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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Int. J. Public Health</journal-id>
<journal-title-group>
<journal-title>International Journal of Public Health</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Int. J. Public Health</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1661-8564</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1608932</article-id>
<article-id pub-id-type="doi">10.3389/ijph.2026.1608932</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Spatiotemporal Characteristics of Health Collaboration Development in China&#x2019;s Urban Agglomerations: An Empirical Analysis of Four Major Regions</article-title>
<alt-title alt-title-type="left-running-head">Li et al.</alt-title>
<alt-title alt-title-type="right-running-head">Health Collaboration in Urban Agglomerations</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes" equal-contrib="yes">
<name>
<surname>Li</surname>
<given-names>Xiangfei</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>&#x2020;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1909894"/>
</contrib>
<contrib contrib-type="author" corresp="yes" equal-contrib="yes">
<name>
<surname>Zhu</surname>
<given-names>Wentao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>&#x2020;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3153815"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhu</surname>
<given-names>Xumin</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<label>1</label>
<institution>School of Economics and Management, Tiangong University</institution>, <city>Tianjin</city>, <country country="CN">China</country>
</aff>
<aff id="aff2">
<label>2</label>
<institution>School of Public Administration and Policy, Renmin University of China</institution>, <city>Beijing</city>, <country country="CN">China</country>
</aff>
<author-notes>
<corresp id="c001">
<label>&#x2a;</label>Correspondence: Xiangfei Li, <email xlink:href="mailto:lxf@tiangong.edu.cn">lxf@tiangong.edu.cn</email>; Wentao Zhu, <email xlink:href="mailto:cuixiwen19990929@163.com">cuixiwen19990929@163.com</email>
</corresp>
<fn id="fn002" fn-type="other">
<p>This Original Article is part of the IJPH Special Issue &#x201c;Urban Health in Transition: Advancing Evidence and Policy for Healthier Cities&#x201d;</p>
</fn>
<fn fn-type="equal" id="fn001">
<label>&#x2020;</label>
<p>These authors have contributed equally to this work</p>
</fn>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-04-09">
<day>09</day>
<month>04</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>71</volume>
<elocation-id>1608932</elocation-id>
<history>
<date date-type="received">
<day>30</day>
<month>07</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>29</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>18</day>
<month>03</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Li, Zhu and Zhu.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Li, Zhu and Zhu</copyright-holder>
<license>
<ali:license_ref start_date="2026-04-09">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<sec>
<title>Objective</title>
<p>This study analyzed China&#x2019;s four most politically significant and economically dynamic urban agglomerations&#x2014;Beijing-Tianjin-Hebei (BTH), Yangtze River Delta (YRD), Pearl River Delta (PRD), and Chengdu-Chongqing (CY)&#x2014;to explore their health development trends from 2005 to 2023 and compare their spatiotemporal characteristics in coordinated health development.</p>
</sec>
<sec>
<title>Methods</title>
<p>We employed an integrated index construction method and an improved urban gravity model to build urban health network models, investigating the coordinated relationships and features of health development in these agglomerations.</p>
</sec>
<sec>
<title>Results</title>
<p>Over 17 years, the four agglomerations showed both commonalities and unique differences in health coordination. The degree of coordinated development strengthened significantly, although it was notably influenced by major policies and public health events. Core cities exhibited substantial radiating effects on regional health coordination. PRD and YRD exhibited more pronounced growth in coordination intensity than BTH and CY. Distinct coordination patterns emerged: BTH displayed a unipolar radiation structure, YRD a polycentric network, PRD a core-periphery structure, and CY a dual-core, policy-driven coordination structure.</p>
</sec>
<sec>
<title>Conclusion</title>
<p>The findings reveal the critical role of core cities and policy interventions in shaping regional health collaboration networks, providing insights into how to achieve more balanced health resource allocation and equity in urban agglomerations.</p>
</sec>
</abstract>
<kwd-group>
<kwd>collaborative governance</kwd>
<kwd>public health</kwd>
<kwd>regional integration</kwd>
<kwd>urban agglomerations</kwd>
<kwd>urban network structure</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the National Social Science Fund of China (Grant Number 22BGL223).</funding-statement>
</funding-group>
<counts>
<fig-count count="4"/>
<table-count count="2"/>
<equation-count count="4"/>
<ref-count count="32"/>
<page-count count="10"/>
</counts>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>Introduction</title>
<p>Within urban clusters, core cities often concentrate high-quality public health and medical resources, not only meeting local demands but also serving as regional hubs for resource distribution. The cross-regional flow and functional spillover of these resources are key indicators of enhanced collaborative health security capabilities within urban clusters. Rational allocation of resources within a region significantly improves the accessibility of medical and health resources across the entire area. Thus, it is necessary to further consider regional medical resource security capabilities from a holistic perspective under urban collaboration [<xref ref-type="bibr" rid="B1">1</xref>]. In these urban regions, medical resources are highly networked and coordinated among cities [<xref ref-type="bibr" rid="B2">2</xref>]. Core cities in these areas hold overwhelming advantages in terms of policy, talent, economic strength, and medical standards, benefiting not only the core cities themselves but also neighboring cities. For example, of China&#x2019;s 125 national regional medical center construction projects, Beijing and Shanghai have exported 50 and 20 projects, respectively, to surrounding cities [<xref ref-type="bibr" rid="B3">3</xref>], achieving a certain degree of radiation effect for high-quality medical services. However, public health services within urban clusters still exhibit structural imbalances. On one hand, core cities possess significant advantages in policy, talent, financial investment, and medical standards; on the other hand, non-core cities and peripheral regions face substantial gaps in resource supply, health facilities, emergency response capabilities, and more. Inter-regional coordination mechanisms remain underdeveloped, forming an asymmetric &#x201c;single-core-multi-periphery&#x201d; structure.</p>
<p>Existing research has found that, in the context of cross-departmental and cross-regional collaboration, ambiguous responsibilities and an absence of performance evaluations lead to inefficiencies in coordination. For example, the imbalanced development of urban functions in China (emphasizing the economy and infrastructure while neglecting social services) has resulted in a gap in public health [<xref ref-type="bibr" rid="B4">4</xref>]. China&#x2019;s grassroots emergency response capabilities in its medical and public health systems are weak [<xref ref-type="bibr" rid="B5">5</xref>]. In Beijing, the accessibility of secondary and tertiary hospitals for low-income communities is only one-fourth that of high-income communities, and the time required to reach primary healthcare institutions is twice as long for low-income groups [<xref ref-type="bibr" rid="B6">6</xref>]. Moreover, primary healthcare institutions provide limited medical services. Shanghai&#x2019;s central urban areas also have insufficient coverage of walkable primary healthcare services, with 22.8% of communities experiencing resource shortages. Older adults and low-income families face exacerbated difficulties accessing healthcare due to socioeconomic barriers [<xref ref-type="bibr" rid="B7">7</xref>, <xref ref-type="bibr" rid="B8">8</xref>]. A significant portion of healthcare resources is concentrated in developed regions, such as Beijing and Zhejiang, leading to resource surpluses, while areas such as Anhui and Jiangxi have a Gini coefficient as high as 0.88 when measured by service area [<xref ref-type="bibr" rid="B9">9</xref>].</p>
<p>Overall, although urban agglomeration integration has promoted resource consolidation and institutional coordination, significant imbalances and fragmentation persist in public health services. Existing literature primarily focuses on the macro-level structure of urban agglomerations, with insufficient comparative analysis of different types of cities within them, especially non-core cities. There is a lack of systematic research on the coordination mechanisms of non-core cities. This study adopts a micro-level perspective, focusing on the role differences of various cities in coordinated health development, aiming to provide theoretical support and empirical analysis to achieve balanced resource allocation and health equity within urban agglomerations.</p>
<p>At the regional level, the collaborative development of public health is not a one-dimensional &#x201c;expansion of quantity&#x201d; but rather a multidimensional, networked evolutionary process influenced by various internal and external factors. Different elements interact and couple to drive the deepening of cross-regional public health partnerships and the integration of service systems, thereby forming a more cohesive and dynamically evolving regional health collaboration network.</p>
<p>In recent years, studies have thoroughly revealed the multidimensional factors influencing the spatiotemporal evolution of public health collaboration in urban agglomerations and regions, particularly highlighting the critical role of transportation, technology, and policy interventions in resource flows and functional spillovers. <xref ref-type="table" rid="T1">Table 1</xref> summarizes these influencing factors.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Multidimensional factors affecting the spatiotemporal evolution of urban agglomerations or regional public health coordination (Beijing-Tianjin-Hebei, Yangtze River Delta, Pearl River Delta region, and Chengdu-Chongqing region, China, 2023).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Category</th>
<th align="center">Authors and year</th>
<th align="center">Research topic</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="4" align="left">Transportation</td>
<td align="left">Wang and Nie [<xref ref-type="bibr" rid="B10">10</xref>]</td>
<td align="left">The association between transportation infrastructure and health</td>
</tr>
<tr>
<td align="left">Dalen [<xref ref-type="bibr" rid="B11">11</xref>]</td>
<td align="left">Changes in the number of Americans seeking medical treatment abroad (2007&#x2013;2017)</td>
</tr>
<tr>
<td align="left">Zhang et al. [<xref ref-type="bibr" rid="B12">12</xref>]</td>
<td align="left">Association between traffic density, population mobility, and confirmed COVID-19 cases</td>
</tr>
<tr>
<td align="left">Li et al. [<xref ref-type="bibr" rid="B13">13</xref>]</td>
<td align="left">Spatiotemporal evolution of COVID-19 in China and its correlation with transportation networks</td>
</tr>
<tr>
<td rowspan="3" align="left">Technology</td>
<td align="left">Zhao et al. [<xref ref-type="bibr" rid="B14">14</xref>]</td>
<td align="left">The impact of the digital economy on public health efficiency</td>
</tr>
<tr>
<td align="left">Yang [<xref ref-type="bibr" rid="B15">15</xref>]</td>
<td align="left">Differences in internet usage frequency and health levels between urban and rural areas</td>
</tr>
<tr>
<td align="left">Haft and Allen [<xref ref-type="bibr" rid="B16">16</xref>]</td>
<td align="left">Effectiveness of the health information exchange platform CRISP</td>
</tr>
<tr>
<td rowspan="6" align="left">Policy intervention</td>
<td align="left">Rangachari et al. [<xref ref-type="bibr" rid="B4">4</xref>]</td>
<td align="left">The U.S. Affordable Care Act and social determinants of health (SDOH) interventions</td>
</tr>
<tr>
<td align="left">Zhao et al. [<xref ref-type="bibr" rid="B17">17</xref>]</td>
<td align="left">The impact of China&#x2019;s low-carbon city pilot program on the structure of the healthcare industry</td>
</tr>
<tr>
<td align="left">Jiao and Zhang [<xref ref-type="bibr" rid="B18">18</xref>]</td>
<td align="left">Cross-regional collaborative governance of Japan&#x2019;s nuclear contaminated water incident</td>
</tr>
<tr>
<td align="left">Guo et al. [<xref ref-type="bibr" rid="B19">19</xref>]</td>
<td align="left">Effectiveness of Beijing-Tianjin-Hebei healthcare collaborative development policies</td>
</tr>
<tr>
<td align="left">Butorina and Borko [<xref ref-type="bibr" rid="B20">20</xref>]</td>
<td align="left">Functional positioning and collaborative mechanisms in regional integration</td>
</tr>
<tr>
<td align="left">Toma and Laurens [<xref ref-type="bibr" rid="B21">21</xref>]</td>
<td align="left">Regional coordination experience of European integration</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In recent years, spatial measurement technology has achieved significant progress both theoretically and practically as a crucial tool for revealing the patterns of public health collaborative development.</p>
<p>Spatial measurement, as a crucial analytical tool, has been widely applied in recent years in the field of public health. For example, Deng et al. studied the Guangdong-Hong Kong-Macao Greater Bay Area, using the space-time cube (STC) model and emerging hot spot analysis to confirm the stress effect of high-temperature environments on public health security, emphasizing the need to embed heat island mitigation strategies in urban planning to reduce population health risks [<xref ref-type="bibr" rid="B22">22</xref>]. Li employed the Dagum Gini coefficient and spatial econometric models to analyze medical service supply across 31 Chinese provinces from 2012 to 2020, revealing regional disparities characterized by &#x201c;convergence in the east and west, lagging in the central region&#x201d; [<xref ref-type="bibr" rid="B23">23</xref>]; Tang and Tan&#x2019;s four-dimensional indicator system found that factors such as soil erosion control and population density directly influence the risk resilience of public health systems [<xref ref-type="bibr" rid="B24">24</xref>]; spatiotemporal evolution models play a key role in simulating epidemic spread and allocating medical resources. For instance, case distribution predictions based on kernel density estimation can improve emergency supply delivery efficiency by 35%, while spatial autocorrelation analysis highlights the need to strengthen vaccination coverage in key areas [<xref ref-type="bibr" rid="B13">13</xref>].</p>
<p>Compared to existing research, the main contributions of this study are as follows:<list list-type="order">
<list-item>
<p>Focusing on China&#x2019;s four most dynamic urban agglomerations, this study constructs a spatial gravity structure among cities in the field of public health, exploring for the first time the characteristics of collaborative healthcare development in China&#x2019;s major urban agglomerations from a spatiotemporal perspective.</p>
</list-item>
<list-item>
<p>Fully considering China&#x2019;s political characteristics, the study examines the leading role of major events, key policies, and politically influential core cities in regional healthcare collaboration.</p>
</list-item>
<list-item>
<p>The study also investigates the role of non-core cities in healthcare collaboration, focusing on internal structural differences within urban agglomerations, and reveals the spatiotemporal network characteristics exhibited during the collaborative development process of China&#x2019;s four major urban agglomerations.</p>
</list-item>
</list>
</p>
</sec>
<sec sec-type="methods" id="s2">
<title>Methods</title>
<sec id="s2-1">
<title>Study Area</title>
<p>This study covers health data from four key regions: the Beijing-Tianjin-Hebei urban agglomeration (BTH), the Yangtze River Delta urban agglomeration (YRD), the Pearl River Delta urban agglomeration (PRD), and the Chengdu-Chongqing metropolitan area (CY).</p>
<p>The most economically developed prefecture-level cities within each urban agglomeration were selected for this research, including 13 cities in the Beijing-Tianjin-Hebei urban agglomeration, 26 cities in the Yangtze River Delta urban agglomeration, 9 cities in the Pearl River Delta urban agglomeration, and 16 cities in the Chengdu-Chongqing urban agglomeration, totaling 64 cities. According to the official administrative hierarchy standards for Chinese cities, the cities in the study area are categorized accordingly [<xref ref-type="bibr" rid="B25">25</xref>, <xref ref-type="bibr" rid="B26">26</xref>].</p>
</sec>
<sec id="s2-2">
<title>Constructing a Healthy Urban Network Model</title>
<p>This study attempts to build a network model between cities based on their different urban health development levels to analyze their coordinated development.</p>
<p>First, we constructed an Urban Health Index (UHI)that represents the health development level of each city to analyze the developmental changes of different cities from 2005 to 2023.</p>
<p>Next, the study analyzed the synergy level of health development among different cities within urban agglomerations and constructed a Regional Health Collaborative Development Index (HCDI) to reflect the internal synergy level of the urban agglomerations.</p>
<p>On this basis, the synergy consistency of health development levels among different cities was analyzed using an improved urban gravity model.</p>
<p>Finally, an in-depth analysis was conducted of the constructed urban network model, extracting and summarizing four structural characteristics of the spatiotemporal collaborative development of urban agglomeration health.</p>
<p>This study, referencing Evangelista et al. [<xref ref-type="bibr" rid="B27">27</xref>], Korir [<xref ref-type="bibr" rid="B28">28</xref>], and Al-Ghamdi et al. [<xref ref-type="bibr" rid="B29">29</xref>], selected representative health development indicators. These include metrics reflecting urban health development levels, such as the quantity of health resources, health status, and local economic development levels. Additionally, indicators influencing inter-city synergy are chosen, including distance between cities, travel time, and policy support for collaborative development, as shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Required indicators for this study (Beijing-Tianjin-Hebei, Yangtze River Delta, Pearl River Delta region, and Chengdu-Chongqing region, China, 2023).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Dimensions</th>
<th align="center">Subordinate indicators</th>
<th align="center">Attribute</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="3" align="left">Health resources</td>
<td align="left">Number of hospitals</td>
<td align="center">&#x2b;</td>
</tr>
<tr>
<td align="left">Number of practicing physicians</td>
<td align="center">&#x2b;</td>
</tr>
<tr>
<td align="left">Number of hospital beds</td>
<td align="center">&#x2b;</td>
</tr>
<tr>
<td align="left">Health expenditure</td>
<td align="left">Per capita total health expenditure (yuan)</td>
<td align="center">-</td>
</tr>
<tr>
<td rowspan="3" align="left">Social development status</td>
<td align="left">GDP</td>
<td align="center">&#x2b;</td>
</tr>
<tr>
<td align="left">Transportation distance between cities</td>
<td align="center">-</td>
</tr>
<tr>
<td align="left">Transportation time between cities</td>
<td align="center">-</td>
</tr>
<tr>
<td align="left">Policy support intensity</td>
<td align="left">Number of coordinated development policies issued</td>
<td align="center">&#x2b;</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>This study primarily utilized data sourced from the <italic>China Health Statistical Yearbook</italic> and the <italic>China City Statistical Yearbook,</italic> along with statistical yearbooks and publicly available data from individual cities and their respective provinces; policy documents were mainly obtained from the official websites of local Health Commissions and Medical Security Bureaus. The health-related policies examined in this study refer to government-issued policy documents closely related to coordinated health development. The selection criteria for the policy samples were as follows: first, ensuring that the policy text content was closely related to health, with systematic searches conducted using keywords such as &#x201c;health coordination&#x201d; &#x201c;medical collaboration&#x201d; and &#x201c;healthcare cooperation&#x201d;; second, government-issued laws, regulations, and measures were filtered, primarily selecting local normative documents while excluding those irrelevant to the research objectives.</p>
<p>Policy Quantification Method: The &#x201c;Policy Support Intensity&#x201d; indicator was quantified through a systematic content analysis of relevant government documents. The process involved three steps: (1) Document Collection: Policy documents were retrieved from the official websites of local Health Commissions and Medical Security Bureaus, using keywords such as &#x201c;health coordination,&#x201d; &#x201c;medical collaboration,&#x201d; and &#x201c;healthcare cooperation.&#x201d; (2) Screening and Classification: Collected documents were filtered to include only those containing substantive measures for promoting regional health collaboration. Each policy was then classified by its administrative level (national, provincial, or municipal). (3) Scoring: A scoring system was applied, wherein each policy received a base score of 1. This score was then weighted by its administrative level (national &#x3d; 3, provincial &#x3d; 2, municipal &#x3d; 1) and by the specificity of its collaborative measures (detailed implementation rules &#x3d; 2, general guidance &#x3d; 1). A city&#x2019;s annual &#x201c;Policy Support Intensity&#x201d; was the sum of the weighted scores of all relevant policies issued that year. This method ensured a more nuanced measurement than a simple policy count.</p>
<sec id="s2-2-1">
<title>Urban Health Level Measurement</title>
<p>To better assess urban health development levels in this study, we constructed a UHI based on the indicator data in <xref ref-type="table" rid="T2">Table 2</xref>. Following the method by Sun et al. [<xref ref-type="bibr" rid="B30">30</xref>], positive and negative indicators were standardized separately to obtain weights. After determining the weights <inline-formula id="inf1">
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</mml:math>
<label>(1)</label>
</disp-formula>
</p>
</sec>
<sec id="s2-2-2">
<title>Regional Health Collaborative Development Index</title>
<p>Based on previous calculations and analyses of various indicators, and considering their impact on regional health collaboration, the Analytic Hierarchy Process (AHP) method was used to score each indicator and construct a judgment matrix [<xref ref-type="bibr" rid="B31">31</xref>]. Based on this, the HCDI for each region from 2014 to 2023 was derived:<disp-formula id="e2">
<mml:math id="m4">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>I</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mfenced open="{" close="}" separators="|">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:msup>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2032;</mml:mo>
</mml:msup>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mroot>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x220f;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:mroot>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mroot>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x220f;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:mroot>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:msup>
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<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mroot>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x220f;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:mroot>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mroot>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x220f;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:mroot>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mi>l</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>In the equation, <inline-formula id="inf3">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the i-th region&#x2019;s j-th standardized indicator value, <inline-formula id="inf4">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the j-th indicator&#x2019;s weight for each year, n &#x3d; 7 represents the number of indicators involved in calculating UHI for each city; <inline-formula id="inf5">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the element in the i-th row and j-th column of the AHP judgment matrix A, used to calculate weights, and <inline-formula id="inf6">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the coefficient related to the i-th indicator.</p>
</sec>
<sec id="s2-2-3">
<title>Construction of an Urban Gravity Model Based on Health</title>
<p>Based on Newton&#x2019;s law of gravitation and complex network theory, an urban gravity model for health was constructed using the formula:<disp-formula id="e3">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>c</mml:mi>
<mml:mo>&#xb7;</mml:mo>
<mml:mfrac>
<mml:mrow>
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<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xb7;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mi mathvariant="italic">exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mi>T</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xb7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
<mml:mo>&#xb7;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">max</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">min</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
<inline-formula id="inf7">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf8">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represent the health index of city <italic>i</italic> and <italic>j</italic>; <inline-formula id="inf9">
<mml:math id="m12">
<mml:mrow>
<mml:msubsup>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> denotes the spatial distance between cities; <inline-formula id="inf10">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the travel time distance; <inline-formula id="inf11">
<mml:math id="m14">
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the gravitational constant (set to 1), <inline-formula id="inf12">
<mml:math id="m15">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1.8 is the distance decay coefficient, and <inline-formula id="inf13">
<mml:math id="m16">
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the time decay threshold. This model overcomes the limitations of traditional gravity models that only consider spatial distance by introducing the time dimension and an exponential decay function, making it more aligned with real-world collaborative mechanisms. This study built on the research of Wei et al. [<xref ref-type="bibr" rid="B32">32</xref>] and introduced <inline-formula id="inf14">
<mml:math id="m17">
<mml:mrow>
<mml:mn mathvariant="italic">1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
<mml:mo>&#xb7;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">max</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">min</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula> as the resource complementarity adjustment factor, where: <inline-formula id="inf15">
<mml:math id="m18">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">max</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">min</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>H</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula> reflects the similarity in health levels between two cities; when the <italic>UHI</italic> of two cities is similar (e.g., Beijing and Tianjin, both with relatively high <italic>UHI</italic>), this ratio approaches 1, and the adjustment factor tends toward 0, suppressing the gravitational value; when the UHI difference between two cities is significant, this ratio approaches 0, and the adjustment factor tends toward 1, leaving the gravitational value unsuppressed. <inline-formula id="inf16">
<mml:math id="m19">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the competition coefficient, representing the weakening effect of resource similarity on collaborative gravity, and has a value of 0.3.</p>
<p>The parameters in the gravity model were determined as follows: The distance decay coefficient (&#x3b3; &#x3d; 1.8) falls within the range commonly used in spatial interaction models in regional studies (e.g., 1.5&#x2013;2.0) and was finalized through iterative testing to best fit the observed inter-city patient flow data from a subset of the study regions. The competition coefficient (&#x3b8; &#x3d; 0.3) was set to reflect the moderate level of resource competition and functional similarity observed among Chinese cities of a similar administrative rank. The time decay threshold (T) was set to 2&#xa0;h, which is a common tolerance for inter-city medical travel. The robustness of these parameter choices was subsequently confirmed through the sensitivity analysis presented in the &#x201c;Model Validation&#x201d; section.</p>
</sec>
<sec id="s2-2-4">
<title>Urban Health Network Model</title>
<p>Using the Pearson correlation coefficient and social network analysis (SNA), a dynamic collaborative network was constructed, calculating the Pearson correlation coefficient of gravitational values between cities <inline-formula id="inf17">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> , with the formula:<disp-formula id="e4">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn mathvariant="italic">1</mml:mn>
</mml:mrow>
<mml:mi>T</mml:mi>
</mml:msubsup>
<mml:mrow>
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</mml:mfrac>
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</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>Among them, represents the gravitational value of city <italic>i</italic> to <italic>j</italic> at time <italic>t</italic>; <inline-formula id="inf18">
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</inline-formula>, <inline-formula id="inf19">
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</inline-formula> is the mean value. Subsequently, degree centrality was calculated to reveal the structural characteristics of the network, with the degree centrality formula as follows: <inline-formula id="inf20">
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</inline-formula>. Here, <inline-formula id="inf21">
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</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the connection strength between city <italic>i</italic> and <italic>j</italic> (with values of 0 or 1).</p>
</sec>
</sec>
<sec id="s2-3">
<title>Model Validation and Robustness Analysis</title>
<p>This study employed the leave-one-out cross-validation (LOOCV) method to verify model stability. Specifically, each time one urban agglomeration dataset was excluded, the model was trained with the remaining three urban agglomeration datasets. The excluded urban agglomeration&#x2019;s collaborative gravity value was predicted, and the root mean square error (RMSE) and coefficient of determination (<inline-formula id="inf22">
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<mml:mi>R</mml:mi>
<mml:mn>2</mml:mn>
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</mml:mrow>
</mml:math>
</inline-formula>) were calculated. The results show that the RMSE values were all less than 0.05 and that the <inline-formula id="inf23">
<mml:math id="m27">
<mml:mrow>
<mml:msup>
<mml:mi>R</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> values were all greater than 0.92, indicating that the model has good generalization capability. This study&#x2019;s sensitivity analysis examined the variation in gravity values when adjusting the distance decay coefficient (1.5&#x2013;2.0) and the time threshold T (&#xb1;20%). The results also demonstrate that, when the distance decay coefficient varies by &#xb1;0.1, the gravity value fluctuates by less than 3%, and when the coefficient varies by &#xb1;20%, the fluctuation is less than 5%, indicating that the model is not sensitive to parameter changes and exhibits strong robustness.</p>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>Results</title>
<sec id="s3-1">
<title>Regional Health Development and Collaborative Level</title>
<p>From <xref ref-type="fig" rid="F1">Figure 1</xref>-UHI, it can be observed that the four urban clusters exhibit similar trends in public health levels, showing a generally upward trajectory before 2020, followed by a significant decline after 2020 due to the impact of a major public health emergency. <xref ref-type="fig" rid="F1">Figure 1</xref>-HCDI reveals that from 2015 to 2019, the four study regions experienced a notable upward trend in their Regional HCDI. This trend correlates with the introduction of collaborative development policies in China during this period, such as the Beijing-Tianjin-Hebei Collaborative Development Plan Outline in 2015, the Yangtze River Delta Regional Integration Development Plan Outline in 2019, the Pan-Pearl River Delta Regional Deepening Cooperation Joint Declaration (2015&#x2013;2025) signed in 2014, and the Chengdu-Chongqing Urban Cluster Development Plan in April 2016. Following the implementation of these regional collaborative policies under strong national-level coordination, the public health collaboration indices of the four major urban clusters saw substantial growth compared to previous years. This demonstrates that national policy support has played a powerful role in advancing public health development within specific regions.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Changes in UHI across the studied urban agglomerations (Beijing-Tianjin-Hebei, Yangtze River Delta, Pearl River Delta region, and Chengdu-Chongqing, China, 2023) and the spatiotemporal variation and synergy index of urban agglomeration health development levels.</p>
</caption>
<graphic xlink:href="ijph-71-1608932-g001.tif">
<alt-text content-type="machine-generated">Line graph tracking UHI values from 2005 to 2022 for BTH, YRD, PRD, and CY regions, with annotations linking inflection points to national development plans and a vertical red dashed line marking the year 2020.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-2">
<title>Network Structure of Collaborative Health Development in Urban Agglomerations</title>
<p>Using ArcGIS Map and Origin 2024 software, the previously constructed health collaboration gravity model was used to calculate the results and visualize the urban network, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. The importance of urban nodes in the region is represented by different colors and sizes; the thickness of the gravity lines indicates the intensity of collaborative gravity between cities, and the gradient from dark to light red represents a city&#x2019;s health level. The overall spatial distribution of urban clusters reflects the development status of health initiatives among cities within the region, alongside the collaborative health development before and after the implementation of coordinated policies. It can be observed that, both before and after policy implementation, the UHI index of key cities within the clusters is higher than that of other cities in the region, indicating that the public health development in these key cities has consistently led the region. The strengthening of this radiating influence is corroborated by the steady rise in the overall HCDI for all urban agglomerations following the enactment of key regional policies around 2015&#x2013;2016, as clearly depicted in <xref ref-type="fig" rid="F2">Figure 2</xref>. This aggregate trend provides indirect evidence of intensifying inter-city connections, which is manifested in the network models as an enhanced gravitational pull from core cities.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The Status of Health Coordination in Four Urban Agglomerations (Beijing-Tianjin-Hebei, Yangtze River Delta, Pearl River Delta region, and Chengdu-Chongqing region, China, 2023).</p>
</caption>
<graphic xlink:href="ijph-71-1608932-g002.tif">
<alt-text content-type="machine-generated">Line graph showing HCDI values from 2005 to 2021 for four Chinese regions: BTH (cyan), YRD (red), PRD (blue), and CY (orange). Key policy milestones are marked and annotated at 2015 and 2019.</alt-text>
</graphic>
</fig>
<p>However, it is also important not to overlook the role of geographical distance in regional health collaboration. The collaborative gravity between the majority of cities tends to exhibit lower intensity levels when the distance between them is large, whereas relatively closer cities&#x2014;especially key cities and other cities in the region&#x2014;show higher collaborative intensity. Examples include Beijing and Langfang.</p>
<p>Within urban clusters, higher traffic accessibility between cities corresponds to higher collaborative intensity levels in the gravity lines. Additionally, in terms of temporal evolution, the gravitational pull among cities in urban clusters has continuously strengthened over time, indicating a gradual increase in regional healthcare collaboration. Compared to the 2014&#x2013;2018 period, medical resource collaboration intensity grew in a more pronounced way across all urban clusters during 2018&#x2013;2023, demonstrating the rapid development of inter-cluster medical collaboration and the further enhancement of interactivity and synergy of medical resources during this period.</p>
</sec>
<sec id="s3-3">
<title>Spatial Characteristics of Coordinated Health Development in Urban Clusters</title>
<p>Combining the previously calculated inter-city <inline-formula id="inf24">
<mml:math id="m28">
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</mml:math>
</inline-formula> and plotting <xref ref-type="fig" rid="F3">Figure 3</xref>, this more intuitively reveals the public health collaborative development relationships within each study area&#x2014;especially between non-core cities in the region. <xref ref-type="fig" rid="F3">Figure 3</xref> displays the correlation of inter-city health collaboration gravity values (<inline-formula id="inf25">
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</inline-formula>) across different urban clusters. Red indicates a positive correlation, with darker red representing higher values, while blue indicates a negative correlation, with darker blue representing lower values. The color intensity reflects the magnitude of the gravity value <inline-formula id="inf26">
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<mml:mrow>
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</mml:math>
</inline-formula> and the strength of the correlation. From the inter-city correlation characteristics, the YRD exhibited the strongest synergy with a high-concentration positive correlation network across the entire region, while the CY, with its mixed red and blue blocks and low synergy among core city pairs, emerged as the region with the weakest synergy. <xref ref-type="fig" rid="F4">Figure 4</xref> was generated by integrating <xref ref-type="fig" rid="F2">Figures 2</xref>, <xref ref-type="fig" rid="F3">3</xref>, illustrating the internal public health collaborative development structures of different urban clusters.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Heat maps of correlation for Beijing-Tianjin-Hebei, Yangtze River Delta, Pearl River Delta, and Chengdu-Chongqing (China, 2023).</p>
</caption>
<graphic xlink:href="ijph-71-1608932-g003.tif">
<alt-text content-type="machine-generated">Four heatmap graphs display inter-city correlation matrices for regions labeled CY, PRD, YRD, and BTH, with color gradients from red to blue indicating correlation coefficients between negative one and one, as shown by the adjacent color bar scale.</alt-text>
</graphic>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>The collaborative structure (Beijing-Tianjin-Hebei, Yangtze River Delta, Pearl River Delta, and Chengdu-Chongqing, China, 2023).</p>
</caption>
<graphic xlink:href="ijph-71-1608932-g004.tif">
<alt-text content-type="machine-generated">Four network diagrams illustrate intercity connections in major Chinese urban regions: BTH, YRD, CY, and PRD. Cities are marked with colored circles whose sizes vary, and lines between them are shaded from blue to red according to the correlation scale shown at right, ranging from negative one in red to positive one in blue. Major cities such as Beijing, Nanjing, Hangzhou, Chengdu, and Guangzhou are labeled in bold and larger font.</alt-text>
</graphic>
</fig>
<p>In <xref ref-type="fig" rid="F3">Figures 3</xref>, <xref ref-type="fig" rid="F4">4</xref>, the analysis reveals the collaborative development structures and characteristics of the four major urban clusters between 2014 and 2023, as detailed below:</p>
<sec id="s3-3-1">
<title>The Beijing-Tianjin-Hebei (BTH) Region Was Found to Exhibit a Unipolar Radiating Collaborative Structure</title>
<p>Beijing forms strong synergies (dark red) with neighboring cities, such as Langfang, Baoding, and Zhangjiakou, as evidenced by the thickest gravity lines radiating from Beijing in <xref ref-type="fig" rid="F2">Figure 2</xref>, while cities farther from Beijing in the region also maintain notable connections (light red). This indicates high gravitational values between Beijing and regional cities, forming a strong correlation axis centered on Beijing, reflecting the spillover effects of the capital&#x2019;s resources. Meanwhile, Tianjin, another key city in the region, is marginalized. Its collaboration with surrounding cities, such as Tangshan and Cangzhou, is weak (blue) due to functional overlap with Beijing, which suppresses its influence over neighboring cities. As the provincial capital of Hebei, Shijiazhuang faces similar challenges to Tianjin, compounded by its significantly lower economic level compared to Beijing and Tianjin. Additionally, due to industrial homogenization and internal competition among Hebei&#x2019;s cities, Shijiazhuang lacks coordination, resulting in a collaborative vacuum with eastern Hebei and a pronounced spatial differentiation of &#x201c;strong around Beijing.&#x201d; Overall, the BTH region was found to present a pattern of &#x201c;one dominant core, weak secondary cores, and fragmented peripheries.&#x201d;</p>
</sec>
<sec id="s3-3-2">
<title>The Yangtze River Delta (YRD) Region Was Found to Exhibit a Polycentric Networked Collaborative Structure</title>
<p>The deep red coloration in the YRD indicates a high overall level of collaboration. Within the region, a strong tri-core collaborative network formed between SH-NJ-HZ, which are connected by the most robust gravitational links in the entire network visualization (<xref ref-type="fig" rid="F2">Figure 2</xref>), with core cities demonstrating significant radiation effects on neighboring areas. Intra-provincial collaboration outperforms cross-provincial cooperation, while distant cities show weaker coordination. Centered on Shanghai, a deep red triangular zone emerges with Nanjing and Hangzhou. Among neighboring cities, Suzhou and Shanghai (100&#xa0;km apart) appear deep red (high gravitational value), while cities such as Chizhou (over 300&#xa0;km away) appear light blue. Intra-provincial city pairs, such as SU-WX, display red coloration, indicating strong collaboration. This demonstrates that in the YRD region, beyond traditional major cities, economically robust cities can also become focal points for regional public health collaboration.</p>
</sec>
<sec id="s3-3-3">
<title>The Pearl River Delta Region (PRD) Was Found to Exhibit a Core-Periphery Collaborative Structure</title>
<p>Guangzhou and Shenzhen form ultra-strong collaborative nodes as dual cores, with the gravitational connection between them being the strongest in the entire study, as represented by the thickest, darkest red link in <xref ref-type="fig" rid="F2">Figure 2</xref>. SZ-DG and GZ-FS show deep red, while neighboring cities display a &#x201c;core-periphery&#x201d; gradient radiation structure due to geographical proximity. Collaboration among other cities within the same province is active, but the collaborative gap between distant cities and core areas is significant. Meanwhile, distant cities, such as Zhaoqing and Jiangmen, display noticeably lighter colors, indicating weaker collaboration with core cities.</p>
</sec>
<sec id="s3-3-4">
<title>The Chengdu-Chongqing Region (CY) Was Found to Exhibit a Dual-Core, Segmented, Policy-Mandated Collaborative Structure</title>
<p>Compared to other city clusters, CY appears lighter with more blue tones in <xref ref-type="fig" rid="F3">Figure 3</xref>, indicating weaker regional collaboration. Collaboration between Chengdu and Chongqing is weak. While Chengdu shows localized red areas with policy-mandated neighboring cities, such as Ya&#x2019;an, in the correlation heatmap (<xref ref-type="fig" rid="F3">Figure 3</xref>), market-driven collaboration with cities, such as Ziyang, is negligible (appearing light blue/white in <xref ref-type="fig" rid="F3">Figure 3</xref>). Non-core cities generally appear blue, showing an obvious lack of collaboration. The grid colors between Chengdu and Chongqing are notably lighter than those between other regional core city pairs. Secondary cities in Sichuan, such as Nanchong and Luzhou, appear blue, showing almost no collaborative signals.</p>
</sec>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>Discussion</title>
<p>This study provides the first systematic spatiotemporal analysis of health collaboration patterns across China&#x2019;s four major urban agglomerations, revealing the distinct structural characteristics of their collaborative networks. Our findings contribute to the understanding of regional health governance in several important ways.</p>
<sec id="s4-1">
<title>Conclusion</title>
<p>Based on the above research findings, this article summarizes some correlations between regional public health collaborative development and key regional cities that may influence the study of coordinated regional public health development.</p>
<p>The PRD urban agglomeration exhibits a relatively high level of coordinated public health development, while the YRD urban agglomeration demonstrates more balanced public health coordination. Beijing and Chengdu exert significant influence over public health coordination within their respective urban clusters. The coordinated development of public health in the YRD region exhibits a multi-point pattern, while other regions show a trend of concentration around key cities. Collaborative relationships in health and wellness among cities of different scales exhibit distinct structures.</p>
</sec>
<sec id="s4-2">
<title>Comparison With Existing Literature</title>
<p>Our identification of four distinct collaboration structures aligns with but also extends previous research on urban networks. The unipolar structure in BTH reflects the &#x201c;core-periphery&#x201d; patterns observed in previous studies of regional development in China [<xref ref-type="bibr" rid="B13">13</xref>], but our analysis reveals the specific mechanisms through which political centrality reinforces health resource concentration. The polycentric network in YRD demonstrates how economic integration can foster more balanced health collaboration, supporting the findings of regional integration studies in Europe and North America [<xref ref-type="bibr" rid="B21">21</xref>].</p>
<p>The core-periphery structure in PRD shows similarities to metropolitan governance patterns observed in global city-regions, where economic complementarity drives functional integration [37]. However, the dual-core, segmented structure in CY represents a unique pattern that reflects China&#x2019;s specific regional development policies and the challenges of cross-provincial coordination.</p>
</sec>
<sec id="s4-3">
<title>Methodological Contributions</title>
<p>Our improved gravity model, which incorporates both spatial and temporal dimensions along with a competition coefficient, addresses the limitations of traditional gravity models in health collaboration research. This approach provides a more nuanced understanding of how geographic proximity, temporal accessibility, and resource complementarity jointly shape collaboration patterns. The integration of policy quantification into our index system also represents an advancement in the measurement of the impact of governance factors on health collaboration.</p>
</sec>
<sec id="s4-4">
<title>Policy Implications</title>
<p>The varying collaboration structures identified in our study suggest the need for differentiated regional health governance approaches. In unipolar structures, such as BTH, policies should focus on strengthening secondary nodes and reducing dependency on the core. In polycentric networks, such as YRD, the emphasis should be on enhancing connectivity between multiple centers. For core-periphery structures, such as PRD, policies should address the collaboration gaps between the core and peripheral areas. In dual-core segmented structures, such as CY, the priority should be to foster cross-jurisdictional integration and reduce policy fragmentation.</p>
</sec>
<sec id="s4-5">
<title>Limitations and Future Research</title>
<p>This study has several limitations that should be addressed in future research. First, our indicator system, while comprehensive, may not capture all dimensions of urban health collaboration. Future studies could incorporate additional indicators, such as environmental factors, health outcomes, and social determinants of health. Second, our data ends in 2023, missing potential post-COVID-19 trends in health collaboration. Further research on post-COVID-19 development trends requires a longer time horizon to fully capture relevant dynamics. Third, the selection of economically developed cities within each agglomeration may introduce sampling bias.</p>
<p>Future research could expand the geographical scope to include more urban agglomerations, incorporate dynamic network analysis to track collaboration evolution in real time, and employ mixed-methods approaches to better understand the mechanisms underlying the observed collaboration patterns.</p>
</sec>
</sec>
</body>
<back>
<sec sec-type="author-contributions" id="s5">
<title>Author Contributions</title>
<p>XL proposed the topic and designed the overall article. WZ processed and analyzed the data. XZ summarized the data. All authors contributed to the article and approved the submitted version.</p>
</sec>
<sec sec-type="COI-statement" id="s7">
<title>Conflict of Interest</title>
<p>The authors declare that they do not have any conflicts of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s8">
<title>Generative AI Statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<ref-list>
<title>References</title>
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<surname>Huang</surname>
<given-names>C</given-names>
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</person-group>. <article-title>Exploring the Impact of Poverty on the Sustainable Development Goals: Inhibiting Synergies and Magnifying Trade-Offs</article-title>. <source>Sustainable Cities Soc</source> (<year>2023</year>) <volume>89</volume>:<fpage>104367</fpage>. <pub-id pub-id-type="doi">10.1016/j.scs.2022.104367</pub-id>
</mixed-citation>
</ref>
</ref-list>
<fn-group>
<fn fn-type="custom" custom-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/443300/overview">Ana Ribeiro</ext-link>, University of Porto, Portugal</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2089972/overview">Jos&#xe9; Chen-Xu</ext-link>, Instituto Salud Global Barcelona (ISGlobal), Spain</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3218276/overview">Qiuyi Wu</ext-link>, Shihezi University, China</p>
<p>One reviewer who chose to remain anonymous</p>
</fn>
</fn-group>
</back>
</article>