The COVID-19 pandemic placed tremendous strain on medical resources. To assess intervention strategies and resource planning for metropolitan pandemic response, a hybrid System Dynamics–Discrete-Event Simulation (SD-DES) framework is developed, using Wuhan as a case study. With SD capturing macroscopic infection dynamics and policy intervention and DES simulating medical resource scheduling, bidirectional feedback between macro and micro levels enables a more holistic and comprehensive evaluation of policy effects. By simulating 132 representative scenarios, key factors including containment measures, medical resource capacity, mask adoption, vaccine rollout speed, and the timing of external medical support were examined. Our analysis provides a comprehensive perspective on pandemic prevention and control decision-making, an aspect often underrepresented in prior studies. The model offers an extensible computational framework for complex socioeconomic systems, such as pandemic emergencies, where dynamic and process complexities coexist. It can assist policymakers in enhancing the healthcare system’s preparedness and mitigating the spread of the pandemic. Future research could improve model robustness by incorporating advanced parameter estimation techniques, such as particle filtering. To address computational challenges, we also recommend implementing asynchronous module execution and optimized programming to improve simulation efficiency and scalability.
QiuYChenXShiW. Impacts of social and economic factors on the transmission of coronavirus disease (COVID-19) in China. J Popul Econ2020; 33: 1127–1172.
3.
StermanJD. System dynamics: systems thinking and modeling for a complex world. Boston, MA: McGraw-Hill Education, 2000.
4.
HomerJBHirschGB. System dynamics modeling for public health: background and opportunities. Am J Public Health2006; 96: 452–458.
5.
LiuSXueHLiY, et al. Investigating the diffusion of agent-based modelling and system dynamics modelling in population health and healthcare research. Syst Res Behav Sci2018; 35: 203–215.
6.
AtkinsonJAPageAWellsR, et al. A modelling tool for policy analysis to support the design of efficient and effective policy responses for complex public health problems. Implement Sci2015; 10: 26.
7.
TobiasMICavanaRYBloomfieldA. Application of a system dynamics model to inform investment in smoking cessation services in New Zealand. Am J Public Health2010; 100: 1274–1281.
8.
TaylorKDangerfieldB. Modelling the feedback effects of reconfiguring health services. J Oper Res Soc2005; 56: 659–675.
9.
DiazRBehrJGTulpuleM. A system dynamics model for simulating ambulatory health care demands. Simul Healthc2012; 7: 243–250.
10.
CavanaRYCliffordLV. Demonstrating the utility of system dynamics for public policy analysis in New Zealand: the case of excise tax policy on tobacco. Syst Dyn Rev2006; 22: 321–348.
11.
LiuSOsgoodNGaoQ, et al. Systems simulation model for assessing the sustainability and synergistic impacts of sugar-sweetened beverages tax and revenue recycling on childhood obesity prevention. J Oper Res Soc2016; 67: 708–721.
12.
MidgleyG. Systemic intervention for public health. Am J Public Health2006; 96: 466–472.
13.
Abdel-HamidTK. Modeling the dynamics of human energy regulation and its implications for obesity treatment. Syst Dyn Rev2002; 18: 431–471.
14.
OsgoodNDyckRGrassmannW. The inter- and intra-generational impact of gestational diabetes on the epidemic of type 2 diabetes. Am J Public Health2011; 101: 173–179.
15.
HirschGHomerJTrogdonJ, et al. Using simulation to compare 4 categories of intervention for reducing cardiovascular disease risks. Am J Public Health2014; 104: 1187–1195.
16.
DangerfieldBCFangYRobertsCA. Model-based scenarios for the epidemiology of HIV/AIDS: the consequences of highly active antiretroviral therapy. Syst Dyn Rev2001; 17: 119–150.
17.
HomerJB. A system dynamics model of national cocaine prevalence. Syst Dyn Rev1993; 9: 49–78.
18.
van den DriesschePWatmoughJ. A simple SIS epidemic model with a backward bifurcation. J Math Biol2000; 40: 525–540.
19.
CaiYKangYWangW. A stochastic SIRS epidemic model with nonlinear incidence rate. Appl Math Comput2017; 305: 221–240.
20.
ChenMKuoCLChanWKV. Control of COVID-19 pandemic: vaccination strategies simulation under probabilistic Node-Level model. In: The 6th international conference on intelligent computing and signal processing (ICSP), Xi’an, China, 9–11 April 2021, pp. 119–125. New York: IEEE.
21.
HeSPengYSunK. SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dyn2020; 101: 1667–1680.
22.
HeidenbergerKFlessaS. A system dynamics model for AIDS policy support in Tanzania. Eur J Oper Res1993; 70: 167–176.
23.
Ritchie-DunhamJLMendez GalvanJF. Evaluating epidemic intervention policies with systems thinking: a case study of dengue fever in Mexico. Syst Dyn Rev1999; 15: 119–138.
24.
HannonBMDealBFarelloC, et al. A dynamic model of the spatial spread of an infectious disease: the case of fox rabies in Illinois. Environ Model Assess2000; 5: 47–62.
25.
LebcirRMAtunRACokerRJ. System dynamic simulation of treatment policies to address colliding epidemics of tuberculosis, drug resistant tuberculosis and injecting drug users driven HIV in Russia. J Oper Res Soc2009; 61: 1238–1248.
26.
VickersDOsgoodND. Current crisis or artifact of surveillance: insights into rebound chlamydia rates from dynamic modelling. BMC Infect Dis2010; 10: 1–10.
27.
ArazOMLantTJehnM, et al. Simulation modeling for pandemic decision making: a case study with bi-criteria analysis on school closures. Decis Support Syst2013; 55: 564–575.
28.
GhaffarzadeganNRahmandadH. Simulation-based estimation of the early spread of COVID-19 in Iran: actual versus confirmed cases. Syst Dyn Rev2020; 36: 101–129.
29.
AliMShahSTHImranM, et al. The role of asymptomatic class, quarantine and isolation in the transmission of COVID-19. J Biol Dyn2020; 14: 389–408.
30.
GiordanoGBlanchiniFBrunoR, et al. Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nat Med2020; 26: 855–860.
31.
TocherKD. The art of simulation. London: English Universities Press Ltd, 1963.
32.
WinsbergE. Science in the age of computer simulation. Chicago, IL: University of Chicago Press, 2010.
33.
StratmanJKRothAVGillandWG. The deployment of temporary production workers in assembly operations: a case study of the hidden costs of learning and forgetting. J Oper Manag2004; 21: 689–707.
34.
DeHoratiusNRabinovichE. Field research in operations and supply chain management. J Oper Manag2011; 29: 371–375.
35.
ÖhmanMHiltunenMVirtanenK, et al. Frontlog scheduling in aircraft line maintenance: from explorative solution design to theoretical insight into buffer management. J Oper Manag2021; 67: 120–151.
36.
HollocksBW. Forty years of discrete-event simulation-a personal reflection. J Oper Res Soc2006; 57: 1383–1399.
37.
DaviesRM. An interactive simulation in the health service. J Oper Res Soc1985; 36: 597–606.
38.
JunJJacobsonSSwisherJ. Applications of discrete events simulation in health care clinics: a survey. J Oper Res Soc1990; 50: 109–123.
39.
JacobsonSHHallSNSwisherJR. Discrete-event simulation of health care systems. In: HallR (ed.) Patient flow: reducing delay in healthcare delivery. New York: Springer, 2006, pp. 210–252.
40.
PengQYangJStromeT, et al. Evaluation of physician in triage impact on overcrowding in emergency department using discrete-event simulation. J Proj Manag2020; 5: 211–226.
41.
AndersenARNielsenBFReinhardtLB, et al. Staff optimization for time-dependent acute patient flow. Eur J Oper Res2019; 272: 94–105.
42.
WeinsteinMC. Recent developments in decision-analytic modelling for economic evaluation. Pharmacoeconomics2006; 24: 1043–1153.
43.
MukherjeeUKSinhaKK. Robot-assisted surgical care delivery at a hospital: policies for maximizing clinical outcome benefits and minimizing costs. J Oper Manag2020; 66: 227–256.
44.
LeunisARedekopWKvan MontfortKA, et al. The development and validation of a decision-analytic model representing the full disease course of acute myeloid leukemia. Pharmacoeconomics2013; 31: 605–621.
45.
DaviesRMCrabbeDRoderickP, et al. A simulation to evaluate screening for Helicobacter pylori infection in the prevention of peptic ulcers and gastric cancers. Health Care Manag Sci2002; 5: 249–258.
46.
DaviesRMRoderickPRafteryJ. The evaluation of disease prevention and treatment using simulation models. Eur J Oper Res2003; 150: 53–66.
47.
KimSHJacksonAJHurR, et al. Individualized, discrete event, simulations provide insight into inter- and intra-subject variability of extended-release, drug products. Theor Biol Med Model2012; 9: 39.
48.
MahmoudiMColemanCISobierajDM. Systematic review of the cost-effectiveness of varenicline vs. bupropion for smoking cessation. Int J Clin Pract2012; 66: 171–182.
49.
LiuSLiYTriantisKP, et al. The diffusion of discrete event simulation approaches in health care management in the past four decades: a comprehensive review. MDM Policy Pract2020; 5: 1–17.
50.
TakoAARobinsonS. Comparing discrete-event simulation and system dynamics: users’ perceptions. J Oper Res Soc2009; 60: 296–312.
51.
MorecroftJRobinsonS. Explaining puzzling dynamics: a comparison of system dynamics and discrete-event simulation. In: BrailsfordSChurilovLDangerfieldB (eds) Discrete-event simulation and system dynamics for management decision making. Hoboken, NJ: John Wiley & Sons, 2014, pp. 165–198.
52.
AguasRWhiteLHupertN, et al. Modelling the COVID-19 pandemic in context: an international participatory approach. BMJ Glob Health2020; 5: e003126.
53.
FrostICraigJOsenaG, et al. Modelling COVID-19 transmission in Africa: countrywise projections of total and severe infections under different lockdown scenarios. BMJ Open2021; 11: e044149.
54.
DaldoulDNouaouriIBouchrihaH, et al. Simulation-based optimisation approach to improve emergency department resource planning: a case study of Tunisian hospital. Int J Health Plann Manage2022; 37: 2727–2751.
55.
AnsermeahMMFProchesCGBodhanyaS, et al. Optimising patient flow dynamics at a south African public hospital with resource constraints. Int J Innov Res Sci Stud2025; 8: 310–325.
56.
AbidATliliMMaaroufiF, et al. Decision models for performance evaluation and human resources planning in Tunisian public hospitals during the COVID-19 pandemic: a case study. J Simul. Epub ahead of print 6November2025. DOI: 10.1080/17477778.2025.2577957.
57.
VermaVRSainiAGandhiS, et al. Capacity-need gap in hospital resources for varying mitigation and containment strategies in India in the face of COVID-19 pandemic. Infect Dis Model2020; 5: 608–621.
58.
BaniasadMGolrokh MofradMBahmanabadiB, et al. COVID-19 in Asia: transmission factors, re-opening policies, and vaccination simulation. Environ Res2021; 202: 111657.
59.
KhairulbahriM. Lessons learned from three Southeast Asian countries during the COVID-19 pandemic. J Policy Model2021; 43: 1354–1364.
60.
ZhuangZCaoPZhaoS, et al. The shortage of hospital beds for COVID-19 and non-COVID-19 patients during the lockdown of Wuhan, China. Ann Transl Med2021; 9: 200.
61.
ShoaibMMustafeeNMadanK, et al. Leveraging multi-tier healthcare facility network simulations for capacity planning in a pandemic. Socioecon Plann Sci2023; 88: 101660.
62.
WangZWuPWangL, et al. Marginal effects of public health measures and COVID-19 disease burden in China: a large-scale modelling study. PLoS Comput Biol2023; 19: e1011492.
63.
MendozaVMPMendozaRKoY, et al. Managing bed capacity and timing of interventions: a COVID-19 model considering behavior and underreporting. AIMS Math2023; 8: 2201–2225.
64.
AlhomaidAAlzeerAHAlsaawiF, et al. The impact of non-pharmaceutical interventions on the spread of COVID-19 in Saudi Arabia: simulation approach. Saudi Pharm J2024; 32: 101886.
65.
FanQLiQChenY, et al. Modeling COVID-19 spread using multi-agent simulation with small-world network approach. BMC Public Health2024; 24: 672.
66.
ZhuHJiaFJiaF. A hybrid simulation approach for analyzing trends of infectious disease development, intervention measures and medical cost. J Simul2025; 20: 167–192.
67.
CôtéFLLahrichiNGrallaE, et al. Within-laboratory SARS-CoV-2 real time PCR testing operations in Nepal: a simulation-based analysis. Lancet Reg Health Southeast Asia2025; 36: 100584.
68.
WeissmanGECrane-DroeschAChiversC, et al. Locally informed simulation to predict hospital capacity needs during the COVID-19 pandemic. Ann Intern Med2020; 173: 21–28.
69.
Alarid-EscuderoFGraciaVLuvianoA, et al. Dependence of COVID-19 policies on end-of-year holiday contacts in Mexico City metropolitan area: a modeling study. MDM Policy Pract2021; 6: 23814683211049249.
70.
Cordova-PozoKLKorziliusHPLMRouwetteEAJA, et al. Using systems dynamics for capturing the multicausality of factors affecting health system capacity in Latin America while responding to the COVID-19 pandemic. Int J Environ Res Public Health2021; 18: 10002.
71.
LyonMEBajkovAHaugrudD, et al. COVID-19 pandemic planning: simulation models to predict biochemistry test capacity for patient surges. J Appl Lab Med2021; 6: 451–462.
72.
GhayoomiHMiller-HooksETariverdiM, et al. Maximizing hospital capacity to serve pandemic patient surge in hot spots via queueing theory and microsimulation. IISE Trans Healthc Syst Eng2023; 13: 314–332.
73.
Perez-TezocoJYAguilar-LasserreAAMoras-SánchezCG, et al. Hospital reconversion in response to the COVID-19 pandemic using simulation and multi-objective genetic algorithms. Comput Ind Eng2023; 182: 109408.
74.
BegenMARodriguesFFRiceT, et al. A forecasting tool for a hospital to plan inbound transfers of COVID-19 patients from other regions. BMC Public Health2024; 24: 505.
75.
MicudaANAndersonMRBabayanI, et al. Exploring a targeted approach for public health capacity restrictions during COVID-19 using a new computational model. Infect Dis Model2024; 9: 234–244.
76.
TianYBasranJMcDonaldW, et al. Early COVID-19 pandemic preparedness: informing public health interventions and hospital capacity planning through participatory hybrid simulation modeling. Int J Environ Res Public Health2024; 22: 39.
77.
WoodRMMcWilliamsCJThomasMJ, et al. COVID-19 scenario modelling for the mitigation of capacity-dependent deaths in intensive care. Health Care Manag Sci2020; 23: 315–324.
78.
AlbanAChickSEDongelmansDA, et al. ICU capacity management during the COVID-19 pandemic using a process simulation. Intensive Care Med2020; 46: 1624–1626.
79.
CaroJJMöllerJSanthirapalaV, et al. Predicting hospital resource use during COVID-19 surges: a simple but flexible discretely integrated condition event simulation of individual patient-hospital trajectories. Value Health2021; 24: 1570–1577.
80.
Garcia-VicuñaDEsparzaLMallorF. Hospital preparedness during epidemics using simulation: the case of COVID-19. Cent Eur J Oper Res2021; 30: 213–249.
81.
McCabeRKontMDSchmitN, et al. Modelling intensive care unit capacity under different epidemiological scenarios of the COVID-19 pandemic in the UK. Int J Epidemiol2021; 50: 753–767.
82.
Groves-KirkbyNWakemanEPatelS, et al. Large-scale calibration and simulation of COVID-19 epidemiologic scenarios to support healthcare planning. Epidemics2023; 42: 100662.
83.
RedondoENicolettaVBélangerV, et al. A simulation model for predicting hospital occupancy for COVID-19 using archetype analysis. Healthc Anal2023; 3: 100197.
84.
PierottiLCooperJJamesC, et al. Can computer simulation support strategic service planning? Modelling a large integrated mental health system on recovery from COVID-19. Int J Ment Health Syst2024; 18: 12.
85.
HendySSteynNJamesA, et al. Mathematical modelling to inform New Zealand’s COVID-19 response. J R Soc N Z2021; 51: S86–S106.
86.
ThompsonJMcClureRBlakelyT, et al. Modelling SARS-CoV-2 disease progression in Australia and New Zealand: an agent-based approach. Aust N Z J Public Health2023; 46: 292–303.
87.
LustigAVattiatoGMaclarenO, et al. Modelling the impact of the Omicron BA.5 subvariant in New Zealand. J R Soc Interface2023; 20: 20220698.
88.
TolkAHarperAMustafeeN. Hybrid models as transdisciplinary research enablers. Eur J Oper Res2021; 291: 1075–1090.
89.
BartonPMTobiasAM. Discrete quantity approach to continuous simulation modelling. J Oper Res Soc2000; 51: 485–489.
90.
BrailsfordSCChurilovLLiewSK. Treating ailing emergency departments with simulation: an integrated perspective. In: AndersonJKatzE (eds) Health sciences simulation. San Diego, CA: Society for Modeling and Computer Simulation, 2003, pp. 25–30.
91.
ZhangWLiuSOsgoodN, et al. Using simulation modelling and systems science to help contain COVID-19: a systematic review. Syst Res Behav Sci2023; 40: 207–234.
92.
ShanthikumarJGSargentRG. A unifying view of hybrid simulation/analytic models and modeling. Oper Res1983; 31: 1030–1052.
93.
BrailsfordSEldabiTKuncM, et al. Hybrid simulation modelling in operational research: a state-of-the-art review. Eur J Oper Res2019; 278: 721–737.
94.
LinnéussonGNgAHCAslamT. A hybrid simulation-based optimization framework supporting strategic maintenance development to improve production performance. Eur J Oper Res2020; 281: 402–414.
95.
TuranHHElsawahSRyanMJ. A long-term fleet renewal problem under uncertainty: a simulation-based optimization approach. Expert Syst Appl2020; 145: 113158.
96.
LuYGuanYZhongX, et al. Hospital beds planning and admission control policies for COVID-19 pandemic: a hybrid computer simulation approach. In: 2021 IEEE 17th international conference on automation science and engineering (CASE), Lyon, 23–27 August 2021, pp. 956–961. New York: IEEE.
97.
WardePRPatelSSFerreiraTD, et al. Linking prediction models to government ordinances to support hospital operations during the COVID-19 pandemic. BMJ Health Care Inform2021; 28: e100248.
98.
VenkateswaranJSonYJ. Hybrid system dynamic-discrete event simulation-based architecture for hierarchical production planning. Int J Prod Res2005; 43: 4397–4429.
99.
GreasleyA. Using system dynamics in a discrete-event simulation study of a manufacturing plant. Int J Oper Prod Manag2005; 25: 534–548.
100.
RabeloLHelalMJonesA, et al. Enterprise simulation: a hybrid system approach. Int J Comput Integr Manuf2005; 18: 498–508.
101.
HelalMRabeloL. Synchronizing discrete event simulation models and system dynamics models. In: Proceedings of the 2017 international conference on industrial engineering and operations management (IEOM), Bristol, 24–25 July 2017, pp. 602–613. New York: IEEE.
102.
PastranaJMarinMHelalM, et al. Enterprise scheduling: hybrid and hierarchical issues. In: Proceedings of the 2010 winter simulation conference, Baltimore, MD, December 5–8 2010, pp. 3350–3362. New York: IEEE.
103.
PrucknerMGermanR. A hybrid simulation model for large-scaled electricity generation systems. In: Proceedings of the 2013 winter simulation conference, Washington, DC, 8–11 December 2013, pp. 1881–1892. New York: IEEE.
104.
OlegheOSalonitisK. The application of a hybrid simulation modelling framework as a decision-making tool for TPM improvement. J Qual Maint Eng2019; 25: 476–498.
105.
Peña-MoraFHanSLeeSH, et al. Strategic-operational construction management: hybrid system dynamics and discrete event approach. J Constr Eng Manag2008; 134: 701–710.
106.
AlvanchiALeeSAbouRizkS. Modeling framework and architecture of hybrid system dynamics and discrete event simulation for construction. Comput Aided Civ Infrastruct Eng2011; 26: 77–91.
107.
AlzraieeHMoselhiOZayedT. A hybrid framework for modeling construction operations using discrete event simulation and system dynamics. In: Construction Research Congress 2012: Construction Challenges in a Flat World: Construction Challenges in a Flat World. West Lafayette, IN, USA., 21-23 May 2012, pp. 1063–1073. American Society of Civil Engineers (ASCE).
108.
AlzraieeHZayedTMoselhiO. Dynamic planning of construction activities using hybrid simulation. Autom Constr2015; 49: 176–192.
109.
MartinRRaffoD. Application of a hybrid process simulation model to a software development project. J Syst Softw2001; 59: 237–246.
110.
ChahalKEldabiT. Applicability of hybrid simulation to different modes of governance in UK healthcare. In: Proceedings of the 2008 winter simulation conference, Gothenburg, 9–12 December 2018, pp. 1469–1477. New York: IEEE.
111.
ChahalKEldabiT. A generic framework for hybrid simulation in healthcare. In: Proceedings of the 28th international conference of the system dynamics society, Seoul, South Korea, 25–29 July 2010, pp. 1–16. Littleton, MA: System Dynamics Society.
112.
ChahalKEldabiTYoungT. A conceptual framework for hybrid system dynamics and discrete event simulation for healthcare. J Enterp Inf Manag2013; 26:50–74.
113.
TejadaJJIvyJSKingRE, et al. Combined DES/SD model of breast cancer screening for older women, II: screening-and-treatment simulation. IIE Trans2014; 46: 707–727.
114.
VianaJ. Reflections on two approaches to hybrid simulation in healthcare. In: Proceedings of the 2015 winter simulation conference, Savanah, GA, 7–10 December 2014, pp. 1585–1596. New York: IEEE.
115.
MielczarekBZabawaJ. Modeling healthcare demand using a hybrid simulation approach. In: Proceedings of the 2016 winter simulation conference, Washington, DC, 11–14 December 2016, pp. 1535–1546. New York: IEEE.
116.
MorganJSBeltonVHowickS. Lessons from mixing OR methods in practice: using DES and SD to explore a radiotherapy treatment planning process. Health Syst2016; 5: 166–177.
117.
MustafeeNPowellJH. From hybrid simulation to hybrid systems modelling. In: Proceedings of the 2018 winter simulation conference, Gothenburg, 9–12 December 2018, pp. 1430–1439. New York: IEEE.
118.
ZulkepliJEldabiTMustafeeN. Hybrid simulation for modelling large systems: an example of integrated care model. In: Proceedings of the 2012 winter simulation conference (WSC), Berlin, 9–12 December 2012, pp. 758–769. New York: IEEE.
119.
MorganJSHowickSBeltonV. A toolkit of designs for mixing Discrete Event Simulation and System Dynamics. Eur J Oper Res2017; 257: 907–918.
120.
PalmerGITianY. Implementing hybrid simulations that integrate DES+SD in Python. J Simul2023; 17: 240–256.
121.
HouCChenJZhouY, et al. The effectiveness of quarantine of Wuhan city against the Corona Virus Disease 2019 (COVID-19): a well-mixed SEIR model analysis. J Med Virol2020; 92: 841–848.
122.
AndersonRMMayRM. Infectious diseases of humans: dynamics and control. Oxford: Oxford University Press, 1991.
123.
MarshallDABurgos-LizLIJzermanMJ, et al. Applying dynamic simulation modeling methods in health care delivery research – the SIMULATE checklist: report of the ISPOR Simulation Modeling Emerging Good Practices Task Force. Value Health2015; 18: 5–16.
124.
National Health Commission of the People’s Republic of China. Diagnosis and treatment options on COVID-19. 4th ed. Beijing, China: National Administration of Traditional Chinese Medicine, 2020, http://www.gov.cn/zhengce/zhengceku/2020-01/28/content_5472673.htm (accessed 15 February 2020).
125.
National Health Commission of the People’s Republic of China. Protocol for prevention and control of COVID-19 (edition 6). China CDC Wkly2020; 2: 321–326.
126.
TianLZhuWLiL, et al. Establishment and application of fever clinics standardized triage. Chin J Nosocomiol2016; 26: 5737–5739.
127.
ZhangCXuJGengX, et al. The outpatient management and strategies for 2019 novel coronavirus. Chin Health Serv Manag2020; 11: 818–819.
128.
ZhangXHanGChaiY, et al. Admission and diagnosis processes and containment practices in COVID-19-designated hospitals. J Qilu Nurs2020; 26: 4–7.
129.
KendallDG. Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov Chain. Ann Math Stat1953; 24: 338–354.
130.
SenRP. Operations research: algorithms and applications. New Delhi, India: PHI Learning, 2010.
131.
LawAM. Simulation modeling and analysis. 5th ed. New York: McGraw-Hill, 2014.
132.
PegdenCDRosenshineM. Some new results for the M/M/1 queue. Manage Sci1982; 28: 821–828.
133.
L’EcuyerPGirouxNGlynnPW. Stochastic optimization by simulation: numerical experiments with the M/M/1 queue in steady-state. Manage Sci1994; 40: 1245–1261.
134.
ZiyaS. On the relationships among traffic load, capacity, and throughput for the M/M/1/M, M/G/1/M-PS, and M/G/c/c queues. IEEE Trans Autom Control2008; 53: 2696–2701.
135.
WangJBaronOScheller-WolfA. M/M/c queue with two priority classes. Oper Res2015; 63: 733–749.
136.
ChandyKMMisraJ. Asynchronous distributed simulation via a sequence of parallel computations. Commun ACM1981; 24: 198–206.
137.
JeffersonDR. Virtual time. ACM Trans Program Lang Syst1985; 7: 404–425.
138.
The Institute of Electrical and Electronics Engineers. IEEE standard for modeling and simulation (M&S) high level architecture (HLA), federate interface specification (IEEE Std. 1516.1-2010). New York: The Institute of Electrical and Electronics Engineers, 2010.
139.
GortázarFDuarteALagunaM, et al. Black box scatter search for general classes of binary optimization problems. Comput Oper Res2010; 37: 1977–1986.
140.
QinYFreebairnLAtkinsonJA, et al. Multi-scale simulation modeling for prevention and public health management of diabetes in pregnancy and sequelae. In: Proceedings of SBP-BRiMS: international conference on social computing, behavioral-cultural modeling and prediction and behavior representation in modeling and simulation, Washington, DC, 9–12 July 2019, pp. 256–265. Cham: Springer International Publishing.
141.
BiQWuYMeiS, et al. Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study. Lancet Infect Dis2020; 20: 911–919.
142.
VerityROkellLCDorigattiI, et al. Estimates of the severity of coronavirus disease 2019: a model-based analysis. Lancet Infect Dis2020; 20: 669–677.
143.
ZhouFYuTDuR, et al. Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study. Lancet2020; 395: 1054–1062.
144.
LiYWongTChungJ, et al. In vivo protective performance of N95 respirator and surgical facemask. Am J Ind Med2006; 49: 1056–1065.
145.
DaviesAThompsonKAGiriK, et al. Testing the efficacy of homemade masks: would they protect in an influenza pandemic?Disaster Med Public Health Prep2013; 7: 413–418.
146.
NeupaneBBMainaliSSharmaA, et al. Optical microscopic study of surface morphology and filtering efficiency of face masks. PeerJ2019; 7: e7142.
147.
CaoSWenDChenX. Study on mask-wearing protective behavior among Chinese residents during the COVID-19 pandemic. Res Environ Sci2020; 33: 1649–1658.
148.
ZhuHLiuSLiX, et al. Using a hybrid simulation model to assess the impacts of combined COVID-19 containment measures in a high-speed train station. J Simul2023; 19: 141–165.
