure of spatial proximity.

1.3.3 Kernel Density Analysis

Kernel density analysis objectively reflects the dispersion or clustering state of point features in geographic space and is widely used in medical facility distribution research.

1.3.4 Improved Two-Step Floating Catchment Area Method

The two-step floating catchment area method can comprehensively and conveniently calculate medical facility accessibility from both supply and demand perspectives. To more accurately measure accessibility, this study improves the method by introducing a distance decay function and establishing multi-level search radii. The specific steps are as follows:

Step 1: For each medical facility (v), using travel time threshold (Tr) as the search radius, search for each street (u) within the radius to calculate the supply-demand ratio (R_v) for each medical facility.

R v = Tuv ≤ 1 - e Tr Pu Tuv ≤ Tuv > 

Where: S_v represents medical facility service capacity, characterized by bed numbers; G(Tr) is a Gaussian function considering time decay, which declines more slowly near the threshold starting point compared to power functions, exponential functions, or kernel density functions, better reflecting actual medical travel behavior; Tr is the travel time threshold; T_uv is the travel time between street u and facility v; and P_u is the total elderly population (persons) of all streets within the threshold range.

Step 2: For each street (u), identify all medical facilities (v) within the travel time threshold (Tr), multiply their supply-demand ratios (R_v) by the Gaussian function value, sum these weighted ratios to obtain the medical accessibility index (A_u) for street u.

Au = ∑v Tuv ≤ Tuv ≤ 

Regarding service thresholds, existing research indicates that although the proportion of private car and emergency vehicle use for medical visits is increasing annually, walking and public transportation remain the primary travel modes for the elderly. Therefore, this study considers "walking" and "public transportation" as the two main travel modes. Based on the "15-minute living circle" planning concept proposed in the "Lanzhou City New Urbanization Development Plan (2021-2025)" and previous research commonly employing 15 minutes as the walking medical travel threshold, "walking" is set as the service threshold for street-level facilities. Considering that the golden hour for medical rescue is 15 minutes, "public transportation" is set as the service threshold for city-level facilities. Referencing existing studies that commonly use 30 minutes as a reasonable medical travel time, "public transportation" is set as the service threshold for district-level facilities.

Pu + ∑u Tuv ≤ Tuv ≤ Au = ∑v Tuv ≤ 

1.3.5 Bivariate Local Spatial Autocorrelation

Bivariate local spatial autocorrelation can reveal spatial association patterns between elderly population and medical facilities. Based on spatial correlation results, four clustering types can be identified: high-high, low-low, high-low, and low-high.

2. Results

2.1 Spatial Distribution Characteristics of the Elderly Population

Using three indicators—elderly population size, elderly population density, and aging rate—this study analyzes the spatial distribution patterns of the elderly population in Lanzhou's main urban area. The Jenks natural breaks method was applied to classify each indicator into five levels. Areas with elderly populations ≥13,788 were designated as high-value zones, and areas with density ≥8,131.31 persons/km² were designated as high-density zones (Figure 2).

The results show that high-value zones for elderly population size are distributed across 11 streets, mainly in Yanbei and Caochang streets in Chengguan District, Xihu and Dunhuang roads in Qilihe District, Xilu Street in Anning District, and Fulu Road in Xigu District. Yanbei Street has the largest elderly population (13,788 persons), while Fulongping Street has the smallest (only 1,189 persons)—a 12-fold difference. High-density zones cover 10 streets, primarily in Jiuquan Road, Gaolan Road, Railway West Village, Railway East Village in Chengguan District, and Fulu Road in Xigu District. The lowest density occurs in Shajingyi Street. The elderly population density in Railway East Village Street is 12 times that of Shajingyi Street. A total of 29 streets in Lanzhou have aging rates exceeding 14%, mainly distributed in Chengguan, Qilihe, and Xigu districts, with 20% of streets having entered the later stage of aging. Xianfeng Road Street in Xigu District has the highest aging rate at 26.36%.

Overall, the spatial distribution of the elderly population in Lanzhou's main urban area shows significant disparities. High-value zones for elderly population size are distributed across Chengguan, Qilihe, Anning, and Xigu districts, while elderly population density and aging rate both exhibit a "dual-core" structure centered on Zhangye Road and other streets in Chengguan District and Fulu Road and other streets in Xigu District. This pattern is related to historical development inertia, urban functional positioning, and industrial development. As the political, commercial, and scientific-educational center of Lanzhou, Chengguan District has a long development history and relatively complete supporting facilities, making it a primary gathering area for the elderly population. Xigu District, known as the "cradle of China's petrochemical industry" during the planned economy era, was a key national industrial base. The establishment of large backbone enterprises such as "Lanlian" and "Lanhua" led to the formation of unified industrial and residential areas, with in-situ aging of workers being the main reason for the large elderly population, high density, and high aging rate in Xigu District.

2.2 Spatial Clustering Characteristics of Medical Facilities

Average nearest neighbor analysis was used to measure the spatial clustering degree of medical facilities at each level. The results show that all three levels of medical facilities exhibit significant clustering characteristics in Lanzhou, though clustering intensity varies. The average nearest neighbor indices for all three facility types are less than 1 and pass significance tests, with clustering intensity ranking as: street-level > district-level > city-level. This is because street-level facilities have small footprints, flexible spatial layouts, and are significantly influenced by market orientation. Driven by economic interests, they demonstrate stronger "location preference" and "population preference," resulting in more intense spatial clustering. City-level and district-level facilities, with larger footprints, wider service and radiation ranges, and greater social impact, are more deeply guided and regulated by government planning, resulting in relatively lower spatial clustering.

Kernel density analysis was further employed to characterize the spatial clustering patterns of medical facilities (Figure 3). Specifically: City-level facilities exhibit a "single-center" structure, with the clustering center located in Weiyuan Road, Jiayuguan Road, and Tuanjie New Village in Chengguan District, while other streets have more dispersed layouts. District-level facilities show a "one main, multiple secondary" distribution pattern. The main center forms a contiguous cluster around Zhangye Road, Jiuquan Road, and Gaolan Road in Chengguan District. Secondary centers are scattered as points, with nuclear density values in Xiyuan Road, Gongjiawan Road, Jianlan Road, Dunhuang Road, Xigu City, and Fulu Road decreasing from the center outward, forming four secondary centers. Street-level facilities display a "multi-center" distribution pattern, which can be roughly divided into five centers based on kernel density distribution: Zhangye Road and Jiuquan Road, Railway West Village and Railway East Village, Xiyuan Road, Jianlan Road and Dunhuang Road, and Xigu City and Fulu Road.

2.3 Analysis of Medical Accessibility for the Elderly Population

2.3.1 Differences in Medical Commute Times for the Elderly

By calculating the average shortest medical commute times for the elderly to reach medical facilities, the average times to city-level, district-level, and street-level facilities are 30.48 minutes, 19.91 minutes, and 6.33 minutes, respectively, indicating substantial differences in commute times across facility levels. Additionally, the unique ribbon-like cluster structure of this valley city has created persistent transportation challenges of "east-west congestion and north-south obstruction." City-level and district-level facilities are mainly concentrated in Chengguan and Qilihe districts, making cross-district medical visits increasingly common and significantly increasing commute times for elderly populations in peripheral areas of Xigu and Anning districts. For example, Lanzhou University First Hospital, located in eastern Chengguan District with a nationally key clinical specialty in geriatrics, requires elderly residents from Shajingyi Street at the westernmost edge of Anning District to travel cross-district for care, with a commute time reaching 84.92 minutes—four times the average street commute time. Although street-level facilities such as clinics and pharmacies have "convenience" characteristics that can basically meet the daily medical needs of the elderly, some streets still have long commute times. For instance, the average medical commute time in Jingyuan Road Street reaches 27.37 minutes, far below the 15-minute planning target for basic medical and health services in Lanzhou's 15-minute living circles. Considering that walking is the primary travel mode for elderly medical visits, improving accessibility to street-level facilities should be prioritized to shorten medical commute times and enhance timeliness of care.

To specifically analyze the proportion of elderly population covered by each facility level within different time thresholds, medical commute times for each street were divided into four threshold ranges, and the proportion of elderly population covered by each facility level within these ranges was calculated (Table 2). The results show that the proportion of elderly population covered by city-level, district-level, and street-level facilities within 15 minutes increases as facility level decreases, while coverage within 30 minutes and 60 minutes decreases as facility level decreases. Street-level facilities cover 98.07% of the elderly population within 15 minutes, while city-level hospitals cover only 29.81% within the same timeframe. This indicates that the more primary the medical facility, the lower the proportion of elderly population it covers. The coverage of street-level and district-level facilities needs further strengthening.

2.3.2 Analysis of Medical Accessibility for the Elderly Population

The improved two-step floating catchment area method was applied to calculate accessibility indices for each street from both supply and demand perspectives. These indices were then standardized and classified into five levels using the Jenks natural breaks method: high, relatively high, medium, relatively low, and low (Figure 4). The results reveal significant spatial disparities in accessibility to medical facilities across different levels in Lanzhou's main urban area.

The average accessibility index for city-level medical facilities is 0.22, with 20% of streets having indices above the average. High-accessibility streets account for 12.50%, mainly concentrated in Zhangye Road, Jiuquan Road, and Gaolan Road in Chengguan District and Jianlan Road and Xihu Road in Qilihe District. In contrast, 42.86% of streets in Anning District and 62.50% in Xigu District are low-accessibility streets, indicating uneven spatial distribution of city-level medical facilities.

For district-level facilities, 7 high-accessibility streets are found in Linxia Road, Zhangye Road, Gaoxin District in Chengguan District, and Jianlan Road in Qilihe District. Relatively high-accessibility streets are distributed around these high-accessibility streets, including Donggang West Road, Xiuchuan, and Gongjiawan. However, they remain mainly in Chengguan and Qilihe districts. Medium-accessibility streets are located around high and relatively high-accessibility streets, while relatively low and low-accessibility streets are roughly distributed in peripheral and marginal areas of the main urban area. Although the distribution scale of high-accessibility streets for district-level facilities is larger than that for city-level facilities, they remain concentrated in Chengguan and Qilihe districts, showing uneven spatial distribution.

Street-level facilities have the broadest distribution of high-accessibility streets, with high and relatively high-accessibility streets accounting for 31.02%, distributed across Chengguan, Qilihe, Anning, and Xigu districts. However, some streets still have low-accessibility "blind spots." For example, Donggang West Road Street in Chengguan's old city has an aging rate of 18.77% but a medical accessibility index of only 0.29, indicating that street-level facility construction does not fully align with elderly population distribution. Overall, accessibility to all facility levels shows a gradually decreasing trend from central areas like Zhangye Road and Fulu Road outward to peripheral and marginal zones. This is because central areas not only have denser medical facilities and road networks but also more developed public transportation services.

2.4 Matching Degree Analysis Between Elderly Population and Medical Accessibility

Gini coefficients were calculated for accessibility indices at each facility level, and Lorenz curves were plotted to analyze the matching degree between medical facility accessibility and elderly population distribution (Figure 5). According to UNDP evaluation standards, a Gini coefficient between 0.30-0.39 indicates a relatively reasonable state, while 0.40-0.59 indicates a large disparity. The Gini coefficients for city-level and district-level facility accessibility are 0.52 and 0.48, respectively, falling in the large disparity range. The street-level facility accessibility Gini coefficient is 0.36, within the relatively reasonable range. This indicates that city-level and district-level facilities fail to benefit elderly populations in most streets, with poor matching between elderly population distribution and medical accessibility.

To specifically measure spatial mismatches between medical facility accessibility and elderly population, bivariate local spatial autocorrelation analysis was conducted using GeoDa software on accessibility indices and elderly population numbers at each street level. Four clustering types were identified (Figure 6). The "high-high cluster" indicates both high medical accessibility indices and high elderly population numbers compared to surrounding areas, mainly including Zhangye Road, Jiuquan Road, and Gaolan Road streets—all located in Chengguan's old city area with long construction history, convenient transportation, large elderly populations, and comprehensive medical facility configurations, showing high matching between facilities and elderly population. The "low-low cluster" indicates both low accessibility indices and low elderly population numbers, including Shajingyi, Anningbao, and Qingbaishi streets in peripheral areas with small elderly populations and limited medical facilities, representing a "dual-low" supply-demand state. The "high-low cluster" indicates low elderly population numbers but high accessibility indices, including Kongjiaya, Xiuchuan, and Donggang streets in peripheral areas with few elderly residents but abundant medical facilities, showing a mismatch where facility construction outpaces elderly population growth. The "low-high cluster" indicates large elderly populations but low accessibility indices, including Baiyin Road, Wuquan Road, and Railway Station streets located around the "high-high cluster" with relatively large elderly populations but severe medical facility shortages. Differentiated improvement strategies should be implemented for different matching types.

Discussion

Facing the pressure of deepening population aging, meeting the medical needs of elderly groups and improving their healthcare accessibility has theoretical and practical significance for enhancing elderly health and well-being and implementing the Healthy China strategy. This study analyzes urban medical facility accessibility and supply-demand matching from the elderly population perspective. The findings show that spatial disparities in elderly healthcare accessibility in Lanzhou are significant, decreasing from central to peripheral areas—a pattern consistent with research findings in eastern plain cities like Shanghai and Nanjing. However, Lanzhou's main urban area is located in the Yellow River valley between north and south mountains, extending east-west along the river in a belt-shaped distribution, forming a "multi-center, cluster-based" urban spatial structure. This topographical constraint has created persistent transportation problems of "east-west congestion and north-south obstruction," resulting in long medical commute times and low accessibility for elderly populations in peripheral areas, particularly for city-level and district-level healthcare needs.

This study's focus on different levels of urban medical facilities from the elderly perspective supplements and extends previous healthcare accessibility research. The introduction of route planning data overcomes the bottleneck of traditional static road network assumptions in accessibility calculations, enabling more scientific and precise accessibility measurement. However, limitations remain: Due to data availability constraints, this study only uses bed numbers to characterize medical facility service capacity. Future research should comprehensively evaluate healthcare service equalization by incorporating facility scale and medical staff numbers. Additionally, actual elderly medical decision-making is complex, related to disease type, hospital preference, and other factors. Future research should obtain micro-level individual spatiotemporal behavior data to further explore elderly medical preferences and spatiotemporal behaviors.

Based on the findings, strategies for medical facility allocation in Lanzhou's main urban area are proposed from three perspectives: (1) All levels of medical facilities exhibit a "core-periphery" spatial distribution pattern. Chengguan and Qilihe districts are concentrated areas for medical facilities, while Anning and Xigu districts have relatively fewer facilities. Future planning should prioritize medical facility layout in Anning and Xigu districts. (2) Significant spatial disparities exist in accessibility across facility levels. Future development should focus on balanced allocation of city-level and district-level facilities while further improving coverage of street-level facilities. (3) Different improvement measures should be formulated based on matching degrees between street-level facility accessibility and elderly population. For streets with large elderly populations but low accessibility indices, medical facility supply should be increased. For streets with small elderly populations but low accessibility, existing facility spatial layouts can be optimized and transportation networks improved to enhance travel capacity.

Conclusions

1. The spatial distribution of the elderly population in Lanzhou is uneven. High-value zones for elderly population size are distributed across Chengguan, Qilihe, Anning, and Xigu districts. Both elderly population density and aging rate exhibit a "dual-core" structure centered on Zhangye Road in Chengguan District and Fulu Road in Xigu District.

2. All three levels of medical facilities show clustered distributions, but with different spatial clustering characteristics. City-level facilities exhibit a "single-center" structure, district-level facilities follow a "one main, multiple secondary" pattern, and street-level facilities adopt a "multi-center" distribution pattern.

3. Significant spatial disparities exist in accessibility across facility levels. High-accessibility areas for city-level facilities are mainly in Chengguan and Qilihe districts. District-level facilities extend somewhat into Anning District but remain centered on Chengguan and Qilihe. Street-level facilities have the broadest distribution of high-accessibility areas, though some streets still have low-accessibility "blind spots."

4. Due to uneven spatial distribution of medical facilities, mismatches between the elderly population and medical facilities exist to varying degrees at city, district, and street scales, with mismatched areas concentrated in both the urban core and peripheral zones.

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