{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T06:58:06Z","timestamp":1785481086724,"version":"3.56.0"},"reference-count":76,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T00:00:00Z","timestamp":1785369600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T00:00:00Z","timestamp":1785369600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theory Biosci."],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1007\/s12064-026-00488-5","type":"journal-article","created":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:28:54Z","timestamp":1785432534000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal strategies for fair vaccine allocation: integrating non-pharmaceutical interventions, regional quarantine, and social challenges in epidemic control"],"prefix":"10.1007","volume":"145","author":[{"given":"Fatemeh","family":"Mirsaeedi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4134-9263","authenticated-orcid":false,"given":"Mohammad","family":"Sheikhalishahi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehrdad","family":"Mohammadi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,30]]},"reference":[{"key":"488_CR1","doi-asserted-by":"publisher","first-page":"108193","DOI":"10.1016\/j.ijpe.2021.108193","volume":"239","author":"ST Alam","year":"2021","unstructured":"Alam ST, Ahmed S, Ali SM, Sarker S, Kabir G, Ul-Islam A (2021) Challenges to COVID-19 vaccine supply chain: implications for sustainable development goals. Int J Prod Econ 239:108193","journal-title":"Int J Prod Econ"},{"key":"488_CR2","doi-asserted-by":"publisher","first-page":"104957","DOI":"10.1016\/j.compbiomed.2021.104957","volume":"139","author":"AH Alamoodi","year":"2021","unstructured":"Alamoodi AH, Zaidan BB, Al-Masawa M et al (2021) Multi-perspectives systematic review on the applications of sentiment analysis for vaccine hesitancy. Comput Biol Med 139:104957","journal-title":"Comput Biol Med"},{"key":"488_CR3","doi-asserted-by":"publisher","first-page":"103572","DOI":"10.1016\/j.csi.2021.103572","volume":"80","author":"AS Albahri","year":"2022","unstructured":"Albahri AS, Albahri OS, Zaidan AA, Alnoor A, Alsattar HA, Mohammed R, Alamoodi AH, Zaidan BB, Aickelin U, Alazab M, Garfan S, Ahmaro IY, Ahmed MA (2022) Integration of fuzzy-weighted zero-inconsistency and fuzzy decision by opinion score methods under a q-rung orthopair environment: a distribution case study of COVID-19 vaccine doses. Comput Stand Interfaces 80:103572","journal-title":"Comput Stand Interfaces"},{"key":"488_CR4","doi-asserted-by":"publisher","first-page":"110042","DOI":"10.1016\/j.chaos.2020.110042","volume":"139","author":"D Aldila","year":"2020","unstructured":"Aldila D, Khoshnaw HA et al (2020) A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: the case of Jakarta, Indonesia. Chaos Solitons Fractals 139:110042","journal-title":"Chaos Solitons Fractals"},{"key":"488_CR5","doi-asserted-by":"publisher","DOI":"10.7717\/peerj.11172","author":"A Alzu\u2019bi","year":"2021","unstructured":"Alzu\u2019bi A, Alasal SA, Kheirallah KA, Watzlaf V (2021) COVID-19 simulation study\u2014the effect of strict non-pharmaceutical interventions (NPIs) on controlling the spread of COVID-19. PeerJ. https:\/\/doi.org\/10.7717\/peerj.11172","journal-title":"PeerJ"},{"key":"488_CR6","doi-asserted-by":"publisher","first-page":"101193","DOI":"10.1016\/j.seps.2021.101193","volume":"80","author":"H Anahideh","year":"2022","unstructured":"Anahideh H, Kang L, Nezami N (2022) Fair and diverse allocation of scarce resources. Socio-Econ Plan Sci 80:101193","journal-title":"Socio-Econ Plan Sci"},{"key":"488_CR7","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1038\/280361a0","volume":"280","author":"RM Anderson","year":"1979","unstructured":"Anderson RM, May RM (1979) Population biology of infectious diseases: part I. Nature 280:361\u2013367","journal-title":"Nature"},{"key":"488_CR8","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1038\/318323a0","volume":"318","author":"RM Anderson","year":"1985","unstructured":"Anderson RM, May RM (1985) Vaccination and herd immunity to infectious diseases. Nature 318:323\u2013329","journal-title":"Nature"},{"key":"488_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jtbi.2016.01.027","volume":"395","author":"MA Andrews","year":"2016","unstructured":"Andrews MA, Bauch CT (2016) The impacts of simultaneous disease intervention decisions on epidemic outcomes. J Theor Biol 395:1\u201310","journal-title":"J Theor Biol"},{"key":"488_CR10","doi-asserted-by":"publisher","first-page":"111621","DOI":"10.1016\/j.chaos.2021.111621","volume":"154","author":"M Angeli","year":"2022","unstructured":"Angeli M, Neofotistos G, Mattheakis M, Kaxiras E (2022) Modeling the effect of the vaccination campaign on the COVID-19 pandemic. Chaos Solitons Fractals 154:111621","journal-title":"Chaos Solitons Fractals"},{"key":"488_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/s12063-021-00225-9","author":"M Ardolino","year":"2022","unstructured":"Ardolino M, Bacchetti A, Ivanov D (2022) Analysis of the COVID-19 pandemic\u2019s impacts on manufacturing: a systematic literature review and future research agenda. Oper Manag Res. https:\/\/doi.org\/10.1007\/s12063-021-00225-9","journal-title":"Oper Manag Res"},{"key":"488_CR12","first-page":"283","volume":"10","author":"M Asghari","year":"2022","unstructured":"Asghari M, Fathollahi-Fard AM, Mirzapour Al-e-hashem SM, Dulebenets MA (2022) Transformation and linearization techniques in optimization: a state-of-the-art survey. Mathematics (Basel) 10:283","journal-title":"Mathematics (Basel)"},{"issue":"4","key":"488_CR13","doi-asserted-by":"publisher","first-page":"226","DOI":"10.5001\/omj.2013.66","volume":"28","author":"A Balkhair","year":"2013","unstructured":"Balkhair A, Maamani KA, Alawi FB (2013) The struggle against MERS-CoV (the novel coronavirus). Oman Med J 28(4):226\u2013227","journal-title":"Oman Med J"},{"key":"488_CR14","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1186\/s12939-021-01611-2","volume":"21","author":"C Bambra","year":"2022","unstructured":"Bambra C (2022) Pandemic inequalities: emerging infectious diseases and health equity. Int J Equity Health 21:6","journal-title":"Int J Equity Health"},{"key":"488_CR15","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1186\/s12939-022-01729-x","volume":"21","author":"M Bayati","year":"2022","unstructured":"Bayati M, Noroozi R, Ghanbari-Jahromi M, Jalali F (2022) Inequality in the distribution of Covid-19 vaccine: a systematic review. Int J Equity Health 21:122","journal-title":"Int J Equity Health"},{"key":"488_CR16","doi-asserted-by":"crossref","unstructured":"Blasioli E, Mansouri B, Tamvada S S, & Hassini E (2023) Vaccine allocation and distribution: a review with a focus on quantitative methodologies and application to equity, hesitancy, and COVID-19 pandemic. In:\u00a0Operations research forum\u00a0(Vol. 4, No. 2, p. 27). Cham: Springer","DOI":"10.1007\/s43069-023-00194-8"},{"issue":"7","key":"488_CR17","doi-asserted-by":"publisher","first-page":"e0236310","DOI":"10.1371\/journal.pone.0236310","volume":"15","author":"A Canabarro","year":"2020","unstructured":"Canabarro A, Tennorio E, Martins R, Martins L, Brito S, Chaves R (2020) Data-driven study of the the COVID-19 pandemic via age-structured modelling and prediction of the health system failure in Brazil amid diverse intervention strategies. PLoS ONE 15(7):e0236310","journal-title":"PLoS ONE"},{"key":"488_CR18","doi-asserted-by":"publisher","first-page":"106876","DOI":"10.1016\/j.compbiomed.2023.106876","volume":"158","author":"P Catelli","year":"2023","unstructured":"Catelli P, Pelosi S, Comito C, Pizzuti C, Esposito M (2023) Lexicon-based sentiment analysis to detect opinions and attitude towards COVID-19 vaccines on Twitter in Italy. Comput Biol Med 158:106876","journal-title":"Comput Biol Med"},{"issue":"6","key":"488_CR19","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1093\/aje\/kwj274","volume":"164","author":"S Cauchemez","year":"2006","unstructured":"Cauchemez S, Bo\u00eblle PY, Thomas G, Valleron AJ (2006) Estimating in real time the efficacy of measures to control emerging communicable diseases. Am J Epidemiol 164(6):591\u2013597","journal-title":"Am J Epidemiol"},{"key":"488_CR20","first-page":"1804","volume":"10","author":"YC Chang","year":"2022","unstructured":"Chang YC, Liu CT (2022) A stochastic multi-strain SIR model with two-dose vaccination rate. Mathematics (Basel) 10:1804","journal-title":"Mathematics (Basel)"},{"issue":"2","key":"488_CR21","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s00285-024-02180-y","volume":"90","author":"Z Chen","year":"2025","unstructured":"Chen Z, Feng H (2025) Numerical dynamics and optimal control for multi-strain age-structured epidemic model. J Math Biol 90(2):17","journal-title":"J Math Biol"},{"issue":"3","key":"488_CR22","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1093\/imammb\/dqz012","volume":"37","author":"AA Chernov","year":"2020","unstructured":"Chernov AA, Kelbert MY, Shemendyuk AA (2020) Optimal vaccine allocation during the mumps outbreak in two SIR centres. Math Med Biol: A J IMA 37(3):303\u2013312","journal-title":"Math Med Biol: A J IMA"},{"key":"488_CR23","doi-asserted-by":"publisher","first-page":"132674","DOI":"10.1016\/j.physd.2020.132674","volume":"413","author":"A Comunian","year":"2020","unstructured":"Comunian A, Gaburro R, Giudici M (2020) Inversion of a SIR-based model: a critical analysis about the application to COVID-19 epidemic. Phys D 413:132674","journal-title":"Phys D"},{"key":"488_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2022.108684","author":"S Dastgoshade","year":"2022","unstructured":"Dastgoshade S, Shafiee M, Klibi W, Shishebori D (2022) Social equity-based distribution networks design for the COVID-19 vaccine. Int J Prod Econ. https:\/\/doi.org\/10.1016\/j.ijpe.2022.108684","journal-title":"Int J Prod Econ"},{"key":"488_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-58414-6","volume-title":"Vaccines: a clinical overview and practical guide","author":"J Domachowske","year":"2021","unstructured":"Domachowske J, Suryadevara M (2021) Vaccines: a clinical overview and practical guide. Springer, New York"},{"key":"488_CR26","doi-asserted-by":"publisher","first-page":"10677","DOI":"10.1007\/s11071-023-08308-x","volume":"111","author":"S Dong","year":"2023","unstructured":"Dong S, Xu L, A Y, Lan Z, Xiao D, Gao B (2023) Application of a time-delay SIR model with vaccination in COVID-19 prediction and its optimal control strategy. Nonlinear Dyn 111:10677\u201310692","journal-title":"Nonlinear Dyn"},{"key":"488_CR27","doi-asserted-by":"publisher","first-page":"2049","DOI":"10.1056\/NEJMsb2005114","volume":"382","author":"EJ Emanuel","year":"2020","unstructured":"Emanuel EJ, Persad G, Upshur R et al (2020) Fair allocation of scarce medical resources in the time of COVID-19. N Engl J Med 382:2049\u20132055","journal-title":"N Engl J Med"},{"key":"488_CR28","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1016\/j.ejor.2019.11.025","volume":"283","author":"S Enayati","year":"2020","unstructured":"Enayati S, Ozaltin OY (2020) Optimal influenza vaccine distribution with equity. Eur J Oper Res 283:714\u2013725","journal-title":"Eur J Oper Res"},{"key":"488_CR29","first-page":"258","volume":"6","author":"JE Gnanvi","year":"2021","unstructured":"Gnanvi JE, Salako KV, Kotanmi GB, Kaka\u00ef RG (2021) On the reliability of predictions on COVID-19 dynamics: a systematic and critical review of modelling techniques. Infect Dis Model 6:258\u2013272","journal-title":"Infect Dis Model"},{"key":"488_CR30","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/s10479-022-04713-4","volume":"328","author":"F Goodarzian","year":"2023","unstructured":"Goodarzian F, Navaei A, Ehsani B, Ghasemi P, Mu\u00f1uzuri J (2023) Designing an integrated responsive-green-cold vaccine supply chain network using internet-of-things: artificial intelligence-based solutions. Ann Oper Res 328:531\u2013575","journal-title":"Ann Oper Res"},{"issue":"3","key":"488_CR31","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/s10441-022-09443-5","volume":"70","author":"GS Harari","year":"2022","unstructured":"Harari GS, Monteiro HA (2022) An epidemic model with pro and anti-vaccine groups. Acta Biotheor 70(3):20","journal-title":"Acta Biotheor"},{"issue":"8","key":"488_CR32","doi-asserted-by":"publisher","first-page":"e0182720","DOI":"10.1371\/journal.pone.0182720","volume":"12","author":"HC Huang","year":"2017","unstructured":"Huang HC, Singh B, Morton DP, Johnson GP, Clements B, Meyers LA (2017) Equalizing access to pandemic influenza vaccines through optimal allocation to public health distribution points. PLoS ONE 12(8):e0182720","journal-title":"PLoS ONE"},{"issue":"11","key":"488_CR34","doi-asserted-by":"publisher","first-page":"e0259700","DOI":"10.1371\/journal.pone.0259700","volume":"16","author":"MR Islam","year":"2021","unstructured":"Islam MR, Oraby T, McCombs A, Chowdhury MM, Al-Mamun M, Tyshenko MG et al (2021) Evaluation of the United States COVID-19 vaccine allocation strategy. PLoS ONE 16(11):e0259700","journal-title":"PLoS ONE"},{"key":"488_CR35","doi-asserted-by":"publisher","first-page":"101922","DOI":"10.1016\/j.tre.2020.101922","volume":"136","author":"D Ivanov","year":"2020","unstructured":"Ivanov D (2020) Predicting the impacts of epidemic outbreaks on global supply chains: a simulation-based analysis on the coronavirus outbreak (COVID-19\/SARS-CoV-2) case. Transp Res E 136:101922","journal-title":"Transp Res E"},{"key":"488_CR36","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2021.1890852","author":"D Ivanov","year":"2021","unstructured":"Ivanov D (2021) Supply chain viability and the COVID-19 pandemic: a conceptual and formal generalisation of four major adaptation strategies. Int J Prod Res. https:\/\/doi.org\/10.1080\/00207543.2021.1890852","journal-title":"Int J Prod Res"},{"issue":"1\u20132","key":"488_CR37","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/BF02283607","volume":"29","author":"D Ivanov","year":"2020","unstructured":"Ivanov D, Rozhkov M (2020) Coordination of production and ordering policies under capacity disruption and productwrite-off risk: an analytical study with real-data. Ann Oper Res 29(1\u20132):387\u2013407","journal-title":"Ann Oper Res"},{"key":"488_CR38","doi-asserted-by":"publisher","first-page":"108031","DOI":"10.1016\/j.cie.2022.108031","volume":"167","author":"P Jarumaneeroj","year":"2022","unstructured":"Jarumaneeroj P, Dusadeerungsikul PO, Chotivanich T, Nopsopon T, Pongpirul K (2022) An epidemiology-based model for the operational allocation of COVID-19 vaccines: a case study of Thailand. Comput Ind Eng 167:108031","journal-title":"Comput Ind Eng"},{"key":"488_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.seps.2022.101378","author":"MA Kamran","year":"2022","unstructured":"Kamran MA, Kia R, Goodarzian F, Ghasemi P (2022) A new vaccine supply chain network under COVID-19 conditions considering system dynamic: artificial intelligence algorithms. Socio-Econ Plan Sci. https:\/\/doi.org\/10.1016\/j.seps.2022.101378","journal-title":"Socio-Econ Plan Sci"},{"key":"488_CR40","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1098\/rspa.1927.0118","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc Lond A Math Phys Charact 115:700\u2013721","journal-title":"Proc R Soc Lond A Math Phys Charact"},{"issue":"10","key":"488_CR41","doi-asserted-by":"publisher","first-page":"e0275851","DOI":"10.1371\/journal.pone.0275851","volume":"17","author":"YR Kim","year":"2022","unstructured":"Kim YR, Choi YJ, Min Y (2022) A model of COVID-19 pandemic with vaccines and mutant viruses. PLoS ONE 17(10):e0275851","journal-title":"PLoS ONE"},{"key":"488_CR42","doi-asserted-by":"publisher","first-page":"108648","DOI":"10.1016\/j.mbs.2021.108648","volume":"339","author":"MJ K\u00fchn","year":"2021","unstructured":"K\u00fchn MJ, Abele D, Mitra T, Koslow W, Abedi M, Rack K, Siggel M, Khailaie S, Klitz M, Binder S, Spataro L, Gilg J, Kleinert J, H\u00e4berle M, Pl\u00f6tzke L, Spinner CD, Stecher M, Zhu XX, Basermann A, Meyer-Hermann M (2021) Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution. Math Biosci 339:108648","journal-title":"Math Biosci"},{"key":"488_CR43","doi-asserted-by":"publisher","first-page":"3861","DOI":"10.1016\/j.vaccine.2018.03.063","volume":"36","author":"S Lane","year":"2018","unstructured":"Lane S, MacDonal NE, Marti M, Dumolard L (2018) Vaccine hesitancy around the globe: analysis of three years of WHO\/UNICEF Joint Reporting Form data-2015-2017. Vaccine 36:3861\u20133867","journal-title":"Vaccine"},{"key":"488_CR44","doi-asserted-by":"publisher","DOI":"10.1007\/s12144-020-01211-3","author":"CA Latkin","year":"2021","unstructured":"Latkin CA, Dayton L, Moran M, Strickland JC, Collins K (2021) Behavioral and psychosocial factors associated with COVID-19 skepticism in the United States. Curr Psychol. https:\/\/doi.org\/10.1007\/s12144-020-01211-3","journal-title":"Curr Psychol"},{"key":"488_CR45","volume-title":"The impact of vaccine hesitancy on epidemic spreading, in American Control Conference (ACC)","author":"CH Leung","year":"2022","unstructured":"Leung CH, Gibbs ME, Pare PE (2022) The impact of vaccine hesitancy on epidemic spreading, in American Control Conference (ACC). Atlanta, USA"},{"key":"488_CR46","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/6125064","author":"S Liu","year":"2021","unstructured":"Liu S, Liu M (2021) Dynamic analysis of a stochastic SEQIR model and application in the COVID-19 pandemic. Discrete Dyn Nat Soc. https:\/\/doi.org\/10.1155\/2021\/6125064","journal-title":"Discrete Dyn Nat Soc"},{"issue":"2","key":"488_CR47","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1287\/msom.2017.0681","volume":"20","author":"EF Long","year":"2018","unstructured":"Long EF, Nohdurft E, Spinler S (2018) Spatial resource allocation for emerging epidemics: a comparison of greedy, myopic, and dynamic policies. Manuf Serv Oper Manag 20(2):181\u2013198","journal-title":"Manuf Serv Oper Manag"},{"key":"488_CR48","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1126\/science.1175570","volume":"325","author":"J Medlock","year":"2009","unstructured":"Medlock J, Galvani AP (2009) Optimizing influenza vaccine distribution. Science 325:1705\u20131708","journal-title":"Science"},{"key":"488_CR50","doi-asserted-by":"publisher","first-page":"132792","DOI":"10.1016\/j.physd.2020.132792","volume":"415","author":"JG Miranda","year":"2021","unstructured":"Miranda JG, Silva MS, Bertolino JG et al (2021) Scaling effect in COVID-19 spreading: the role of heterogeneity in a hybrid ODE-network model with restrictions on the inter-cities flow. Physica D 415:132792","journal-title":"Physica D"},{"key":"488_CR51","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/978-3-031-85508-5_12","volume-title":"Handbook of ripple effects in the supply chain","author":"F Mirsaeedi","year":"2025","unstructured":"Mirsaeedi F, Sheikhalishahi M, Mohammadi M, Ivanov D (2025a) Epidemiological models to predict infection epidemic: a literature review. Handbook of ripple effects in the supply chain. Springer Nature Switzerland, pp 249\u2013330"},{"issue":"2","key":"488_CR52","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1007\/s10479-025-06893-1","volume":"357","author":"F Mirsaeedi","year":"2025","unstructured":"Mirsaeedi F, Sheikhalishahi M, Mohammadi M, Pirayesh A, Ivanov D (2025b) Compartmental models in epidemiology: bridging the gap with operations research for enhanced epidemic control. Ann Oper Res 357(2):1021\u20131078","journal-title":"Ann Oper Res"},{"key":"488_CR53","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1134\/S1560354721030072","volume":"26","author":"G Nakamura","year":"2021","unstructured":"Nakamura G, Grammaticos B, Badoual M (2021) Recruitment effects on the evolution of epidemics in a simple SIR model. Regul Chaotic Dyn 26:305\u2013319","journal-title":"Regul Chaotic Dyn"},{"key":"488_CR55","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s40819-022-01411-4","volume":"8","author":"S Paul","year":"2022","unstructured":"Paul S, Mahata A, Mukherjee S, Roy B, Salimi M, Ahmadian A (2022) Study of fractional order SEIR epidemic model and effect of vaccination on the spread of COVID-19. Int J Appl Comput Math 8:237","journal-title":"Int J Appl Comput Math"},{"key":"488_CR56","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2021.02.001","volume":"913","author":"N Perra","year":"2021","unstructured":"Perra N (2021) Non-pharmaceutical interventions during the COVID-19 pandemic: a review. Phys Rep 913:1\u201352","journal-title":"Phys Rep"},{"key":"488_CR57","first-page":"012083","volume":"738","author":"DB Prates","year":"2016","unstructured":"Prates DB, Jardim C, Ferreira LAF, da Silva JM, Kritz MV (2016) Vaccination strategies: a comparative study in an epidemic scenario. J Phys: Conf Ser 738:012083","journal-title":"J Phys: Conf Ser"},{"key":"488_CR58","doi-asserted-by":"publisher","first-page":"1159","DOI":"10.1007\/s10479-020-03685-7","volume":"319","author":"MM Queiroz","year":"2020","unstructured":"Queiroz MM, Ivanov D, Dolgui A, Fosso Wamba S (2020) Impacts of epidemic out-breaks on supply chains: mapping a research agenda amid the COVID-19 pandemic through a structured literature review. Ann Oper Res 319:1159\u20131196","journal-title":"Ann Oper Res"},{"key":"488_CR59","doi-asserted-by":"publisher","first-page":"15660","DOI":"10.1038\/s41598-022-19630-6","volume":"12","author":"G Rinaldi","year":"2022","unstructured":"Rinaldi G, Menon PP, Ferrara A, Strain WD, Edwards C (2022) Epidemiological model based periodic intervention policies for COVID-19 mitigation in the United Kingdom. Sci Rep 12:15660","journal-title":"Sci Rep"},{"key":"488_CR60","doi-asserted-by":"crossref","unstructured":"Roda W, Varughese M, Han D and Li, M (2020) Infectious Disease Modelling, vol. 5, p. 271","DOI":"10.1016\/j.idm.2020.03.001"},{"key":"488_CR61","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s10654-022-00938-6","volume":"38","author":"I Rodiah","year":"2023","unstructured":"Rodiah I, Vanella P, Kuhlmann A, Jaeger VK, Harries M, Krause G, Karch A, Bock W, Lange B (2023) Age-specific contribution of contacts to transmission of SARS-CoV-2 in Germany. Eur J Epidemiol 38:39\u201358","journal-title":"Eur J Epidemiol"},{"issue":"3","key":"488_CR62","doi-asserted-by":"publisher","first-page":"e0001693","DOI":"10.1371\/journal.pgph.0001693","volume":"3","author":"FJ Ruiz","year":"2023","unstructured":"Ruiz FJ, Torres-Rueda S et al (2023) What, how and who: cost-effectiveness analyses of COVID-19 vaccination to inform key policies in Nigeria. PLoS Glob Public Health 3(3):e0001693","journal-title":"PLoS Glob Public Health"},{"key":"488_CR63","doi-asserted-by":"publisher","DOI":"10.1007\/s13369-021-05904-0","author":"R Saxena","year":"2021","unstructured":"Saxena R, Jadeja M, Bhateja V (2021) Propagation analysis of COVID-19: an SIR model-based investigation of the pandemic. Arab J Sci Eng. https:\/\/doi.org\/10.1007\/s13369-021-05904-0","journal-title":"Arab J Sci Eng"},{"key":"488_CR64","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/978-3-319-65455-3_11","volume-title":"Operations research applications in health care management","author":"N Shamsi","year":"2017","unstructured":"Shamsi N, Torabi SA (2017) Vaccine supply management. Operations research applications in health care management, vol vol. 262. pp 267\u2013294"},{"key":"488_CR65","doi-asserted-by":"publisher","first-page":"102314","DOI":"10.1016\/j.dsx.2021.102314","volume":"15","author":"P Sharma","year":"2021","unstructured":"Sharma P, Pardeshi G (2021) COVID-19 vaccination in India: an ethical perspective. Diabetes Metab Syndr 15:102314","journal-title":"Diabetes Metab Syndr"},{"key":"488_CR66","first-page":"553","volume":"88","author":"JF Tapia","year":"2021","unstructured":"Tapia JF, Manzano J, Ona IB, Chua U (2021) Development of a web-based application for optimal allocation of COVID-19 vaccine. Chem Eng Trans 88:553\u2013558","journal-title":"Chem Eng Trans"},{"issue":"1","key":"488_CR67","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s10479-021-04130-z","volume":"360","author":"M Tavana","year":"2026","unstructured":"Tavana M, Govindan K, Nasr AK, Heidary MS, Mina H (2026) A mathematical programming approach for equitable COVID-19 vaccine distribution in developing countries. Annals Operat Res 360(1):391\u2013424","journal-title":"Annals Operat Res"},{"key":"488_CR68","unstructured":"Thompson M G (2021) Interim estimates of vaccine effectiveness of BNT162b2 and mRNA-1273 COVID-19 vaccines in preventing SARS-CoV-2 infection among health care personnel, first responders, and other essential and frontline workers\u2014Eight US Locations, December 2020\u2013March 2021,\" Morbidity and Mortality Weekly Report"},{"key":"488_CR69","doi-asserted-by":"publisher","first-page":"127429","DOI":"10.1016\/j.physa.2022.127429","volume":"598","author":"M Turkyilmazoglu","year":"2022","unstructured":"Turkyilmazoglu M (2022) An extendedepidemicmodelwithvaccination: weak-immune SIRVI. Phys A 598:127429","journal-title":"Phys A"},{"key":"488_CR70","doi-asserted-by":"publisher","first-page":"1249","DOI":"10.1016\/j.ejor.2023.03.032","volume":"310","author":"B Vahdani","year":"2023","unstructured":"Vahdani B, Mohammadi M, Thevenin S, Gendreau M, Dolgui A, Meyer P (2023) Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: the case study of COVID-19. Eur J Oper Res 310:1249\u20131272","journal-title":"Eur J Oper Res"},{"issue":"1-2","key":"488_CR71","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Van den Driessche","year":"2002","unstructured":"Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1\u20132):29\u201348","journal-title":"Math Biosci"},{"key":"488_CR72","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1186\/s12879-024-09007-7","volume":"24","author":"YY Wang","year":"2024","unstructured":"Wang YY, Zhang WW, Lu Z, Sun J, Jing M (2024) Optimal resource allocation model for COVID-19: a systematic review and meta-analysis. BMC Infect Dis 24:200","journal-title":"BMC Infect Dis"},{"issue":"12","key":"488_CR73","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1136\/medethics-2012-100750","volume":"38","author":"A Wardrope","year":"2012","unstructured":"Wardrope A (2012) Scarce vaccine supplies in an influenza pandemic should not be distributed randomly: reply to McLachlan. J Med Ethics 38(12):765\u2013767","journal-title":"J Med Ethics"},{"issue":"5","key":"488_CR74","doi-asserted-by":"publisher","first-page":"510","DOI":"10.1001\/jama.2020.11787","volume":"324","author":"SH Woolf","year":"2020","unstructured":"Woolf SH, Chapman DA, Sabo RT, Weinberger DM, Hill L (2020) Excess deaths from COVID-19 and other causes. JAMA 324(5):510\u2013513","journal-title":"JAMA"},{"issue":"1627","key":"488_CR75","doi-asserted-by":"publisher","first-page":"2811","DOI":"10.1098\/rspb.2007.0893","volume":"274","author":"JT Wu","year":"2007","unstructured":"Wu JT, Riley S, Leung GM (2007) Patial considerations for the allocation of pre-pandemic influenza vaccination in the United States. Proc Royal Soc b: Biol Sci 274(1627):2811\u20132817","journal-title":"Proc Royal Soc b: Biol Sci"},{"key":"488_CR76","doi-asserted-by":"publisher","first-page":"101052","DOI":"10.1016\/j.cegh.2022.101052","volume":"15","author":"N Yaladanda","year":"2022","unstructured":"Yaladanda N, Mopuri R, Vavilala HP, Mutheneni SR (2022) Modelling the impact of perfect and imperfect vaccination strategy against SARS CoV-2 by assuming varied vaccine efficacy over India. Clin Epidemiol Glob Health 15:101052","journal-title":"Clin Epidemiol Glob Health"},{"key":"488_CR77","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jmaa.2010.07.017","volume":"372","author":"W Yang","year":"2010","unstructured":"Yang W, Sun C, Arino J (2010) Global analysis for a general epidemiological model with vaccination and varying population. J Math Anal Appl 372:208\u2013223","journal-title":"J Math Anal Appl"},{"key":"488_CR78","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1016\/j.jval.2014.11.009","volume":"18","author":"M Yi","year":"2015","unstructured":"Yi M, Marathe A (2015) Fairness versus efficiency of vaccine allocation strategies. Value Health 18:278\u2013283","journal-title":"Value Health"},{"key":"488_CR79","doi-asserted-by":"publisher","first-page":"B73","DOI":"10.1016\/j.vaccine.2012.11.036","volume":"31","author":"M Zaffran","year":"2013","unstructured":"Zaffran M, Vandelaer J, Kristensen D, Melgaard B, Yadav P, Antwi-Agyei KO, Lasher H (2013) The imperative for stronger vaccine supply and logistics systems. Vaccine 31:B73\u2013B80","journal-title":"Vaccine"}],"container-title":["Theory in Biosciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12064-026-00488-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12064-026-00488-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12064-026-00488-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T06:04:57Z","timestamp":1785477897000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12064-026-00488-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,30]]},"references-count":76,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["488"],"URL":"https:\/\/doi.org\/10.1007\/s12064-026-00488-5","relation":{},"ISSN":["1431-7613","1611-7530"],"issn-type":[{"value":"1431-7613","type":"print"},{"value":"1611-7530","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,30]]},"assertion":[{"value":"19 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 July 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors have no conflict of interests to disclose.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}],"article-number":"40"}}