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Article(id=1240726761038737749, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1240722566957027366, articleNumber=null, orderNo=null, doi=10.20043/j.cnki.MPM.202504517, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1745683200000, receivedDateStr=2025-04-27, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773741911420, onlineDateStr=2026-03-17, pubDate=1760025600000, pubDateStr=2025-10-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773741911420, onlineIssueDateStr=2026-03-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773741911420, creator=13701087609, updateTime=1773741911420, updator=13701087609, issue=Issue{id=1240722566957027366, tenantId=1146029695717560320, journalId=1227665162245664772, year='2025', volume='52', issue='19', pageStart='3457', pageEnd='3648', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=0, createTime=1773740911472, creator=13701087609, updateTime=1773740981732, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1240722861736906836, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1240722566957027366, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1240722861736906837, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1240722566957027366, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=3490, endPage=3495, ext={EN=ArticleExt(id=1240726761248452951, articleId=1240726761038737749, tenantId=1146029695717560320, journalId=1227665162245664772, language=EN, title=Python-enabled development and implementation of a prediction and early warning model for vector-borne infectious diseases, columnId=1240413921954295836, journalTitle=Modern Preventive Medicine, columnName=Epidemiology and Statistical Methods, runingTitle=null, highlight=null, articleAbstract=

Objective Based on the Python platform, the entire process of vector-borne infectious disease mathematical models is expanded to better fit models and evaluate intervention effects, to provide new ideas for grassroots prevention and control, and to open up new perspectives. Methods The SmEmIm-SpEpIpApRp model was fitted using the lmfit library, solved with the solve_ivp function, and sensitivity analysis of key model parameters was performed. The Rt calculation was based on the next generation matrix method, and all results were visually displayed with the help of Matplotlib. Results The results showed that R2=0.98 and RMSE=2.07. Rt was 5.607 in the early stage of the epidemic, and Rtpeak was 8.439 on day 41. The period with Rt>1 lasted 81 days, and q had the highest sensitivity (S=35.435). Under a single intervention, when βmp and βpm<0.01, Rt<1 and the epidemic disappeared. Controlling only γ and q would not eliminate the epidemic. Under comprehensive intervention, Scenario 1 could reduce the cumulative cases by 98.64%, and Rtpeak=0.868. Scenario 2 could reduce the cumulative cases by 87.95%,and Rtpeak=1.988. For Scenario 3, Rtpeak=4.78. Although the increase in Rt was smaller and the change rate was low, the longer duration could increase cumulative cases by 161.47%. Scenario 4 could reduce the cumulative cases by 99.38%, and Rtpeak=0.28. Conclusions The high goodness of fit of the model based on the Python platform verifies the necessity of seasonal dynamic modeling, provides an integrated solution for the prevention and control of vector-borne infectious diseases, expands the practical boundaries of theoretical models, and opens a new perspective for precise prevention and control at the grassroots level.

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目的 基于Python平台，对媒介传染病数学模型全流程进行拓展，以期更好拟合模型并评估干预效果，为基层防控提供新思路，打开新视角。方法 对SmEmIm-SpEpIpApRp模型采用lmfit库拟合，采用solve_ivp函数求解，对模型关键参数进行敏感性分析，Rt计算依据下一代矩阵法，所有结果借助Matplotlib进行可视化展示。结果 结果显示R2=0.98，RMSE=2.07，疫情初期Rt=5.607，第41 d达到Rtpeak=8.439，Rt>1的疫情持续期为81 d，q的敏感度最高（S= 35.435），单一干预措施下βmp、βpm<0.01时，Rt<1，疫情消失；仅控制γ、q疫情并不会消失；综合干预下场景1可使累积病例减少98.64%，Rtpeak=0.868；场景2可使累积病例下降87.95%，Rtpeak=1.988；场景3的Rtpeak=4.78，Rt上升幅度较小，变化速率低，但持续时间更长，可使累积病例上升161.47%；场景4可使累积病例减少99.38%，Rtpeak=0.28。结论 基于Python平台的模型高拟合优度验证了季节性动态建模的必要性，为媒介传染病防控提供了“数据-模型-决策”的一体化解决方案，拓展了理论模型的实践边界，也为基层精准防控打开了新视角。

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李锐，E-mail:
, copyrightStatement=本刊刊出的所有文章不代表中华预防医学会和本刊编委会的观点，除非特别声明。, copyrightOwner=中华预防医学会和四川大学华西公共卫生学院, extLink=null, articleAbsUrl=null, sourceXml=AGJypU2Yt6NkDu+0wqQYjA==, magXml=QuE/NBpxTAvvIMpsjDWV/w==, pdfUrl=null, pdf=DybKbg8z5+HZDuXZtEDZbw==, pdfFileSize=1057743, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=yQ1OOD3rEixCZJr4LHOuqw==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=RceyvXsOMqx/CmFRBrvdYw==, mapNumber=null, authorCompany=null, fund=null, authors=

李国群（1994—），男，硕士，助教，研究方向：传染病建模

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李国群（1994—），男，硕士，助教，研究方向：传染病建模

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李国群（1994—），男，硕士，助教，研究方向：传染病建模

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注：A为模型拟合图，B为模型残差图。

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注：A1为初始状态下媒介数量变化图；A2为初始状态下人群数量变化图；B1为βmp在不同值下的Rt变化图；B2为βpm在不同值下的Rt变化图；B3为γ在不同值下的Rt变化图；B4为q在不同值下的Rt变化图；C1为综合干预措施下的Rt值；C2为综合干预措施下的每日发病数曲线。

, figureFileSmall=D1o5fXUC8isW5iWI5c6mgA==, figureFileBig=/aiXWB9mxUShUOz8TCR37w==, tableContent=null), ArticleFig(id=1240933504540791700, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240726761038737749, language=EN, label=Table 1, caption=

Package code table

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程序包版本加载代码功能
numpy2.2.3import numpy as np对数据进行计算和数组操作
import matplotlib
matplotlib3.10.1matplotlib.use('TkAgg')指定使用TkAgg后端对数据进行可视化分析
import matplotlib.pyplot as plt
pandas2.2.3import pandas as pd对数据进行清洗和分析
lmfit1.3.2from lmfit import Model, Parameters导入Model和Parameters类，用于非线性最小二乘拟合
scipy1.15.2from scipy.integrate import solve_ivp导入solve_ivp函数求解常微分方程（ODE）的初值问题
os3.12.4import os将数据保存到Excel文件
), ArticleFig(id=1240933504628872090, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240726761038737749, language=CN, label=表1, caption=

程序包代码表

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程序包版本加载代码功能
numpy2.2.3import numpy as np对数据进行计算和数组操作
import matplotlib
matplotlib3.10.1matplotlib.use('TkAgg')指定使用TkAgg后端对数据进行可视化分析
import matplotlib.pyplot as plt
pandas2.2.3import pandas as pd对数据进行清洗和分析
lmfit1.3.2from lmfit import Model, Parameters导入Model和Parameters类，用于非线性最小二乘拟合
scipy1.15.2from scipy.integrate import solve_ivp导入solve_ivp函数求解常微分方程（ODE）的初值问题
os3.12.4import os将数据保存到Excel文件
), ArticleFig(id=1240933504708563873, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240726761038737749, language=EN, label=Table 2, caption=

Overview of model parameters

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符号含义初始值校正值敏感度S*/备注
βmp媒介到人群的传播率0.10.1860.046
βpm人群到媒介的传播率0.10.1790.038
a媒介繁殖率0.080.0990
b媒介自然死亡率0.080.0500.537
wm媒介潜伏期转为感染期的速率0.10.1340.032
wp人群潜伏期转为感染期的速率0.150.1640.033
q潜伏者转为无症状感染者的比例0.70.70635.435
γ有症状感染者恢复率0.150.1810.010
γ1无症状感染者恢复率0.150.1680.032
n垂直传播系数0.120.1990
Np人口总量5 000固定值假设人蚊比：1：2
Nm 媒介总量10 000固定值
c季节性因子c=0.2+0.8*0.5[cos2Π(t-76)/365+1]*
), ArticleFig(id=1240933504805032874, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240726761038737749, language=CN, label=表2, caption=

模型参数一览表

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符号含义初始值校正值敏感度S*/备注
βmp媒介到人群的传播率0.10.1860.046
βpm人群到媒介的传播率0.10.1790.038
a媒介繁殖率0.080.0990
b媒介自然死亡率0.080.0500.537
wm媒介潜伏期转为感染期的速率0.10.1340.032
wp人群潜伏期转为感染期的速率0.150.1640.033
q潜伏者转为无症状感染者的比例0.70.70635.435
γ有症状感染者恢复率0.150.1810.010
γ1无症状感染者恢复率0.150.1680.032
n垂直传播系数0.120.1990
Np人口总量5 000固定值假设人蚊比：1：2
Nm 媒介总量10 000固定值
c季节性因子c=0.2+0.8*0.5[cos2Π(t-76)/365+1]*
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Python赋能媒介传染病预测预警模型建立及实现
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李国群 , 段小峰 , 王海清 , 陈海平 , 杨文倩 , 李锐
现代预防医学 | 流行病与统计方法 2025,52(19): 3490-3495
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现代预防医学 | 流行病与统计方法 2025, 52(19): 3490-3495
Python赋能媒介传染病预测预警模型建立及实现
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李国群, 段小峰, 王海清, 陈海平, 杨文倩, 李锐
作者信息
  • 宜春学院公共卫生与健康学院，江西 宜春 336000

    • 李国群（1994—），男，硕士，助教，研究方向：传染病建模

通讯作者:

李锐，E-mail:
Python-enabled development and implementation of a prediction and early warning model for vector-borne infectious diseases
Guo-qun LI, Xiao-feng DUAN, Hai-qing WANG, Hai-ping CHEN, Wen-qian YANG, Rui LI
Affiliations
  • Yichun University School of Public Health, Yichun, Jiangxi 336000, China
出版时间: 2025-10-10 doi: 10.20043/j.cnki.MPM.202504517
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摘要
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目的 基于Python平台，对媒介传染病数学模型全流程进行拓展，以期更好拟合模型并评估干预效果，为基层防控提供新思路，打开新视角。方法 对SmEmIm-SpEpIpApRp模型采用lmfit库拟合，采用solve_ivp函数求解，对模型关键参数进行敏感性分析，Rt计算依据下一代矩阵法，所有结果借助Matplotlib进行可视化展示。结果 结果显示R2=0.98，RMSE=2.07，疫情初期Rt=5.607，第41 d达到Rtpeak=8.439，Rt>1的疫情持续期为81 d，q的敏感度最高（S= 35.435），单一干预措施下βmp、βpm<0.01时，Rt<1，疫情消失；仅控制γ、q疫情并不会消失；综合干预下场景1可使累积病例减少98.64%，Rtpeak=0.868；场景2可使累积病例下降87.95%，Rtpeak=1.988；场景3的Rtpeak=4.78，Rt上升幅度较小，变化速率低，但持续时间更长，可使累积病例上升161.47%；场景4可使累积病例减少99.38%，Rtpeak=0.28。结论 基于Python平台的模型高拟合优度验证了季节性动态建模的必要性，为媒介传染病防控提供了“数据-模型-决策”的一体化解决方案，拓展了理论模型的实践边界，也为基层精准防控打开了新视角。

Python  /  媒介传染病  /  实时再生数  /  干预

Objective Based on the Python platform, the entire process of vector-borne infectious disease mathematical models is expanded to better fit models and evaluate intervention effects, to provide new ideas for grassroots prevention and control, and to open up new perspectives. Methods The SmEmIm-SpEpIpApRp model was fitted using the lmfit library, solved with the solve_ivp function, and sensitivity analysis of key model parameters was performed. The Rt calculation was based on the next generation matrix method, and all results were visually displayed with the help of Matplotlib. Results The results showed that R2=0.98 and RMSE=2.07. Rt was 5.607 in the early stage of the epidemic, and Rtpeak was 8.439 on day 41. The period with Rt>1 lasted 81 days, and q had the highest sensitivity (S=35.435). Under a single intervention, when βmp and βpm<0.01, Rt<1 and the epidemic disappeared. Controlling only γ and q would not eliminate the epidemic. Under comprehensive intervention, Scenario 1 could reduce the cumulative cases by 98.64%, and Rtpeak=0.868. Scenario 2 could reduce the cumulative cases by 87.95%,and Rtpeak=1.988. For Scenario 3, Rtpeak=4.78. Although the increase in Rt was smaller and the change rate was low, the longer duration could increase cumulative cases by 161.47%. Scenario 4 could reduce the cumulative cases by 99.38%, and Rtpeak=0.28. Conclusions The high goodness of fit of the model based on the Python platform verifies the necessity of seasonal dynamic modeling, provides an integrated solution for the prevention and control of vector-borne infectious diseases, expands the practical boundaries of theoretical models, and opens a new perspective for precise prevention and control at the grassroots level.

Python  /  Vector-borne infectious diseases  /  Real-time reproduction number  /  Intervention
李国群, 段小峰, 王海清, 陈海平, 杨文倩, 李锐. Python赋能媒介传染病预测预警模型建立及实现. 现代预防医学, 2025 , 52 (19) : 3490 -3495 . DOI: 10.20043/j.cnki.MPM.202504517
Guo-qun LI, Xiao-feng DUAN, Hai-qing WANG, Hai-ping CHEN, Wen-qian YANG, Rui LI. Python-enabled development and implementation of a prediction and early warning model for vector-borne infectious diseases[J]. Modern Preventive Medicine, 2025 , 52 (19) : 3490 -3495 . DOI: 10.20043/j.cnki.MPM.202504517
正文
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传染病动力学模型是研究疾病传播规律、预测疫情发展趋势及评估防控措施效果的重要工具。近年来，随着全球范围内新发和再发传染病的频繁出现，传染病动力学模型的研究得到了广泛关注。经典动力学SIR模型及其变体已被广泛应用于模拟疾病的传播过程[1-2]。此外，基于网络的传播模型、空间异质性模型以及多群体耦合模型等也逐渐成为研究热点[3-6]。这些模型不仅能够帮助研究者理解疾病的传播机制，还能为公共卫生决策提供科学依据。
目前，常用的传染病建模软件包括Berkeley Madonna、MATLAB、R等。其中，Berkeley Madonna以其直观的图形化界面和高效的微分方程求解能力受到青睐，但其闭源性限制了算法扩展与复杂模型定制[7]；MATLAB虽具备强大的数值计算功能，却因商业授权费用高昂难以普及；R语言虽开源且生态丰富，但在处理大规模并行计算时效率不足。相比之下，Python作为一种开源编程语言，凭借其丰富的科学计算库（如NumPy、SciPy、Pandas）和强大的可视化工具（如Matplotlib、Seaborn），在传染病建模中展现出独特的优势。Python不仅能够高效处理大规模数据，还支持多种模型的灵活构建与扩展，为研究者提供了更多的自由度[8-10]。然而，对于基层公共卫生人员而言，Python的使用仍面临一定的挑战，如编程基础薄弱、缺乏系统的培训等。因此，开发基于Python的传染病动力学模型实现方法，不仅能够降低建模门槛，还能为基层人员提供更加灵活和高效的建模工具，具有重要的研究价值和现实意义。本研究以构建的SmEmIm-SpEpIpApRp双群体动力学模型为例进行实例演示和讲解，旨在为基层防控人员在疫情预判能力提升、防控措施量化评估和应急响应标准化方面打开了新思路。
1　资料与方法
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1.1　一般建模流程
翻阅资料了解疾病自然史，构建疾病在自然状态下的传播动力学模型，收集疫情数据和相应模型参数对真实疫情数据进行拟合，并添加不同仓室和参数评估防控的效果。见图1。
1.2　数据来源及模型构建
本研究数据示例及模型参考陈田木教授[11-12]团队前期研究基础，对SmEmIm- SpEpIpApRp模型及参数进行调整，并引入偏移量和振幅对季节性因子进行校正，将人群和媒介分别划分为不同的状态，其中人群状态包括易感者（susceptible）、潜伏者（exposed）、有症状感染者（infected）、无症状感染者（asymptomatic）、康复者（recovered）和累积病例（cumulative cases）；媒介状态Mosquitos包括易感媒介（Sm）、潜伏媒介（Eem）和感染媒介（Im），该模型的构建主要基于以下假设:假定各自内部均匀混合,相互接触的概率相同；假定人群为相对封闭的系统，同时考虑到蚊虫繁殖快和寿命短，纳入了其自然出生和死亡率；考虑传染病的双向传播并假定传播过程为线性；假定季节性因子c随季节呈现周期性的变化，该函数中添加季节性振幅和偏移量，其中偏移量和振幅因子初始值来源于文献数据，高峰滞后时间初始值来源于真实疫情数据[13-15]；假定人群进入康复状态后具有永久免疫力；假定媒介存在垂直传播率为n。见图2。
1.3　统计方法
采用最小残差平方和优化参数，BDF法对方程进行求解，可变参数在估计值基础上采用5%小幅度扰动进行敏感性分析，计算决定系数R2等指标评估模型拟合优度和复杂度，根据下一代矩阵法和蒙特卡罗模拟估算实时再生数Rt[16]。
1.4　环境及程序包配置
本文使用的Python软件版本为Python 3.12.4，借助PyCharm平台进行操作。考虑到安装程序库下载速度慢问题，因此完成软件安装后可在PyCharm中添加清华镜像源。接着在其终端输入以下代码实现疫情模拟所要用的相应程序库的安装:pip install matplotlib numpy pandas scipy lmfit,具体加载代码及使用说明见表1。
2　结果
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2.1　模型拟合
SmEmIm-SpEpIpApRp双群体动力学模型采用非线性最小二乘法对观测数据进行了拟合。模型拟合优度指标显示：R2=0.98，RMSE=2.07，AIC=224.51，BIC=253.99，见图3A；残差分析显示，残差随机分布均匀，见图3B。
2.2　参数拟合及全局敏感性分析
通过最小化残差平方和优化模型的10个参数，其中Np和Nm采取固定值，对可变参数进行微扰分析发现可知，q的敏感度最高（S=35.435），其他参数敏感性较低，见表2。
2.3　实时再生数Rt计算及动态分析
实时再生数Rt的计算基于模型的双向传播机制，需综合人群(p)→媒介(m)与媒介(m)→人群(p)的传播贡献，其中单个感染人群在传染期内感染媒介的数量：单个感染媒介在存活期内感染人群的数量：，双向传播链的总效应为两者的乘积，并考虑媒介潜伏期转化效率，代入参数并化简，即。通过蒙特卡罗模拟可知，疫情初期Rt=5.607，第41 d达到Rtpeak=8.439，Rt>1的疫情持续期为81 d。
2.4　干预措施效果评估
采用初始参数对各状态仓室进行模拟可知，媒介易感态呈先增后减趋势，第55 d达峰值16 668只后进入衰减期，媒介感染者第 99 d达到峰值 5 039只，暴露者与感染者数量趋势一致，见图4A1；人群易感者从4 992人锐减至第119 d 1人，暴露者数量在第 75 d达到峰值837人，有症状感染者与无症状感染者在第 79 d同时达到峰值，分别为200和514人，康复者数量持续增加，最终在第138 d达到稳态的1 470人，见图4A2。
通过分别调节βmp、βpm、γ、q四个参数模拟单一从媒介防控、感染者管理、医疗干预、早期筛检和管理四个维度之一来评价干预措施的效果，结果显示，当βmp、βpm小于0.01时，Rt<1，疫情消失；仅改变γ、q疫情并不会明显被遏制，见图4B。
通过组合调节参数变化，我们模拟了双传播率降低（两者下降50%）、双传播率降低（两者下降20%）+恢复率提高（γ提高35%）、无症状比例降低（q下降28.6%）+恢复率提高（γ提高66.7%）、高强度综合干预（传播率均下降70%，q下降57%，γ提高100%）四个场景。结果显示：场景1可使累积病例减少98.64%，Rtpeak=0.868；场景2可使累积病例下降87.95%，Rtpeak=1.988；场景3Rtpeak=4.78，Rt上升幅度较原始数据小，变化速率低，但持续时间更长，可使累积病例上升161.47%；场景4可使累积病例减少99.38%，Rtpeak=0.28，见图4C。
3　讨论
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基于Python平台，在SmEmIm-SpEpIpApRp模型上引入季节性因子，实现了在媒介-人群交互传播框架中疾病季节性暴发的动态特征，一定程度上解决了传统模型在媒介传播疾病研究中的局限性。传统模型（如经典SEIR或SEIR-SI模型）通常假设传播率为恒定值[17-18]，难以捕捉季节性气候波动对媒介繁殖和疾病传播的影响，如Aguiar团队引入低、中、高季节性固定参数模拟媒介传染病传播特征，而本研究通过拟合季节函数，将气候驱动的媒介繁殖周期动态嵌入传播链，其R2显著高于既往模型[19]，模型的高拟合优度验证了季节性动态建模的必要性，这一改进不仅完善了媒介传播疾病的理论框架，还为基层防控提供了两方面实践价值。一方面，基于Python开源工具（lmfit，scipy）开发的参数本地化模块，使基层人员仅需调整季节相位参数即可适配不同气候区（如热带雨季提前地区），显著降低了技术应用门槛，克服了模型可视化需依赖专业软件（MATLAB）和定制化编程的障碍；另一方面，可通过可视化模块将复杂的Rt曲线转化为防控指令,如Rt>1时启动全域消杀，推动基层防控从经验驱动向数据驱动转型，这一建模实践不仅完善了媒介传播疾病的理论框架，更通过技术下沉解决了基层“有数据无模型”的痛点，为数字化转型提供了范式。
参数敏感性分析揭示了无症状感染者的核心传播风险。结果显示，潜伏者转为无症状感染者的比例（q）对疫情传播的敏感度（S=35.435）远高于媒介自然死亡率（b=0.537），这一发现与既往研究形成重要对比。例如，Chen等人[20]在寨卡病毒模型中指出，媒介控制参数（如叮咬率）的敏感度最高（S=28.7），而本研究表明，在存在显著无症状传播的疾病（如登革热或基孔肯雅热）中，隐性感染者的管控优先级可能高于媒介密度调控。这一差异提示，防控策略的设计需结合病原体特异性传播特征。值得注意的是，媒介自然死亡率b的敏感度S=0.537提示，通过环境干预（如清除孳生地）提高b值也可实现长效防控，这种“生态防控”思路与WHO倡导的媒介综合治理策略高度契合[21]。
对综合实时再生数的动态解析揭示了双向传播路径的交互作用。研究发现，疫情初期人群暴露者累积与媒介繁殖高峰的协同作用导致Rt在第41 d达到峰值8.439，这可能是因为双向传播相互促进，形成正反馈，导致传播效率倍增。
多场景干预模拟揭示了单一措施的效能瓶颈与协同策略的潜在优势。在单一措施中，媒介控制需维持极低传播率（βmp<0.01，βpm<0.01）方可压制Rt<1，但现实中难以持续维持极低媒介密度（如热带雨季蚊虫快速繁殖）[22-23]；采取单一医疗干预如仅提高恢复率γ或降低无症状比例q的压制效果有限，甚至可能因传播链延长导致累积病例上升（如场景3），这揭示了单一措施的“天花板效应”，与2016年新加坡登革热防控教训一致。多参数联合调控模拟显示：场景1（双传播率降低50%）通过“环境治理+社区防护”组合，累积病例减少98.64%，适用于资源匮乏地区，例如，动员社区志愿者开展爱国卫生运动以及健康宣教可显著降低双传播率[24]；场景4（高强度综合干预）整合“传播率下降70% +q下降57% +γ提高100%”，累积病例减少99.38%，但需跨部门协作（如疾控-医院-社区联防）；值得注意的是，场景2提示过度依赖医疗干预可能适得其反；场景3中提高γ虽加速病例康复，但因未阻断隐性媒介传播链，导致累积病例增加161.47%，这警示基层需避免“重治轻防”的认知偏差[25]，提示在后期防治过程中，应关口前移、提高无症状感染者的发现率，如扩大检测范围、高灵敏度筛查、密切接触者追踪。
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  • 江西省大学生创新创业训练计划(S202510417018)
  • 宜春市社会科学规划项目(JXYC2024KSA118)
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doi: 10.20043/j.cnki.MPM.202504517
  • 接收时间：2025-04-27
  • 首发时间：2026-03-17
  • 出版时间：2025-10-10
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  • 收稿日期：2025-04-27
基金
江西省大学生创新创业训练计划(S202510417018)
宜春市社会科学规划项目(JXYC2024KSA118)
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    宜春学院公共卫生与健康学院，江西 宜春 336000

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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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