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Article(id=1320438437136683355, tenantId=1146029695717560320, journalId=1319373219989389464, issueId=1320438168613138789, articleNumber=null, orderNo=null, doi=10.11847/zgggws1148341, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1750953600000, receivedDateStr=2025-06-27, revisedDate=1755100800000, revisedDateStr=2025-08-14, acceptedDate=1760630400000, acceptedDateStr=2025-10-17, onlineDate=1792746655972, onlineDateStr=2026-10-23, pubDate=1778342400000, pubDateStr=2026-05-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792746655972, onlineIssueDateStr=2026-10-23, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792746655972, creator=13701087609, updateTime=1792746655972, updator=13701087609, issue=Issue{id=1320438168613138789, tenantId=1146029695717560320, journalId=1319373219989389464, year='2026', volume='42', issue='5', pageStart='513', pageEnd='640', issueExtLink='null', onlineDate='null', pubDate='1778342400000', pubDateStr='2026-05-10', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792746591952, creator='13701087609', updateTime=1792748055079, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1320444305479684446, tenantId=1146029695717560320, journalId=1319373219989389464, issueId=1320438168613138789, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1320444305479684447, tenantId=1146029695717560320, journalId=1319373219989389464, issueId=1320438168613138789, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=606, endPage=614, ext={EN=ArticleExt(id=1320438437954572636, articleId=1320438437136683355, tenantId=1146029695717560320, journalId=1319373219989389464, language=EN, title=Optimization of personnel allocation in disease prevention and control institutions of China based on multi-objective genetic algorithm, columnId=1320427686514770171, journalTitle=Chinese Journal of Public Health, columnName=Survey and Report, runingTitle=null, highlight=null, articleAbstract=
Objective

To construct a demand-oriented fairness optimization model to provide decision-making support for scientific allocation in response to the shortage and regional inequity in personnel allocation in disease prevention and control institutions of China.

Methods

On the basis of the provincial panel data from 2006 to 2019, the entropy weight method was used to integrate the indicators of infectious disease dimension (morbidity/mortality of five key infectious diseases, such as plague and cholera) and population dimension (such as density, dependency ratio, and topographic relief) for building the regional priority index. The index was embedded into the population-weighted Gini coefficient function, and thus the improved fairness metrics was proposed. A multi-objective optimization model with the dual objectives of minimizing the fairness coefficient and minimizing the amount of personnel adjustment was established, and the nondominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) was used to solve the Pareto optimal solution sets.

Results

The priority index showed that Sichuan, Xinjiang, and Guangxi were the areas with high demand for disease prevention and control personnel. Through the Pareto frontier, 80 sets of optimal solutions were obtained, revealing a significant trade-off between fairness and implementation cost. The cost of maximizing fairness (reducing the Gini coefficient value by 0.066 8) was the largest adjustment amount (19 410 people). It was possible to only alleviate the fairness issue to a certain extent (reducing the Gini coefficient by 0.014 4) with the minimum adjustment amount (1 660 people).

Conclusions

This study innovatively incorporates the quantification of demand differences into the assessment of resource allocation fairness and employees a multi-objective genetic algorithm to generate the Pareto solution sets, providing a quantitative tool for differentiated personnel allocation strategies in disease prevention and control institutions.

, authors=Shengjie ZHANG1, Lieyu HUANG2, Fei MO2, Yan GUO2, authorsList=Shengjie ZHANG, Lieyu HUANG, Fei MO, Yan GUO, authorCompany=null, correspAuthors=Yan GUO, authorNote=null, correspAuthorsNote=
GUO Yan, E-mail:
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目的

针对当前全国疾病预防控制中心（简称“疾控”）人员配置存在的总量不足与区域不公问题，构建需求导向的公平性优化模型，为科学配置提供决策支持。

方法

基于2006—2019年省级面板数据，运用熵权法融合传染病维度（鼠疫、霍乱等五类重点传染病发病率/死亡率）与人口维度（密度、抚养比、地形起伏度等）指标，构建地区优先级指数；将其嵌入人口加权基尼系数函数，提出改进的公平性度量指标；建立以最小化公平性系数和最小化人员调整量为双目标的多目标优化模型，采用非支配排序遗传（NSGA-Ⅱ）算法求解帕累托最优解集。

结果

优先级指数显示四川省、新疆维吾尔自治区、广西壮族自治区等省（自治区、直辖市）为疾控人员高需求地区，通过帕累托前沿获得80组最优解，揭示公平性与实施成本的显著权衡关系，最大化公平性（基尼系数值降低0.066 8）的代价是更大的调整量（19 410人）；而最小化调整量（1 660人）仅一定程度缓解公平性问题（基尼系数值降低0.014 4）。

结论

本研究创新性地将需求差异量化纳入资源配置公平性评估，结合多目标遗传算法生成的帕累托解集，为差异化疾控人员配置策略提供量化工具。

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张圣捷（1994—），讲师，博士，研究方向：公共卫生应急管理

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郭岩，E-mail：
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注：图中的A、B、C三个点分别为80个点中的第1、40、80个点，代表三套优化方案；X值为优化目标一基尼系数值，Y值为优化目标二疾控人员配置的总调整量。

, figureFileSmall=Nkb7LyueN4Smj/o2CP8bTQ==, figureFileBig=krR9WJUjdzbD/u8tI7GGVA==, tableContent=null), ArticleFig(id=1320438474344354336, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=EN, label=Tab.1, caption=

Composition and weighting of the fairness index system for disease prevention and control personnel allocation

, figureFileSmall=null, figureFileBig=null, tableContent=
目标层权重二级指标三级指标指标属性权重
传染病维度0.927 2传染病发病率鼠疫发病率/（1/10万）正向0.206 3
霍乱发病率/（1/10万）正向0.122 8
病毒性肝炎发病率/（1/10万）正向0.013 6
艾滋病发病率/（1/10万）正向0.033 1
肺结核发病率/（1/10万）正向0.008 1
传染病死亡率鼠疫死亡率/（1/10万）正向0.275 5
霍乱死亡率/（1/10万）正向0.251 6
病毒性肝炎死亡率/（1/10万）正向0.031 6
艾滋病死亡率/（1/10万）正向0.040 5
肺结核死亡率/（1/10万）正向0.016 9
人口维度0.072 8集群效应人口密度/（人/km2）反向0.035 6
人口结构总抚养比正向0.103 1
乡村人口占比/%正向0.127 5
人口增长人口自然增长率/‰正向0.128 6
生活居住环境地形起伏度/m正向0.605 2
), ArticleFig(id=1320438474419851809, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=CN, label=表1, caption=

疾控人员配置公平性指标体系构成及权重

, figureFileSmall=null, figureFileBig=null, tableContent=
目标层权重二级指标三级指标指标属性权重
传染病维度0.927 2传染病发病率鼠疫发病率/（1/10万）正向0.206 3
霍乱发病率/（1/10万）正向0.122 8
病毒性肝炎发病率/（1/10万）正向0.013 6
艾滋病发病率/（1/10万）正向0.033 1
肺结核发病率/（1/10万）正向0.008 1
传染病死亡率鼠疫死亡率/（1/10万）正向0.275 5
霍乱死亡率/（1/10万）正向0.251 6
病毒性肝炎死亡率/（1/10万）正向0.031 6
艾滋病死亡率/（1/10万）正向0.040 5
肺结核死亡率/（1/10万）正向0.016 9
人口维度0.072 8集群效应人口密度/（人/km2）反向0.035 6
人口结构总抚养比正向0.103 1
乡村人口占比/%正向0.127 5
人口增长人口自然增长率/‰正向0.128 6
生活居住环境地形起伏度/m正向0.605 2
), ArticleFig(id=1320438474495349282, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=EN, label=Tab.2, caption=

Priority indices and rankings of provincial-level administrative regions

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省（自治区、直辖市）传染病维度
优先级指数		传染病维度
优先级排名		人口维度
优先级指数		人口维度
优先级排名		综合
优先级指数		综合
优先级排名
四川0.059 130.045 130.104 21
新疆0.059 420.034 960.094 32
广西0.066 910.023 9110.090 93
云南0.044 060.039 540.083 54
西藏0.011 9190.068 110.080 05
贵州0.045 940.031 370.077 16
青海0.020 2100.052 320.072 57
重庆0.044 750.024 6100.069 38
内蒙古0.028 370.018 9210.047 29
甘肃0.009 5250.035 450.044 910
湖南0.022 490.020 7150.043 011
宁夏0.008 5260.030 880.039 312
北京0.027 380.011 8260.039 113
河南0.017 2120.019 5190.036 814
陕西0.011 0210.025 590.036 515
江西0.016 0130.020 4160.036 316
广东0.019 0110.016 9240.035 917
海南0.015 6140.019 3200.034 918
湖北0.013 8160.020 4170.034 219
福建0.012 4180.021 8130.034 220
山西0.009 7240.023 3120.033 121
安徽0.011 3200.019 6180.030 922
浙江0.010 9220.017 9220.028 923
河北0.006 9290.021 8140.028 724
黑龙江0.014 0150.011 0280.025 125
辽宁0.013 6170.010 5290.024 126
山东0.007 0280.017 0230.024 127
吉林0.008 3270.013 0250.021 328
江苏0.006 7300.011 2270.017 929
上海0.009 7230.005 3310.015 130
天津0.006 4310.006 4300.012 931
), ArticleFig(id=1320438474575041059, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=CN, label=表2, caption=

各省优先级指数及优先级排名

, figureFileSmall=null, figureFileBig=null, tableContent=
省（自治区、直辖市）传染病维度
优先级指数		传染病维度
优先级排名		人口维度
优先级指数		人口维度
优先级排名		综合
优先级指数		综合
优先级排名
四川0.059 130.045 130.104 21
新疆0.059 420.034 960.094 32
广西0.066 910.023 9110.090 93
云南0.044 060.039 540.083 54
西藏0.011 9190.068 110.080 05
贵州0.045 940.031 370.077 16
青海0.020 2100.052 320.072 57
重庆0.044 750.024 6100.069 38
内蒙古0.028 370.018 9210.047 29
甘肃0.009 5250.035 450.044 910
湖南0.022 490.020 7150.043 011
宁夏0.008 5260.030 880.039 312
北京0.027 380.011 8260.039 113
河南0.017 2120.019 5190.036 814
陕西0.011 0210.025 590.036 515
江西0.016 0130.020 4160.036 316
广东0.019 0110.016 9240.035 917
海南0.015 6140.019 3200.034 918
湖北0.013 8160.020 4170.034 219
福建0.012 4180.021 8130.034 220
山西0.009 7240.023 3120.033 121
安徽0.011 3200.019 6180.030 922
浙江0.010 9220.017 9220.028 923
河北0.006 9290.021 8140.028 724
黑龙江0.014 0150.011 0280.025 125
辽宁0.013 6170.010 5290.024 126
山东0.007 0280.017 0230.024 127
吉林0.008 3270.013 0250.021 328
江苏0.006 7300.011 2270.017 929
上海0.009 7230.005 3310.015 130
天津0.006 4310.006 4300.012 931
), ArticleFig(id=1320438474667315748, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=EN, label=Tab.3, caption=

Comparison of Gini coefficients before and after optimization

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基尼系数类型基尼系数值与基线的基尼系数差
优化前最新一年、未经优先级指数调整的按人口加权基尼系数（基线）0.160 9—
优化前最新一年、经过优先级指数调整的按人口加权基尼系数0.155 0−0.005 9 ↓
优化后方案A、经过优先级指数调整的按人口加权基尼系数0.094 1−0.066 8 ↓
优化后方案B、经过优先级指数调整的按人口加权基尼系数0.108 2−0.052 7 ↓
优化后方案C、经过优先级指数调整的按人口加权基尼系数0.146 5−0.014 4 ↓
), ArticleFig(id=1320438475040608805, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=CN, label=表3, caption=

优化前后基尼系数对比

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基尼系数类型基尼系数值与基线的基尼系数差
优化前最新一年、未经优先级指数调整的按人口加权基尼系数（基线）0.160 9—
优化前最新一年、经过优先级指数调整的按人口加权基尼系数0.155 0−0.005 9 ↓
优化后方案A、经过优先级指数调整的按人口加权基尼系数0.094 1−0.066 8 ↓
优化后方案B、经过优先级指数调整的按人口加权基尼系数0.108 2−0.052 7 ↓
优化后方案C、经过优先级指数调整的按人口加权基尼系数0.146 5−0.014 4 ↓
), ArticleFig(id=1320438476697358886, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=EN, label=Tab.4, caption=

Adjustment amount of disease prevention and control personnel per 10 000 population in each provincial-level administrative region before and after optimization

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省（自治区、直辖市）优化前每万人
疾控人员数		优化后方案A
每万人疾控人员数		方案A调整
量/人		优化后方案B
每万人疾控人员数		方案B调整
量/人		优化后方案C
每万人疾控人员数		方案C调整
量/人
北京1.400 51.433 271.81.410 722.61.400 50.2
天津1.332 91.402 496.31.345 817.91.336 04.3
河北1.156 71.406 51 859.51.187 6230.11.164 457.3
山西1.193 31.411 0761.31.215 878.71.203 636.0
内蒙古2.262 12.263 02.22.267 813.82.277 236.2
辽宁1.403 31.418 565.01.413 543.61.410 329.9
吉林1.749 21.750 12.41.754 914.21.754 513.0
黑龙江1.723 81.727 211.11.728 013.71.727 913.3
上海1.233 81.388 5383.81.263 674.21.244 426.3
江苏0.967 51.257 82 458.61.161 11 639.60.982 1123.6
浙江0.939 31.221 11 796.51.153 71 366.80.953 087.3
安徽0.897 11.166 21 639.41.134 61 446.90.922 6155.3
福建1.017 41.322 61 262.61.071 8225.11.025 031.4
江西0.877 51.140 81 189.11.043 1747.40.881 116.3
山东0.922 91.199 82 798.41.156 92 364.80.927 849.5
河南1.632 81.633 24.01.637 142.61.637 546.5
湖北1.368 81.412 7259.61.379 462.21.371 314.2
湖南1.400 81.426 3169.31.409 659.11.404 121.9
广东0.803 01.043 93 008.61.040 32 962.40.822 9247.3
广西1.553 21.563 450.81.560 234.91.556 415.9
海南1.143 71.341 0196.31.186 242.31.178 034.1
重庆0.913 71.187 9873.81.046 9424.30.971 9185.5
四川1.618 11.621 730.11.628 283.51.651 6278.9
贵州1.383 31.472 2341.71.396 851.91.388 620.0
云南1.833 91.835 57.51.836 914.11.835 99.4
西藏2.964 02.975 74.22.978 05.12.973 13.3
陕西1.507 41.518 644.21.524 165.91.524 366.7
甘肃1.870 51.871 83.31.878 319.81.877 918.6
青海2.532 22.537 02.82.537 73.22.533 80.9
宁夏1.666 71.687 815.11.679 59.21.672 64.3
新疆2.117 22.117 81.32.122 012.32.122 012.0
总调整量——19 410.5—12 192.0—1 659.9
), ArticleFig(id=1320438476890296871, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1320438437136683355, language=CN, label=表4, caption=

优化前后的各省份每万人疾控人员数调整量（人/万人）

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省（自治区、直辖市）优化前每万人
疾控人员数		优化后方案A
每万人疾控人员数		方案A调整
量/人		优化后方案B
每万人疾控人员数		方案B调整
量/人		优化后方案C
每万人疾控人员数		方案C调整
量/人
北京1.400 51.433 271.81.410 722.61.400 50.2
天津1.332 91.402 496.31.345 817.91.336 04.3
河北1.156 71.406 51 859.51.187 6230.11.164 457.3
山西1.193 31.411 0761.31.215 878.71.203 636.0
内蒙古2.262 12.263 02.22.267 813.82.277 236.2
辽宁1.403 31.418 565.01.413 543.61.410 329.9
吉林1.749 21.750 12.41.754 914.21.754 513.0
黑龙江1.723 81.727 211.11.728 013.71.727 913.3
上海1.233 81.388 5383.81.263 674.21.244 426.3
江苏0.967 51.257 82 458.61.161 11 639.60.982 1123.6
浙江0.939 31.221 11 796.51.153 71 366.80.953 087.3
安徽0.897 11.166 21 639.41.134 61 446.90.922 6155.3
福建1.017 41.322 61 262.61.071 8225.11.025 031.4
江西0.877 51.140 81 189.11.043 1747.40.881 116.3
山东0.922 91.199 82 798.41.156 92 364.80.927 849.5
河南1.632 81.633 24.01.637 142.61.637 546.5
湖北1.368 81.412 7259.61.379 462.21.371 314.2
湖南1.400 81.426 3169.31.409 659.11.404 121.9
广东0.803 01.043 93 008.61.040 32 962.40.822 9247.3
广西1.553 21.563 450.81.560 234.91.556 415.9
海南1.143 71.341 0196.31.186 242.31.178 034.1
重庆0.913 71.187 9873.81.046 9424.30.971 9185.5
四川1.618 11.621 730.11.628 283.51.651 6278.9
贵州1.383 31.472 2341.71.396 851.91.388 620.0
云南1.833 91.835 57.51.836 914.11.835 99.4
西藏2.964 02.975 74.22.978 05.12.973 13.3
陕西1.507 41.518 644.21.524 165.91.524 366.7
甘肃1.870 51.871 83.31.878 319.81.877 918.6
青海2.532 22.537 02.82.537 73.22.533 80.9
宁夏1.666 71.687 815.11.679 59.21.672 64.3
新疆2.117 22.117 81.32.122 012.32.122 012.0
总调整量——19 410.5—12 192.0—1 659.9
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中国疾控机构人员配置优化分析：基于多目标遗传算法
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张圣捷 1 , 黄烈雨 2 , 莫非 2 , 郭岩 2, *, *
中国公共卫生 | 调查报告与分析 2026,42(5): 606-614
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中国公共卫生 |调查报告与分析 2026 , 42 (5) : 606 -614
中国疾控机构人员配置优化分析：基于多目标遗传算法
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张圣捷1, 黄烈雨2, 莫非2, 郭岩2, *, *
作者信息
  • 1中共中央党校（国家行政学院）应急管理研究院公共卫生应急管理教研室，北京 100091
  • 2中国疾病预防控制中心，北京 102206
通讯作者:
郭岩，E-mail：
作者简介:

张圣捷（1994—），讲师，博士，研究方向：公共卫生应急管理

Optimization of personnel allocation in disease prevention and control institutions of China based on multi-objective genetic algorithm
Shengjie ZHANG1, Lieyu HUANG2, Fei MO2, Yan GUO2
Affiliations
  • 1Department of Public Health Emergency Management, Institute of Emergency Management, Party School of the CPC Central Committee (National Academy of Governance), Beijing 100091, China
  • 2Chinese Center for Disease Control and Prevention, Beijing 102206, China
    • Corresponding Author:
    GUO Yan, E-mail:
出版时间: 2026-05-10 doi: 10.11847/zgggws1148341
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摘要
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目的

针对当前全国疾病预防控制中心（简称“疾控”）人员配置存在的总量不足与区域不公问题，构建需求导向的公平性优化模型，为科学配置提供决策支持。

方法

基于2006—2019年省级面板数据，运用熵权法融合传染病维度（鼠疫、霍乱等五类重点传染病发病率/死亡率）与人口维度（密度、抚养比、地形起伏度等）指标，构建地区优先级指数；将其嵌入人口加权基尼系数函数，提出改进的公平性度量指标；建立以最小化公平性系数和最小化人员调整量为双目标的多目标优化模型，采用非支配排序遗传（NSGA-Ⅱ）算法求解帕累托最优解集。

结果

优先级指数显示四川省、新疆维吾尔自治区、广西壮族自治区等省（自治区、直辖市）为疾控人员高需求地区，通过帕累托前沿获得80组最优解，揭示公平性与实施成本的显著权衡关系，最大化公平性（基尼系数值降低0.066 8）的代价是更大的调整量（19 410人）；而最小化调整量（1 660人）仅一定程度缓解公平性问题（基尼系数值降低0.014 4）。

结论

本研究创新性地将需求差异量化纳入资源配置公平性评估，结合多目标遗传算法生成的帕累托解集，为差异化疾控人员配置策略提供量化工具。

疾病预防控制机构  /  人员配置  /  多目标优化
Objective

To construct a demand-oriented fairness optimization model to provide decision-making support for scientific allocation in response to the shortage and regional inequity in personnel allocation in disease prevention and control institutions of China.

Methods

On the basis of the provincial panel data from 2006 to 2019, the entropy weight method was used to integrate the indicators of infectious disease dimension (morbidity/mortality of five key infectious diseases, such as plague and cholera) and population dimension (such as density, dependency ratio, and topographic relief) for building the regional priority index. The index was embedded into the population-weighted Gini coefficient function, and thus the improved fairness metrics was proposed. A multi-objective optimization model with the dual objectives of minimizing the fairness coefficient and minimizing the amount of personnel adjustment was established, and the nondominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) was used to solve the Pareto optimal solution sets.

Results

The priority index showed that Sichuan, Xinjiang, and Guangxi were the areas with high demand for disease prevention and control personnel. Through the Pareto frontier, 80 sets of optimal solutions were obtained, revealing a significant trade-off between fairness and implementation cost. The cost of maximizing fairness (reducing the Gini coefficient value by 0.066 8) was the largest adjustment amount (19 410 people). It was possible to only alleviate the fairness issue to a certain extent (reducing the Gini coefficient by 0.014 4) with the minimum adjustment amount (1 660 people).

Conclusions

This study innovatively incorporates the quantification of demand differences into the assessment of resource allocation fairness and employees a multi-objective genetic algorithm to generate the Pareto solution sets, providing a quantitative tool for differentiated personnel allocation strategies in disease prevention and control institutions.

disease prevention and control institutions  /  personnel allocation  /  multi-objective optimization
张圣捷, 黄烈雨, 莫非, 郭岩. 中国疾控机构人员配置优化分析：基于多目标遗传算法. 中国公共卫生, 2026 , 42 (5) : 606 -614 . DOI: 10.11847/zgggws1148341
Shengjie ZHANG, Lieyu HUANG, Fei MO, Yan GUO. Optimization of personnel allocation in disease prevention and control institutions of China based on multi-objective genetic algorithm[J]. Chinese Journal of Public Health, 2026 , 42 (5) : 606 -614 . DOI: 10.11847/zgggws1148341
正文
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疾病预防控制（以下简称“疾控”）体系是公共卫生服务体系的重要组成部分[1–3]。疾控人员配置优化的意义在于更有效地完成疾控岗位分配，更好地满足疾病防控的需求，以提高疾病防控的效率和效果，从而有效降低疾病的传播和发病率。根据2014年中央编办、财政部、国家卫生计生委《关于印发疾病预防控制中心机构编制标准指导意见》提出的按照常住人口万分之1.75的比例核定疾控人员数量，地域面积在50万平方公里以上且人口密度<25人/平方千米的省（自治区、直辖市），可按照不高于本地区常住人口万分之3的比例核定[4]。根据中国卫生统计年鉴，截至2019年，全国疾控人员总数仅为常住人口的万分之1.33，距离国家要求的标准有一定提升空间；虽然经过近几年疾控体系改革，全国疾控队伍人员数量已有较大提升，但是整体来说距离万分之1.75的比例仍有差距，无法满足日益增长且复杂多变的公共卫生防控需求[5]。从省级层面来看，各地实际情况也有所不同[6]。在政府财政资源有限的情况下，如何科学决策，在兼顾公平性的情况下依据每省的实际需求找到最需要补充的人员数量是值得研究的问题。已有研究主要使用传统基尼系数度量公平维度[7–8]，从基尼系数本身计算过程来看，所反映的是平等理念，即个体相等时基尼系数最小，但所谓的平等并不一定意味着公平。传统基尼系数对地区间公平性考虑不够全面，采用传统基尼系数进行优化研究无法实现基于差异化需求的测量。为解决这一问题，本研究在传统基尼系数函数的基础上引入客观赋权法得出的权重，考虑到偏远、高传染病风险地区的客观需求，更具公平性视角。具体如何达成优化目标等方法报告如下。
1　资料与方法
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1.1　数据来源
本研究数据来源于《中国卫生统计年鉴》、《中国统计年鉴》、各省份统计年鉴以及相关统计公报。由于传染病报告情况受新冠病毒感染疫情影响较之前有明显变化，因此，本研究将研究时间范围设置为2006—2019年。测度范围包括2006—2019年中国大陆的31个省（自治区、直辖市）。需要说明的是，传染病维度将致死率高、社会影响巨大的传染病纳入指标体系，分别是鼠疫、霍乱、病毒性肝炎、艾滋病、肺结核。人口维度中总人口是指年末常住人口数，地理起伏度变量来自封志明等[9]《中国地形起伏度及其与人口分布的相关性》。对于极个别缺失数据点，本研究使用相邻年份数据线性内插法以填补缺失数据，此外对于异常数据，使用相邻年份数据平均值进行平滑处理[10]。
1.2　方法
1.2.1　基于熵权法构建疾控人员配置公平性指标体系
2014年中央编办印发《中央编办财政部国家卫生计生委关于印发疾病预防控制中心机构编制标准指导意见的通知》（中央编办发〔2014〕2号），明确提出传染病因素和人口因素是人员配置的重要影响因素。故本研究从传染病维度和人口维度构建人员配置公平性指标体系，用来分析各地区传染病风险程度、人口经济水平，并为后续面向地区差异化的优先级设计提供较为客观的评价信息。疾控人员配置公平性指标体系的目标层和指标层设置见图1。人口维度则关注社会结构因素，传染病维度聚焦疾病本身的风险特征，包含鼠疫、霍乱、病毒性肝炎、艾滋病和肺结核5种重点传染病的发病率和死亡率，直接反映区域疾病负担与传播风险。五种传染病的发病率和死亡率越高，表示该地区的传染病风险程度越高，对疾控人员配置的需求度更高。因此，5种传染病的发病率和死亡率指标均为正向指标。选择这5种典型传染病是因为鼠疫和霍乱是法定最高等级的甲类传染病，具有暴发性传播与高致死风险；而艾滋病、病毒性肝炎及肺结核虽属乙类传染病，却因慢性化特征对社会和家庭产生深层影响，这些疾病依赖疾控系统承担患者随访、用药督导和耐药监测等长期管理任务，防止治疗中断导致的公共卫生危机[11–12]。目标层中人口维度选取人口密度、总抚养比、乡村人口占比、人口自然增长率和地形起伏度5个具体指标。其中人口密度是指在单位土地面积内的人口数量，反映地区人口的集群效应。人口密度越低，表示该地区对疾控人员配置的需求度越高。因此，该指标为负向指标。总抚养比和乡村人口占比表征地区人口结构。人口自然增长率是指一段时间内人口的自然增长数量与该时间段内的平均人口数量的比值，反映地区人口自然增长的趋势和速度，衡量人口增长状况。地形起伏度是指在指定区域内的最低点与最高点的海拔高度差，可以宏观地描述一个区域的地形特征，反映地区生活居住环境状况。总抚养比越高、乡村人口占比越高、人口自然增长率越高、地形起伏度越大，表示该地区对疾控人员配置的需求度越高。因此，这四项指标均为正向指标。指标体系权重确定的方法为客观赋权法中的熵权法，即根据指标离散程度确定各个指标对各地区疾控人员配置公平性的影响程度，所得到的权重客观性更强，精确性更高[13–17]。
1.2.2　按人口加权的基尼系数和基于优先级指数的基尼系数计算
如果将每个“省（自治区、直辖市）”视为相同个体，不进行按人口的加权，将会对基尼系数结果产生偏误[18]。更合理的做法是将“省”看作所辖人口的集合，人口越多的省在计算基尼系数时给予更大权重，此时得到的全国基尼系数更具代表性。人口加权后基尼系数计算方法为：设$n$为省份总数量，${m_i}$表示第$i$个省份的年末常住人口数（万人）。将各省份每万人疾控人员数按人口加权后，可以得到包含${m_i}$个${x_i}$（$i = 1, \ldots ,n$）的人口加权样本值集合$ \mathbb{Y} $，表示为：
$ \mathbb{Y} = \left\{ \begin{gathered} \underbrace {{x_1}, \ldots ,{x_1}}_{{m_1}},\underbrace {{x_2}, \ldots ,{x_2}}_{{m_2}}, \ldots ,\underbrace {{x_n}, \ldots ,{x_n}}_{{m_n}}\, \end{gathered} \right\} $
其中，人口加权样本值集合$ \mathbb{Y} $中共有${n_Y} = \displaystyle\sum\nolimits_{i = 1}^n {{m_i}} $项样本数据。接着使用基尼系数的直接计算法，则按人口加权的基尼系数${G_p}$可以表示为：
$ {G_p} = \frac{1}{{2n_Y^2\bar y}}\sum\limits_{k = 1}^{{n_Y}} {\sum\limits_{l = 1}^{{n_Y}} {\left| {{y_k} - {y_l}} \right|} } $
$ \bar y = \frac{1}{{{n_Y}}}\sum\limits_{k = 1}^{{n_Y}} {{y_k}} $
其中，${n_Y}$是人口加权样本值集合$ \mathbb{Y} $中的样本量，${y_k},{y_l} \in \mathbb{Y}$，$\left| {{y_k} - {y_l}} \right|$表示任意两项样本值之差的模值，$ \bar y $表示人口加权样本值集合$ \mathbb{Y} $中所有样本值的均值。
基于疾控人员配置公平性指标权重，各地区传染病维度优先级指数$ \gamma _i^D $和人口维度优先级指数$ \gamma _i^P $分别为传染病和人口维度所有三级指标标准化后的数值与对应权重的乘积之和再乘以该维度的目标层权重，可以表示为：
$ \gamma _i^D = {\omega ^D}\sum\nolimits_{j = 1}^{10} {{\omega _j}{\alpha _{ij}}} $
$ \gamma _i^P = {\omega ^P}\sum\nolimits_{j = 1}^5 {{\omega _j}{\alpha _{ij}}} $
其中，$ {\omega ^D} $和$ {\omega ^P} $分别为传染病和人口维度目标层权重，$ {\omega _j} $为对应的三级指标权重，$ {\alpha _{ij}} $为第$ i $个省份的第$ j $个指标值。综合传染病维度和人口维度，面向地区差异化的综合优先级指数${\gamma _i}$为二者之和，可以表示为：
$ {\gamma _i} = \gamma _i^D + \gamma _i^P $
因此，在按人口加权的基尼系数基础上，可以进一步将第$i$个省份的每万人疾控人员数${x_i}$（$i = 1, \ldots ,n$）基于优先级指数进行调整。基于优先级指数调整后的每万人疾控人员数${\tilde x_i}$可表示为：
$ {\tilde x_i} = \frac{1}{{1 + {\gamma _i}}}{x_i},\quad \left( {i = 1, \ldots ,n} \right) $
将基于优先级指数调整后的每万人疾控人员数${\tilde x_i}$作为基尼系数中的样本值，同样使用${m_i}$表示第$i$个省份的年末常住人口数（万人），则将各省份基于优先级指数调整后的每万人疾控人员数${\tilde x_i}$按人口加权后，可以得到包含${m_i}$个${\tilde x_i}$（$i = 1, \ldots ,n$）的人口加权样本值集合$ \mathcal{Z} $，可以表示为：
$ \mathcal{Z} = \left\{ \begin{gathered} \,\underbrace {{{\tilde x}_1}, \ldots ,{{\tilde x}_1}}_{{m_1}},\underbrace {{{\tilde x}_2}, \ldots ,{{\tilde x}_2}}_{{m_2}}, \ldots ,\underbrace {{{\tilde x}_n}, \ldots ,{{\tilde x}_n}}_{{m_n}}\, \end{gathered} \right\} $
其中，人口加权样本值集合$ \mathcal{Z} $中共有${n_Z} = \displaystyle\sum\nolimits_{i = 1}^n {{m_i}} $项样本数据。接着使用基尼系数的直接计算法，则基于优先级指数的按人口加权基尼系数${G_\gamma }$可以表示为：
$ {G_\gamma } = \frac{1}{{2n_Z^2\bar z}}\sum\limits_{k = 1}^{{n_Z}} {\sum\limits_{l = 1}^{{n_Z}} {\left| {{z_k} - {z_l}} \right|} } $
$ \bar z = \frac{1}{{{n_Z}}}\sum\limits_{k = 1}^{{n_Z}} {{z_k}} $
其中，${n_Z}$是人口加权样本值集合$ \mathcal{Z} $中的样本量，$ {z_k},{z_l} \in \mathcal{Z} $，$\left| {{z_k} - {z_l}} \right|$表示任意两项样本值之差的模值，$ \bar z $表示人口加权样本值集合$ \mathcal{Z} $中所有样本值的均值。
1.2.3　基于多目标遗传算法的疾控人员配置优化
传统优化方法在求解时需要先将多目标优化问题转化为单目标优化问题，一般每次只能得到一个解[19–21]。与传统优化方法不同，智能优化算法可针对更普适、更复杂的多极值问题，通过进化迭代自适应学习，根据问题的特征以不同方式编码，进行全局优化搜索，获得更加可靠、稳定的结果。同时在解决多目标优化问题时，能够求得帕累托最优解集，展示出多个冲突目标之间的权衡。遗传算法是目前最为成熟的智能优化算法之一，在多目标优化领域得到了广泛应用[22]。本文所采用的非支配排序遗传（Non-dominated Sorting Genetic Algorithm Ⅱ, NSGA-Ⅱ）算法是对传统遗传算法的改进与提升[23]。对疾控人员配置优化问题主要考虑以下2项目标：一是要通过最小化基于优先级指数的按人口加权基尼系数${G_\gamma }$，来实现各地区之间综合考虑传染病维度和人口维度的疾控人员配置公平性。二是要通过最小化所有地区疾控人员配置的总调整量$D$，让方案更具现实可操作性，在资源有限的情况下以适应需求，使得疾控人员的优化配置更具实际意义。考虑到当前每万人疾控人员数还远未达到国家要求，本研究优化问题中的疾控人员优化配置为增量配置，即各地区优化后的每万人疾控人员数需大于优化前的每万人疾控人员数：$ {x_i} \geqslant {\hat x_i} $，$ \left( {i = 1, \ldots ,n} \right) $；考虑到各地区对疾控人员优化配置的实际调整具有平稳性，优化配置对各地区每万人疾控人员数的调整幅度（调整量占原数值的比例）$ {\lambda _i} $需不超过设定比例上限$ {\lambda ^{{\text{ub}}}} $，即：$ 0 \leqslant {\lambda _i} \leqslant {\lambda ^{{\text{ub}}}} $，$ \left( {i = 1, \ldots ,n} \right) $。
综上，构建优化变量为各省份每万人疾控人员数${x_i}$（$i = 1, \ldots ,n$）的疾控人员配置多目标优化模型可以表示为：
$\left\{ \begin{array}{l}\;\;\min {G_\gamma } = \dfrac{1}{{2n_Z^2\bar z}}\displaystyle\sum\limits_{k = 1}^{{n_Z}} {\displaystyle\sum\limits_{l = 1}^{{n_Z}} {\left| {{z_k} - {z_l}} \right|} } \\\;\;\min D = \displaystyle\sum\limits_{i = 1}^n {\left( {{x_i} - {{\hat x}_i}} \right)} \end{array} \right.$
$ \begin{aligned} {\text{s}}{\text{.t}}{\text{.}}\quad \quad \quad \quad \;{x_i} \geqslant {{\hat x}_i},\quad \quad \quad \quad \left( {i = 1, \ldots ,n} \right) & \\ \quad \quad \quad \quad \;\;0 \leqslant {\lambda _i} \leqslant {\lambda ^{{\text{ub}}}},\quad \quad \;\;\left( {i = 1, \ldots ,n} \right) & \\ \end{aligned} $
该模型中，以最小化基于优先级指数的按人口加权基尼系数来提高地区间疾控人员配置的公平性。该基尼系数越小，表示各地区经优先级指数调整后的每万人疾控人员数的差异越小，公平性越好；以最小化所有地区疾控人员配置的总调整量来保证方案的现实可操作性，能够在资源有限的情况下以适应需求。该数值越小，表示各地区在原配置方案上所需要做出的调整越小，越具有实际可操作性。本研究所设计的疾控人员配置多目标优化模型，采用NSGA-Ⅱ算法进行求解，该算法的基本流程见图2。
该多目标遗传算法中需要设定的运行参数[23]主要包括：（1） 种群规模。群体大小表示群体中所含个体的数量，取值较小可提高运算速度，但是会降低种群的多样性，出现提前收敛；而取值较大会使算法效率降低。本研究种群规模设置为200。（2）交叉概率。交叉操作是遗传算法中产生新个体的主要方法，取值过小产生新个体速度较慢；但若取值过大会破坏种群中的优良模式，不利于算法收敛。本研究交叉概率设置为0.8。（3）变异概率。变异概率直接影响算法的搜索和收敛性能，取值较大可产生出较多新个体，提高算法搜索能力，但降低收敛性能；取值较小可使算法更易收敛，但产生新个体的能力和算法搜索能力较差。本研究变异概率设置为0.01。（4）最大遗传代数。最大遗传代数是表示算法运行结束条件的重要参数。本研究最大遗传代数设置为2 000。（5）帕累托集比例。帕累托集比例为帕累托前沿上个体在种群中所占的比例。本研究帕累托集比例设置为0.4，按种群规模为200计算，帕累托前沿上保留的个体数目为80。此外，本研究中的选择策略使用锦标赛选择（tournament selection）策略[24]，函数容差设置为10−6。
1.3　统计分析
本研究数据处理与分析综合运用了Microsoft Excel和MATLAB软件，以完成不同阶段的计算与建模求解任务。对于指标体系权重构建和优先级指数计算部分，采用 Microsoft Excel（Version: Office LTSC 2021）完成基础数据的整理、标准化处理，基于熵权法构建了目标层及各项三级指标的权重，并计算优先级指数及排名。对于多目标优化问题建模和求解部分，采用 MATLAB R2021b（The MathWorks, Inc.）平台，基于优化工具箱（Optimization Toolbox，Version 9.1）和可视化优化工具“优化实时编辑器任务（Optimize Live Editor Task）”，使用gamultiobj求解器进行建模与求解。该算法旨在同时优化基于优先级指数的按人口加权基尼系数（最小化）和所有地区疾控人员配置的总调整量（最小化）两个目标函数，从而获得一组帕累托最优的疾控人员优化配置解决方案。
2　结　果
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2.1　疾控人员配置公平性指标体系构成及权重（表1）
将2006—2019年31个省份的各项指标数据代入，根据上述熵权法的具体步骤，计算得出目标层权重以及各项三级指标权重值。
2.2　各省优先级指数及优先级排名（表2）
将2019年31个省（自治区、直辖市）的各项指标数据代入优先级指数$ \gamma _i^D $、$ \gamma _i^P $和${\gamma _i}$的计算公式，得到当前各地区的优先级指数。优先级指数越大的地区，优先级排名越高，表示该地区对疾控人员配置的需求度越高。
2.3　多目标遗传算法求解
基于以上数据、模型和运行参数对疾控人员配置多目标优化模型进行求解。需要说明的是，由于算法的初始种群是随机产生的。因此，每次运行的结果存在一定差异，本文展示的模型求解结果是一次运行得到的结果。遗传算法中的平均距离指的是一个种群内解之间相似性的度量，计算方式为每个解与其最相邻解之间的平均欧式距离。通过观察个体间平均距离，可以评估优化过程的收敛性。本研究中，算法能够在迭代初期迅速收敛，随着遗传代数迭代至2000代，个体间平均距离的散点分布逐渐在0.3附近趋于稳定。平均帕累托散布是用来衡量由多目标优化算法生成的一组解决方案分布均匀程度的一个重要指标。平均帕累托散布越小，解的分布越均匀，解集越多样化。本研究中，随着算法遗传代数迭代至2000代，平均帕累托散布的散点分布逐渐降低并趋于稳定，最终的平均帕累托散布值约为0.15，表明算法所得出的解集具有良好的多样性。
在多目标优化中，帕累托前沿（Pareto Front）为不受任何其他解决方案支配的最优解集的图形展示，可以清晰直观展示出每个解决方案相对于多个目标的相对性能以及不同目标之间的权衡，是在多目标优化问题中做出冲突目标之间最理想权衡的重要工具。针对本研究的多目标优化问题，帕累托前沿如图3所示，二维图中的每一个点表示一个解决方案。其中横轴的优化目标一是指最小化基于优先级指数的按人口加权基尼系数，纵轴的优化目标二是指最小化所有地区疾控人员配置的总调整量。从图中可以看出这两项优化目标之间是存在冲突的，与多目标优化定义符合。从图中还可以看出，帕累托前沿上的最优解分布较为均匀，80个点展示出本研究多目标优化问题在循环迭代2 000次之后的帕累托最优解集。
2.4　优化前后基尼系数对比（表3）
在多目标优化中，很难确定单一的“最佳”解决方案，因为多个目标经常相互冲突。帕累托前沿代表了非支配解的集合，其中任何解决方案都能在不剥夺另一个目标的情况下改善当前目标。因此，评估哪种帕累托解决方案更好取决于特定环境以及决策者偏好。为便于结果说明和方案分析，本文选取图3中帕累托前沿面80个点中比较具有特征的A、B、C三个点进行分析。依据前文的计算和上述求解结果，疾控人员配置优化前后的基尼系数如表3所示。将优化前未经优先级指数调整的按人口加权基尼系数作为基线，可以看出，优化前经过优先级指数调整的按人口加权基尼系数有小幅的降低，这说明本研究构建和设计的疾控人员配置公平性指标体系和优先级指数，通过使用综合优先级指数对每万人疾控人员数进行调整，可以一定程度上降低基尼系数，提高地区间疾控人员配置的公平性。多目标优化后的三种方案均得到了更低的基尼系数，有效地提高了地区间疾控人员配置的公平性。其中，优化方案A的基尼系数下降得最为明显，说明优化方案A是地区间公平性相对更好的优化配置方案。优化方案B下降的基尼系数差。其次，优化方案C下降的基尼系数差最小。
2.5　优化前后的各省份每万人疾控人员数调整量（表4）
各省份在三种优化方案下的每万人疾控人员数及相应的调整量如表4所示。相比于疾控人员配置优化前最新一年的每万人疾控人员数，三种优化方案中，优化方案A的总调整量最大，优化方案B的总调整量次之，优化方案C的总调整量最小。
3　讨　论
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以往人力资源配置公平性的研究主要依赖传统基尼系数[25]、泰尔指数[26]、集中指数[8]衡量人口或地理维度的平等性。本研究通过构建各地区疾控人员配置公平性指标体系，设计面向地区差异化的优先级指数以体现传染病风险程度和人口特点，在使用按人口加权基尼系数的同时，将优先级放入基尼系数函数中，对基尼函数进行改进，使得疾控人数的优化配置向传染病风险高、人口密度低、工作开展难度大的地区予以倾斜，提升了客观性和公平性。又进一步基于多目标遗传算法进行疾控人员配置优化，得出具有现实可操作性的帕累托最优解决方案。
将基于熵权法、融合多维需求的优先级指数嵌入基尼系数计算，是本研究的方法创新。通过表2中各地区优先级指数可以看出传染病维度排名较为靠前的省（自治区、直辖市）包括广西、新疆、四川、贵州、重庆、云南、内蒙古；人口维度优先级指数较大、排名较为靠前的包括西藏、青海、四川、云南、甘肃、新疆、贵州等省（自治区、直辖市），表明这些省份人口维度下居民居住较为分散，地形地势海拔变化大。综合传染病维度和人口维度，可以得出综合优先级指数较大、排名较为靠前的省（自治区、直辖市）包括四川、青海、西藏、新疆、河南、云南、重庆等，表明这些省份对疾控人员配置的需求度相对更高。由此可见，优先级指数显著拓展了公平性内涵，使优化结果更倾向于传染病高发、人口稀疏、自然环境恶劣的高需求地区。
针对疾控人员配置这一涉及31个连续决策变量、非线性目标、复杂约束的优化问题，人工智能NSGA-Ⅱ算法展现出显著优势，为领域前沿。从优化前后基尼系数的对比结果来看，表3和表4中三种优化方案各有优势和劣势。三种方案中，优化方案A能够得到最低的基尼系数，最大程度提高地区间疾控人员配置的公平性，不过所需要做出的总调整量也是最大的，意味着该方案实施难度最大；优化方案C所需要做出的总调整量最小，意味着该方案最易于实施，但其所能够降低的基尼系数最小，对地区间公平性的提升较为有限；优化方案B则是二者的折中方案，需要做出的总调整量和对公平性提升的贡献均较为适中。
优化方案A、B、C只是对应为便于结果说明所选取的三个帕累托最优解，实际上本次模型求解所得出的帕累托前沿面上的所有点均对应一套最优方案，具体选择哪一点上的人员配置方案需要依据现实情况分类讨论。若想最大化公平性，则选择靠近纵轴的点，代价是会增加调整幅度，政府短时间内可能难以满足这样的人员配置方案。现阶段若想用最小的调整量一定程度缓解公平性问题，则尽可能选择靠近横轴的点。而如果想短时间内提升疾控服务的公平性，且财政保障能力允许，则尽可能选择靠近纵轴的点。在现有约束和目标函数下，实现“极高公平性”（基尼系数<0.09）所需的调整量会非线性地急剧增加，边际成本递增，而实现“基本可接受公平性”（基尼系数0.14～0.15）的调整成本则相对可控。这与资源配置问题中常见的“效率边界”特征相符。
疾控人员配置优化的目标不仅仅包含公平性和最小化调整幅度，还包括如配置效率最大化等，但现阶段人员配置的效率难以定义并进行量化，尚不具备纳入模型的条件，未来条件成熟后有必要加以研究。基于本研究结果，建议国家及省级在核定和调整疾控编制时，应突破单一人口比例限制，建立综合考虑传染病负担、人口密度、地理环境等多维需求的动态配置标准，对四川、青海、西藏、新疆、云南等省（自治区、直辖市）高优先级地区给予重点倾斜。

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2026年第42卷第5期
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doi: 10.11847/zgggws1148341
  • 接收时间：2025-06-27
  • 首发时间：2026-10-23
  • 出版时间：2026-05-10
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  • 收稿日期：2025-06-27
  • 修回日期：2025-08-14
  • 录用日期：2025-10-17
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    1中共中央党校（国家行政学院）应急管理研究院公共卫生应急管理教研室，北京 100091
    2中国疾病预防控制中心，北京 102206

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郭岩，E-mail：
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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