摘要
为缓解重大传染病疫情下疫苗的短缺现状,本文结合传染病模型(susceptible-infected-recovered-deceased,SIRD)考虑疫苗需求与疫区医院收治容量的关系,以期望短缺数最小为目标建立疫苗分配模型,推导分析了最佳服务水平和储备量,并给出了不同情形下疫苗的最优分配方案。此外,通过数值模拟,进一步探究了紧急调配成本、资金预算、需求变化、疫区数量以及疫区间相关性等外生变量带来的影响,验证了模型推导结果,为疫苗分配和储备策略提供了科学依据。研究发现:疫苗接种有助于促进病毒感染曲线平坦化和降低疫情峰值,从而减轻医疗系统超负荷运转的现象,降低因感染而死亡的人数;在不考虑储备疫苗的情况下,无论需求的不确定性程度如何,为每个地区提供同等的服务水平有利于最小化疫苗期望短缺量;考虑储备疫苗的情况下,向需求波动幅度较大的疫区提供更高的服务水平可以减少期望短缺,但疫区数量较多时,为每个疫区提供同等服务水平更具公平性,即使会导致疫苗的次优覆盖;是否考虑储备疫苗取决于紧急调配成本、预算的高低以及疫区需求情况等。
After the outbreak of large-scale infectious diseases,vaccines are often the most effective means to eradicate the pandemic.Many infectious diseases,such as smallpox,poliovirus,hepatitis B virus,measles,epidemic parotitis etc.,are suppressed by extensive vaccination.In the protracted coronavirus disease 2019(COVID-19)pandemic,various effective and safe vaccines have miraculously broken through.All countries in the world are doing their utmost to vaccinate against COVID-19 on the largest scale and in the shortest possible time.Vaccination is a powerful preventive measure to avoid large-scale outbreaks of infectious diseases.Nevertheless,the social planners worldwide share common challenges in meeting the vaccine requirments of overall population,especially in the case of sudden outbreaks of infectious diseases where vaccines are often lack of supplies.For instance,during the 2004-2005 influenza season in the United States,unexpected supply disruptions led to a serious shortage of vaccines.Hence,in the event of a major epidemic,there is a need for a scientific and rational allocation of vaccines according to the evolution characteristics of infectious diseases and the severity of epidemic situations in distinct regions.Inadequate funding and limited information on vaccine needs in multiple regions pose a great challenge for many aid organizations.This present study examines how a decision maker can minimize the expected shortage in delivering relief aid to regions of need,through vaccine allocation and temporary reserve,in the presence of demand uncertainty with a budget constraint.The study obtains four contributions for existing literatures related to this topic.This study briefly analyzes the allocation structure of vaccine emergency funds,proposing that a portion of funds be set aside for stockpiling vaccines for emergency allocation scenarios.Aiming at the problem of vaccine allocation and reserve to control the spread of infectious diseases,first this study designs model hypothesis and sets some variables and parameters.Secondly,to explore the impact of vaccine supply on epidemic trends,this study analyzes the situation of mutual contact infection between epidemic areas using the SIRD(Susceptible-Infected-Recovered-Deceased)infectious disease model.Meanwhile,this study analyzes the demand for vaccines in different epidemic areas based on the hospital admission capacity in each epidemic area,and exploits the differences in the demand for vaccines in different epidemic areas.The fundamental demand of the epidemic area is set as the minimum vaccine supply with the peak value of the infection curve in the SIRD model lower than the hospital admission capacity in each epidemic area.Thirdly,we develop the allocation model with either stockpile vaccines are reserved or not.And,the KKT conditions(Karush-Kuhn-Tucker conditions)of lagrange function and derivative of the double integral are used to solve the model.Six interesting propositions are obtained,which are analyzed from the perspectives of service level,epidemic area demand and allocation equity.It is found that,under the senario of without considering the reserve vaccine,providing the identical service level to each region is the best scheme;while in the context of considering the reserve vaccine,providing higher service levels to affected areas where demand fluctuatesis the optimal sheme that can mitigate the vacanine shortage.Besides,if there are multiple epidemic areas,in order to promote fairness,equal service levels should be provided to each epidemic area,even if it incurs suboptimal vaccine coverage.It is important to note that,even on the identical level of service,affected areas with smaller hospital capacity receive more vaccines per person.Finally,the effects of exogenous variables such as emergency deployment cost per unit,capital budget,demand distribution parameters,the number of epidemic areas and inter-area demand relationships on vaccine allocation and reserve decision are explored by numerical analysis.The results of numerical analysis verify the previous analysis and derivation,and show that:1)vaccination contributes to flatten the infection curve and reduce the peak incidence of the epidemic;2)reserve vaccines provide flexibility for the social planners to conduct allocation,thus the existence of reserve vaccines depends on the level of emergency deployment costs and budgets and the demands of affected areas;3)in the face of major infectious disease outbreaks,the centralized storage and unified allocation strategy is effective.Therefore,in the event of a vaccine shortage,all epidemic areas must make concerted efforts to obtain more vaccine supplies;4)furthermore,cash donations are encouraged to personalize vaccine needs in affected areas,in turn,in-kind donations of vaccines have an unsatisfactory effect on increasing vaccination rates in affected areas.To sum up,this study combines SIRD epidemic model with underlying economic modeling concepts to investigate epidemic development and vaccine demand in the case of limited budget,builds an allocation and reserve model aiming at minimizing the expected shortage of vaccine,and gives the vaccine optimal allocation scheme under different situations,which provide valuable suggestions for vaccine allocation under major infectious diseases.
作者
冯春
蒋雪
周鑫昕
罗茂
FENG Chun;JIANG Xue;ZHOU Xinxin;LUO Mao(School of Transportation and Logistics,Southwest Jiao tong University,Chengdu 610031)
出处
《管理工程学报》
CSSCI
CSCD
北大核心
2024年第2期232-242,共11页
Journal of Industrial Engineering and Engineering Management
基金
国家软科学研究计划项目(2014GXS4D146)
成都市哲学社会科学规划专项课题项目(2020ZXB08)。
关键词
重大传染病
需求不确定
疫苗分配
服务水平
SIRD模型
Infectious diseases
Uncertain demand
Vaccine allocation and reserve
Service level
SIRD model
