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2020年新冠肺炎疫情暴发初期，医疗物资的优化配置是疫情防控的关键问题之一。基于疫情蔓延程度、医疗资源禀赋和救治能力，一个国家或地区采取怎样的分配策略才能有效减少疫情的传播？本文针对这一问题进行理论探讨，在标准SIS传染病动力学模型和有限资源约束下，讨论如何最小化感染人数以实现医疗物资在民众和医院之间的最优配置，给出不同先决条件下的配置最优解，并以模拟的方式验证计算结果的合理性及感染比例的长期趋势。针对疫情迅速蔓延的情形，本文讨论如何增加医疗物资和医护人员的数量来控制感染率水平。本文提出的模型探讨了新冠肺炎疫情期间各个国家和地区的物资分配方式，为重大新发传染病的应对提供理论依据。
Abstract：In the early stage of COVID-19 outbreak in 2020, the optimal allocation of medical supplies was a key issue for disease control. Based on the spread of the epidemic, the endowment of medical resources, and the ability of treatment, what kind of allocation strategy should a country or region adopt to reduce the spread of the epidemic? To discusses this issue theoretically, under the standard SIS model and limited resources constraint, we investigate the optimal allocation of medical supplies between people and hospitals that minimizes the number of infected people. We give the optimal solution under different prerequisites and verify the correctness of solutions and the long-term trend of infection rate through simulation data. We also expand the model to handle rapidly spreading outbreaks by increasing the number of medical supplies or ambulance personnel. This paper reflects on the medical supply allocation ways in different countries and regions during the epidemic and provides a theoretical analysis for the response to major emerging infectious diseases.
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(1)因篇幅所限，其他情形的求解细节以附录A展示，见《统计研究》网站所列附件。下同。(2)备注：这里数值算例的参数组合并不是唯一的，本文只是为了图3中最优解的可视化程度才设置了这样一组参数。例如0A=10,0R=2.5，μ=0.2, 0.20ti=, m=0.50, c=8也满足要求，但是可视化程度非常差，而且最优解的图示很难像图3表达得如此清晰。更多的参数设置情况见本文数值分析部分。
(1)因篇幅所限，情形2的数值分析以附录B展示。
(1)因篇幅所限，情形4的数值分析以附录C展示。
(1)数据来源：https://data.oecd.org/pop/population.htm。
(2)数据来源：https://ourworldindata.org/coronavirus。
(1)该调查中，三个科室的样本量分别为96、520和333人，总样本量为10065人，对该三个科室于本地直接接诊或管理确诊新冠肺炎患者的医护人员比例加权平均，可得该三个重要科室中于本地直接接诊或管理确诊新冠肺炎患者的医护人员占全部卫生技术人员的比例，即(96×62%+520×35%+333×20%)/10065=3.1%。
(2)数据来源：https://export.shobserver.com/baijiahao/html/262251.html,https://new.qq.com/omn/20220316/20220316A03ZUE00.html。
(3)一名新冠肺炎普通型患者需要3.5名医生医治，一名新冠肺炎重型患者需要8名医生救治。截至2020年2月15日，武汉重症占确诊病例的比例为21.6%，全国其他省份重症占确诊病例的比例为7.2%。新冠肺炎治疗的平均时间为2周~3周。按照以上数据计算每名医生在一周内大概能治愈0.1名患者：(1/3.5×92.8%+1/8×7.2%)/2.5≈0.1097;(1/3.5×78.4%+1/8×21.6%)/2.5≈0.1004。
基本信息:
DOI：10.19343/j.cnki.11-1302/c.2022.11.008
中图分类号:R197.1
引用信息:
[1]孙强,陈阳,张晓梅,等.新冠肺炎疫情背景下有限医疗物资在民众和医院之间的优化配置研究[J].统计研究,2022,39(11):102-116.DOI:10.19343/j.cnki.11-1302/c.2022.11.008.
基金信息:
对外经济贸易大学中央高校基本科研业务费专项资金资助“大数据下重大传染病的监测和预警研究”（20YQ12）;“经济发展新动能的核心内涵和统计测度”（ZD3-05）;对外经济贸易大学惠园杰出青年学者项目“重大传染病下稀缺物资的分配策略研究”（20JQ07）
2022-11-25
2022-11-25