The solutions to the supply and allocation of medical emergency resources during public health emergencies greatly affect the efficiency of epidemic prevention and control. Currently, the main problem in computational epidemiology is how the allocation scheme should be adjusted in accordance with epidemic trends to satisfy the needs of population coverage, epidemic propagation prevention, and the social allocation balance. More specifically, the metropolitan demand for medical emergency resources varies depending on different local epidemic situations. It is therefore difficult to satisfy all objectives at the same time in real applications. In this paper, a data-driven multi-objective optimization method, called as GA-PSO, is proposed to address such problem. It adopts the one-way crossover and mutation operations to modify the particle updating framework in order to escape the local optimum. Taking the megacity Shenzhen in China as an example, experiments show that GA-PSO effectively balances different objectives and generates a feasible allocation strategy. Such a strategy does not only support the decision-making process of the Shenzhen center in terms of disease control and prevention, but it also enables us to control the potential propagation of COVID-19 and other epidemics. © Copyright © 2020 Wang, Deng, Yuan, Zhang, Zhang, Cai, Gao and Kurths

Cai, Qing

Deng, Yue

Gao, Chao

Kurths, Jürgen

Wang, Chunyu

Yuan, Ziheng

Zhang, Chijun

Zhang, Fan

Frontiers in Physics

English

The solutions to the supply and allocation of medical emergency resources during public health emergencies greatly affect the efficiency of epidemic prevention and control. Currently, the main problem in computational epidemiology is how the allocation scheme should be adjusted in accordance with epidemic trends to satisfy the needs of population coverage, epidemic propagation prevention, and the social allocation balance. More specifically, the metropolitan demand for medical emergency resources varies depending on different local epidemic situations. It is therefore difficult to satisfy all objectives at the same time in real applications. In this paper, a data-driven multi-objective optimization method, called as GA-PSO, is proposed to address such problem. It adopts the one-way crossover and mutation operations to modify the particle updating framework in order to escape the local optimum. Taking the megacity Shenzhen in China as an example, experiments show that GA-PSO effectively balances different objectives and generates a feasible allocation strategy. Such a strategy does not only support the decision-making process of the Shenzhen center in terms of disease control and prevention, but it also enables us to control the potential propagation of COVID-19 and other epidemics.Published versio

Kurths, Jurgen

DR-NTU (Digital Repository of NTU)

How to optimize the supply and allocation of medical emergency resources during public health emergencies

Repositorium für Naturwissenschaften und Technik  (TIB Hannover)

BRIEF RESEARCH REPORTpublished: 28 October 2020doi: 10.3389/fphy.2020.00383Frontiers in Physics | www.frontiersin.org 1 October 2020 | Volume 8 | Article 383Edited by:Lin Wang,University of Cambridge,United KingdomReviewed by:Peican Zhu,Northwestern Polytechnical University,ChinaJinzhuo Liu,Yunnan University, China*Correspondence:Chao Gaocgao@swu.edu.cnSpecialty section:This article was submitted toSocial Physics,a section of the journalFrontiers in PhysicsReceived: 04 July 2020Accepted: 07 August 2020Published: 28 October 2020Citation:Wang C, Deng Y, Yuan Z, Zhang C,Zhang F, Cai Q, Gao C and Kurths J(2020) How to Optimize the Supplyand Allocation of Medical EmergencyResources During Public HealthEmergencies. Front. Phys. 8:383.doi: 10.3389/fphy.2020.00383How to Optimize the Supply andAllocation of Medical EmergencyResources During Public HealthEmergenciesChunyu Wang 1, Yue Deng 1, Ziheng Yuan 2, Chijun Zhang 3, Fan Zhang 1, Qing Cai 4,Chao Gao 5,1* and Jurgen Kurths 6,71College of Computer and Information Science, Southwest University, Chongqing, China, 2 Faculty of Humanities, Chang’anUniversity, Xi’an, China, 3College of Management Science and Information Engineering, Jilin University of Finance andEconomics, Changchun, China, 4 School of Mechanical and Aerospace Engineering, Nanyang Technological University,Singapore, Singapore, 5 Key Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Natural Resourcesof the People’s Republic of China, Shenzhen, China, 6 Potsdam Institute for Climate Impact Research, Potsdam, Germany,7Nizhny Novgorod State University, Nizhny Novgorod, RussiaThe solutions to the supply and allocation of medical emergency resources during publichealth emergencies greatly affect the efficiency of epidemic prevention and control.Currently, the main problem in computational epidemiology is how the allocation schemeshould be adjusted in accordance with epidemic trends to satisfy the needs of populationcoverage, epidemic propagation prevention, and the social allocation balance. Morespecifically, the metropolitan demand for medical emergency resources varies dependingon different local epidemic situations. It is therefore difficult to satisfy all objectives at thesame time in real applications. In this paper, a data-driven multi-objective optimizationmethod, called as GA-PSO, is proposed to address such problem. It adopts the one-waycrossover and mutation operations to modify the particle updating framework in orderto escape the local optimum. Taking the megacity Shenzhen in China as an example,experiments show that GA-PSO effectively balances different objectives and generatesa feasible allocation strategy. Such a strategy does not only support the decision-makingprocess of the Shenzhen center in terms of disease control and prevention, but it alsoenables us to control the potential propagation of COVID-19 and other epidemics.Keywords: COVID-19, computational epidemiology, epidemic propagation, emergence management, multi-objective optimization, medical emergency resources1. INTRODUCTIONIn December 2019, a few patients with atypical pneumonia were first diagnosed in Wuhan, China,and this was reported to the World Health Organization (WHO) [1]. Then, its etiology wasidentified as the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It is obvious thatthe disease was spreading continuously from person to person at the end of January 2020 [2]. Theconfirmed and imported cases in the Hubei province, China, brought about severe coronavirusoutbreaks in many cities across China. More seriously, the disease, called COVID-19, has sincespread rapidly across China and to the rest of the world [1]. By the end of June 30, 2020, there were10,185,374 confirmed cases and 503,862 deaths in 210 countries [3].Wang et al. Optimizations of Medical Resources AllocationsCurrently, vaccines and antiviral medicines for COVID-19 are still under development. Besides, other pharmaceuticaltreatments (e.g., plasma therapy) are not likely to be implementedon a large scale. Therefore, the use of a personal protectiveequipment (PPE) (e.g., hand sanitizers, surgical face masks,and protective clothing) becomes one of the major non-pharmaceutical measures to reduce the infectious hazard [4].The sudden outbreak throughout China has exacerbated anunprecedented PPE shortage, causing austere challenges toepidemic control [5]. Due to the limited stock of a PPE during theearly phase of COVID-19 epidemic, the local health organizationsuffered great challenges. It has been an open problem for us toefficiently allocate a PPE during an epidemic propagation.Currently, various models (e.g., SIS, SIR, and SVIR) areconsidered to model the spreading process for the purpose ofestimating the affecting scope from the perspective of theoreticalanalysis [6–10]. It is also possible to introduce evolutionary gametheory during the resource allocation process [11]. However,balancing the allocation of a PPE in different regions is stilla tough task due to multiple risk factors and high interest.Two key factors are a high-risk population and the severity ofinfection [12]. As a result, this paper develops an improvedparticle swarm optimization algorithm to reconcile this decisionTABLE 1 | Parameters are used in the experiments of the GA-PSO algorithm.Parameters SourceNi Population size in the ith district in 2016 [13]Oi Population size of people aged 65 or more in the ith district in 2015[15]Ii The number of confirmed cases in the ith district by February 1,2020[16]Ai The number of impacted individuals in per confirmed case which isassumed as 1,000X The PPE allocation over 10 districts where X = (x1, ..., x10)G The total allocation in Shenzhen where G =∑i xiFIGURE 1 | The overview of the GA-PSO algorithm, which comprises three components, i.e., the random initialization, the genetic operations, and the particle swarmoptimization framework. The initial particles are selected by the roulette method. When a random number is less than the mutation rate, the particle is executed theinitialization operation.making problem. It balances the heterogeneity of a high-riskpopulation and the severity of infection by incorporating the one-way crossover and mutation operations into the particle swarmoptimization framework and eventually generates a reasonableallocation strategy of a PPE.We apply this algorithm for balancing the allocation of PPEin Shenzhen, which is one of the largest megacities [with apopulation ofmore than 11million [13]] in Guangdong province,China. During the COVID-19 epidemic in China, Shenzhenreported 195 confirmed COVID-19 cases as of February 1, 2020,which was higher than all other cities except Hebei province atthat time. Therefore, improving the medical emergency systemhas been one of the highest priorities in Shenzhen [14]. Morespecifically, the supply and allocation of PPE is an urgent matterin Shenzhen.2. METHODSShenzhen is divided into ten administrative districts. Allparameters are set in Table 1. Let X = (x1, ..., x10) denote a PPETABLE 2 | The demographic information of 10 districts in Shenzhen and thepredicated PPE allocation of the highest risk and the greatest severity objectives.District Thepredictedallocation ofthe largesthigh-riskThepredictedallocation ofthe greatestseverityPopulationin 2016Age 65 in2015Cumulativecases onfebruary 1,2020Bao’an 3 21 2,863,300 51,938 22Dapeng 36 36 135,600 4,499 2Futian 84 705 1,440,600 80,605 36Guangming 4 3 531,200 8,620 5Luohu 13 61 975,600 44,210 11Longhua 48 4 1,511,500 23,434 24Longgang 61 25 2,052,400 44,620 41Nanshan 705 84 1,291,200 57,477 46Pingshan 25 13 356,100 5,935 5Yantian 21 48 221,200 8,173 3Frontiers in Physics | www.frontiersin.org 2 October 2020 | Volume 8 | Article 383Wang et al. Optimizations of Medical Resources Allocationsallocation over 10 districts, and G =∑i xi represent the totalallocation. The optimization strategy is based on the followingassumptions and objectives:• High-risk population: Due to multiple complications and ahigh fatality rate of people over 65, we select people over65 [17]. The ith district with Oi people aged 65 or more isallocated xi sets of PPE defined in Equation (1), where Ni isthe population size in the ith district.∑ixi × Oi/Ni (1)• The severity of infection: The ith district with Ii confirmedcases is allocated xi sets of PPE defined in Equation (2). Ai isthe number of impacted individuals per confirmed case, whichis assumed to be 1,000 for all districts.∑ixi × Ai × Ii/Ni (2)Based on the above two objectives, this paper proposes anovel multi-objective optimization algorithm, named as GA-PSO, developed on the basis of MODPSO [18]. More specifically,GA-PSO is partially modified to simultaneously optimize thehigh-risk population and the severity of infection. The overviewof GA-PSO is shown in Figure 1. It adopts one-way crossover andmutation operations to modify MODPSO in order to enhancethe quality of solutions and escape the local optimum [19, 20].FIGURE 2 | Estimated PPE optimized allocation in the 10 districts of Shenzhen on February 14, 2020. The Pareto frontier uses the two objectives of high-risk andseverity priorities in the middle right inset. The predicted allocation of the greatest high-risk priority in (A) and the predicted allocation of the greatest severity priorityin (B).Frontiers in Physics | www.frontiersin.org 3 October 2020 | Volume 8 | Article 383Wang et al. Optimizations of Medical Resources AllocationsEvery population is composed of a set of particles which is afeasible solution (i.e.,X). Firstly, a random population of particlesis initialized. X is a random integer vector by G =∑i xi. Then,X is evaluated by the high-risk population and the severity ofinfection. It adopts the roulette method to select the preferablefitness particles. After that, it executes the one-way crossoveroperation. When a random number is less than the mutationvalue, it generates random particles. Finally, it iterativelygenerates new populations using particle status updating rules.During each iteration, the algorithm updates the Pareto solutions.When the number of iterations reaches the set value, thecurrently obtained Pareto solutions are the final solutions for theoptimization problem.3. RESULTSThe Shenzhen dataset is shown in Table 2 and includes thepopulation size in 2016 [13], the number of people aged 65 ormore in 2015 [15], and the cumulative cases on February 1,2020 [16]. Besides, the PPE optimized allocation is calculatedby GA-PSO as shown in Table 2. Figure 2 describes thatthe GA-PSO detects the Pareto front solutions for the PPEoptimized allocation over 10 districts in Shenzhen. EveryPareto front solution indicates a feasible allocation. Differentsolutions can lead to different objective function values asquantified by the high-risk and severity priorities. The valueof high-risk priority has ranged from 4.1% to 5.0%, and thevalue of the severity priority has ranged from 2.5% to 3.1%in Figure 2.In summary, two objectives (i.e., the high-risk populationand the severity of inflection) are added to obtain the PPEaccessibility. The maximum value of the PPE accessibility is7.53% for older or impacted individuals. When only the maximalhigh-risk population is the objective, the optimized allocation isestimated across 10 districts in Shenzhen, ranging from 3‰ insuburban Bao’an to 705‰ in central Nanshan. If the severityis the solitary objective, the allocation is from 3‰ in suburbanGuangming to 705‰ in central Futian. The central districts ofFutian and Nanshan top the PPE priority because of the maximalolder people and confirmed cases.4. DISCUSSIONMetropols (e.g., New York, London, Paris, and San Paulo) havebeen experiencing an urgent demand for medical emergencyresources since the early phase of the COVID-19 epidemic.The use of a personal protective equipment (PPE) (e.g., handsanitizers, surgical face masks, and protective clothing) hasbecome one of the major non-pharmaceutical measures withwhich to reduce the infectious hazard. Due to the limited stockof PPE in particular during the early phase of the COVID-19epidemic, the local health organization has suffered greatly. Itis therefore a challenge to balance the supply and allocationof PPE during the available time. To overcome this challengefor practical applications, the multi-objective optimization is apromising method.A multi-objective optimization algorithm generates a set ofPareto solutions each of which is a tradeoff between multipleobjectives. Consequently, the multi-objective optimizationfacilitates the decision making problem. In addition to PPE,the pharmaceutical prophylactics (e.g., antibiotics, vaccines,antitoxins, and other critical medical supplies) are also facedwith the decision making problem because of the limited supplyin the early phase. Our optimization algorithm for PPE cantherefore be extended to other pharmaceutical prophylactics tonarrow the scope of a disease spread and to avoid catastrophiceconomic and social consequences.DATA AVAILABILITY STATEMENTThe raw data supporting the conclusions of this article will bemade available by the authors, without undue reservation.AUTHOR CONTRIBUTIONSCW, CG, YD, ZY, and QC performed the experiments. CW,CG, and FZ analyzed the data. CW, CG, YD, and JK wrote thepaper. CW, CG, ZY, CZ, and JK planned the study. All authorscontributed to the article and approved the submitted version.FUNDINGThis work was supported in part by the National NaturalScience Foundation of China (No. 61976181), Natural ScienceFoundation of Chongqing (No. cstc2018jcyjAX0274), theFundamental Research Funds for the Central Universities(No. XDJK2020D022), the Open Fund of Key Laboratoryof Urban Land Resources Monitoring and Simulation(No. MNR KF-2019-04-034), Chongqing Graduate StudentResearch Innovation Project (No. CYS20116), and theRussian Ministry of Science and Education Agreement(No. 13.1902.21.0026).REFERENCES1. Chen S, Yang J, Yang W, Wang C, Barnighausen T. COVID-19 controlin China during mass population movements at New Year. Lancet. (2020)395:764–6. doi: 10.1016/S0140-6736(20)30421-92. Wu P, Hao X, Lau EHY,Wong JY, Leung KSM,Wu JT, et al. Real-time tentativeassessment of the epidemiological characteristics of novel coronavirusinfections in Wuhan, China, as at 22 January 2020. Eurosurveillance. (2020)25:2000044. doi: 10.2807/1560-7917.ES.2020.25.3.20000443. World Health Organization. Coronavirus Disease 2019 (COVID-19): SituationReport - 162 (2020). Available online at: https://www.who.int/docs/default-source/coronaviruse/20200630-covid-19-sitrep-162.pdf?sfvrsn=e00a5466_2.4. Leung NH, Chu DK, Shiu EY, Chan KH, McDevitt JJ, Hau BJ,et al. Respiratory virus shedding in exhaled breath and efficacy offace masks. Nat Med. (2020) 26:676–80. doi: 10.1038/s41591-020-0843-25. Ranney ML, Griffeth V, Jha AK. Critical supply shortages-the need forventilators and personal protective equipment during the covid-19Frontiers in Physics | www.frontiersin.org 4 October 2020 | Volume 8 | Article 383Wang et al. Optimizations of Medical Resources Allocationspandemic. N Engl J Med. (2020) 382:e41. doi: 10.1056/NEJMp20061416. Zhu P, Wang X, Zhi Q, Ma J, Guo Y. Analysis of epidemic spreading processin multi-communities. Chaos Solitons Fractals. (2018) 109:231–7.7. Zhu P, Wang X, Li S, Guo Y, Wang Z. Investigation of epidemic spreadingprocess on multiplex networks by incorporating fatal properties. Appl MathComput. (2019) 359:512–24. doi: 10.1016/j.amc.2019.02.0498. Du Z, Holme P. Coupling the circadian rhythms of population movementand the immune system in infectious disease modeling. PLoS ONE. (2020)15:e0234619. doi: 10.1371/journal.pone.02346199. Du Z, Nugent C, Galvani AP, Krug RM, Meyers LA. Modeling mitigationof influenza epidemics by baloxavir. Nat Commun. (2020) 11:1–6.doi: 10.1038/s41467-020-16585-y10. Du Z, Xu X, Wang L, Fox SJ, Cowling BJ, Galvani AP, et al. Proactive socialdistancingmitigates COVID-19 outbreaks within amonth across 58mainlandChina cities. Emerg Infect Dis. (2020) 26. doi: 10.1101/2020.04.22.2007576211. Zhu P, Wang X, Jia D, Guo Y, Li S, Chu C. Investigating the co-evolutionof node reputation and edge-strategy in prisoners dilemma game. Appl MathComput. (2020) 386:125474. doi: 10.1016/j.amc.2020.12547412. Bansal S, Pourbohloul B, Meyers LA. A comparative analysisof influenza vaccination programs. PLoS Med. (2006) 3:e387.doi: 10.1371/journal.pmed.003038713. Yang X, Xie Z. Shenzhen Statistical Yearbook. Shenzhen.14. Zhang D, Mou J, Cheng J, Griffiths S. Public health services in Shenzhen: acase study. Public Health. (2011) 125:15–19. doi: 10.1016/j.puhe.2010.10.00715. Futian Government. Study on Evaluation of Population Aging in FutianDistrict. Shenzhen (2017). Available online at: http://www.szft.gov.cn/wap/ftzw/tjxx/qttjgb_41536/content/post_3321769.html16. Shenzhen Health Commission. Distribution of districts in Shenzhen onFebruary 1, 2020. Tencent (2020). Available online at: https://xw.qq.com/cmsid/20200202A04J5Y0017. The Novel Coronavirus Pneumonia Emergency Response EpidemiologyTeam. The Epidemiological Characteristics of an Outbreak of 2019Novel Coronavirus Diseases (COVID-19)–China, 2020 (2020). Availableonline at: http://weekly.chinacdc.cn//article/id/e53946e2-c6c4-41e9-9a9b-fea8db1a8f5118. Cai Q, Gong M, Ruan S, Miao Q, Du H. Network structural balancebased on evolutionary multiobjective optimization: a two-step approach.IEEE Trans Evol Comput. (2015) 19:903–16. doi: 10.1109/TEVC.2015.242408119. Wang C, Deng Y, Li X, Chen J, Gao C. Dynamic communitydetection based on a label-based swarm intelligence. IEEEAccess. (2019) 7:161641–53. doi: 10.1109/ACCESS.2019.295152720. Wang C, Deng Y, Li X, Xin Y, Gao C. A label-based nature heuristic algorithmfor dynamic community detection. In: PRICAI 2019: Trends in ArtificialIntelligence. Fiji (2019). p. 621–632.Disclaimer: Frontiers Media SA remains neutral with regard to jurisdictionalclaims in published maps and institutional affiliations.Conflict of Interest: The authors declare that the research was conducted in theabsence of any commercial or financial relationships that could be construed as apotential conflict of interest.Copyright © 2020 Wang, Deng, Yuan, Zhang, Zhang, Cai, Gao and Kurths. Thisis an open-access article distributed under the terms of the Creative CommonsAttribution License (CC BY). The use, distribution or reproduction in other forumsis permitted, provided the original author(s) and the copyright owner(s) are creditedand that the original publication in this journal is cited, in accordance with acceptedacademic practice. No use, distribution or reproduction is permitted which does notcomply with these terms.Frontiers in Physics | www.frontiersin.org 5 October 2020 | Volume 8 | Article 383

How to Optimize the Supply and Allocation of Medical Emergency Resources During Public Health Emergencies

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How to Optimize the Supply and Allocation of Medical Emergency Resources During Public Health Emergencies

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