{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:27:28Z","timestamp":1753889248908,"version":"3.41.2"},"reference-count":56,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T00:00:00Z","timestamp":1724976000000},"content-version":"vor","delay-in-days":242,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Applied Computational Intelligence and Soft Computing"],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>The aim of this paper is to determine approximate Pareto optimal (efficient) pulse vaccination strategies for epidemics modeled by the susceptible\u2010infected\u2010removed (SIR) without population dynamics, characterized by a single epidemic wave. Pulse vaccination is the application of the vaccination campaign over a limited time interval, by vaccinating susceptible individuals at a constant vaccination rate. A pulse vaccination strategy includes the determination of the beginning date and duration of the campaign and the vaccination rate. SIR with vaccination (SIRV) epidemic model is applied during pulse vaccination campaign, resulting in final proportions of removed (<jats:italic>R<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub>) and vaccinated (<jats:italic>V<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub>) individuals at the end of the epidemic. The burden of the epidemic is estimated in terms of <jats:italic>R<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub> and <jats:italic>V<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub>; two criteria are simultaneously minimized: vaccination cost and treatment cost of infected individuals and other economic losses due to sickness that are assumed to be proportional to <jats:italic>V<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub> and <jats:italic>R<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub>, respectively. To find approximate efficient solutions to this bicriteria problem, ODE and genetic algorithm toolboxes of MATLAB are integrated (GA\u2010ODE). In GA\u2010ODE, an augmented weighted Tchebycheff program is used as the evaluation function, calculated by solving the SIRV model and obtaining <jats:italic>R<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub> and <jats:italic>V<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub> values. Sample approximate efficient vaccination strategies are determined for diseases with a basic reproduction number (<jats:italic>R<\/jats:italic><jats:sub>0<\/jats:sub>) 1.2 to 2.0. Consequently, obtained strategies are characterized as short\u2010period campaigns that start as early as possible, i.e., as soon as vaccines are available and the vaccination rate increases with the severity of the disease (<jats:italic>R<\/jats:italic><jats:sub>0<\/jats:sub>) and the importance weight given to minimization of <jats:italic>R<\/jats:italic><jats:sub><jats:italic>f<\/jats:italic><\/jats:sub>.<\/jats:p>","DOI":"10.1155\/2024\/5531062","type":"journal-article","created":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T15:48:31Z","timestamp":1725032911000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Bicriteria Model to Determine Pareto Optimal Pulse Vaccination Strategies"],"prefix":"10.1155","volume":"2024","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3838-8824","authenticated-orcid":false,"given":"Funda","family":"Samanlioglu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nauman","family":"Tabassum","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5562-6367","authenticated-orcid":false,"given":"Tolga Kudret","family":"Karaca","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6043-0833","authenticated-orcid":false,"given":"Ayse Humeyra","family":"Bilge","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,8,30]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_11_1_2","DOI":"10.1016\/S0092-8240(05)80042-4"},{"doi-asserted-by":"publisher","key":"e_1_2_11_2_2","DOI":"10.1155\/2016\/5965836"},{"doi-asserted-by":"publisher","key":"e_1_2_11_3_2","DOI":"10.1007\/s00285-014-0838-z"},{"doi-asserted-by":"publisher","key":"e_1_2_11_4_2","DOI":"10.1142\/S1793524518500213"},{"doi-asserted-by":"publisher","key":"e_1_2_11_5_2","DOI":"10.1073\/pnas.90.24.11698"},{"doi-asserted-by":"publisher","key":"e_1_2_11_6_2","DOI":"10.1007\/s00285-016-0997-1"},{"doi-asserted-by":"publisher","key":"e_1_2_11_7_2","DOI":"10.1142\/9789814261265_0006"},{"doi-asserted-by":"publisher","key":"e_1_2_11_8_2","DOI":"10.1038\/nrmicro1845"},{"doi-asserted-by":"publisher","key":"e_1_2_11_9_2","DOI":"10.1155\/2013\/670263"},{"doi-asserted-by":"publisher","key":"e_1_2_11_10_2","DOI":"10.2807\/ese.14.41.19358-en"},{"doi-asserted-by":"publisher","key":"e_1_2_11_11_2","DOI":"10.1007\/978-3-0348-0122-5"},{"doi-asserted-by":"publisher","key":"e_1_2_11_12_2","DOI":"10.2807\/ese.17.04.20064-en"},{"doi-asserted-by":"publisher","key":"e_1_2_11_13_2","DOI":"10.3390\/electronics11223711"},{"doi-asserted-by":"publisher","key":"e_1_2_11_14_2","DOI":"10.1016\/S0096-3003(03)00331-X"},{"doi-asserted-by":"publisher","key":"e_1_2_11_15_2","DOI":"10.1016\/j.amc.2007.12.019"},{"doi-asserted-by":"publisher","key":"e_1_2_11_16_2","DOI":"10.1155\/2015\/532494"},{"doi-asserted-by":"publisher","key":"e_1_2_11_17_2","DOI":"10.1016\/j.idm.2023.08.001"},{"doi-asserted-by":"publisher","key":"e_1_2_11_18_2","DOI":"10.1016\/j.rinp.2023.107028"},{"doi-asserted-by":"publisher","key":"e_1_2_11_19_2","DOI":"10.1016\/j.amc.2007.07.083"},{"doi-asserted-by":"publisher","key":"e_1_2_11_20_2","DOI":"10.1016\/j.cam.2011.05.040"},{"doi-asserted-by":"publisher","key":"e_1_2_11_21_2","DOI":"10.1016\/S0092-8240(98)90005-2"},{"doi-asserted-by":"publisher","key":"e_1_2_11_22_2","DOI":"10.1080\/19488300.2012.666780"},{"doi-asserted-by":"publisher","key":"e_1_2_11_23_2","DOI":"10.1016\/j.jtbi.2019.02.013"},{"doi-asserted-by":"publisher","key":"e_1_2_11_24_2","DOI":"10.1016\/j.chaos.2018.12.023"},{"volume-title":"Sociophysics Approach to Epidemics, Series (Evolutionary Economics and Social Complexity Science)","year":"2021","author":"Tanimoto J.","key":"e_1_2_11_25_2"},{"doi-asserted-by":"publisher","key":"e_1_2_11_26_2","DOI":"10.1371\/journal.pone.0030018"},{"doi-asserted-by":"publisher","key":"e_1_2_11_27_2","DOI":"10.2807\/ese.15.31.19633-en"},{"unstructured":"MathWorksM. Genetic algorithm 2018 https:\/\/www.mathworks.com\/help\/gads\/genetic-algorithm.html.","key":"e_1_2_11_28_2"},{"unstructured":"MathWorksM. Ode45 2018 https:\/\/www.mathworks.com\/help\/matlab\/ref\/ode45.html.","key":"e_1_2_11_29_2"},{"volume-title":"Adaptation in Natural and Artificial Systems","year":"1975","author":"Holland J. H.","key":"e_1_2_11_30_2"},{"doi-asserted-by":"publisher","key":"e_1_2_11_31_2","DOI":"10.1155\/2013\/506240"},{"key":"e_1_2_11_32_2","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1007\/978-3-319-95165-2_5","volume-title":"Computational Science and its Applications \u2013 ICCSA 2018","author":"Rodrigues R. F.","year":"2018"},{"doi-asserted-by":"publisher","key":"e_1_2_11_33_2","DOI":"10.1109\/TFUZZ.2018.2843330"},{"doi-asserted-by":"publisher","key":"e_1_2_11_34_2","DOI":"10.1016\/j.asoc.2016.08.017"},{"doi-asserted-by":"publisher","key":"e_1_2_11_35_2","DOI":"10.1016\/j.jtbi.2004.11.032"},{"doi-asserted-by":"publisher","key":"e_1_2_11_36_2","DOI":"10.1007\/s10845-013-0773-7"},{"doi-asserted-by":"publisher","key":"e_1_2_11_37_2","DOI":"10.1016\/j.mbs.2015.08.019"},{"doi-asserted-by":"publisher","key":"e_1_2_11_38_2","DOI":"10.1126\/science.abe6959"},{"doi-asserted-by":"publisher","key":"e_1_2_11_39_2","DOI":"10.1007\/s10479-022-04926-7"},{"doi-asserted-by":"publisher","key":"e_1_2_11_40_2","DOI":"10.1016\/j.ins.2023.119065"},{"doi-asserted-by":"publisher","key":"e_1_2_11_41_2","DOI":"10.14745\/ccdr.v48i10a05"},{"doi-asserted-by":"publisher","key":"e_1_2_11_42_2","DOI":"10.1016\/j.ibmed.2022.100060"},{"doi-asserted-by":"publisher","key":"e_1_2_11_43_2","DOI":"10.1155\/2014\/702973"},{"doi-asserted-by":"publisher","key":"e_1_2_11_44_2","DOI":"10.1016\/j.asoc.2016.11.010"},{"doi-asserted-by":"publisher","key":"e_1_2_11_45_2","DOI":"10.1016\/j.chaos.2020.109892"},{"doi-asserted-by":"publisher","key":"e_1_2_11_46_2","DOI":"10.1002\/mma.8874"},{"doi-asserted-by":"publisher","key":"e_1_2_11_47_2","DOI":"10.26713\/cma.v10i4.1172"},{"doi-asserted-by":"publisher","key":"e_1_2_11_48_2","DOI":"10.1186\/s13662-021-03347-3"},{"doi-asserted-by":"publisher","key":"e_1_2_11_49_2","DOI":"10.3390\/physics3020028"},{"doi-asserted-by":"publisher","key":"e_1_2_11_50_2","DOI":"10.1057\/palgrave.jors.2600611"},{"doi-asserted-by":"publisher","key":"e_1_2_11_51_2","DOI":"10.1007\/bf02591870"},{"volume-title":"Multiple Criteria Optimization: Theory, Computation, and Application","year":"1989","author":"Steuer R. E.","key":"e_1_2_11_52_2"},{"key":"e_1_2_11_53_2","first-page":"25","article-title":"Advantages and disadvantages of using MATLAB\/ode45 for solving differential equations in engineering applications","volume":"7","author":"Ahmed W.","year":"2013","journal-title":"International Journal of Engineering"},{"doi-asserted-by":"publisher","key":"e_1_2_11_54_2","DOI":"10.1016\/J.CIE.2008.01.005"},{"doi-asserted-by":"publisher","key":"e_1_2_11_55_2","DOI":"10.1504\/IJOR.2007.011443"},{"doi-asserted-by":"publisher","key":"e_1_2_11_56_2","DOI":"10.1016\/j.mbs.2017.07.011"}],"container-title":["Applied Computational Intelligence and Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2024\/5531062","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T15:48:39Z","timestamp":1725032919000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2024\/5531062"}},"subtitle":[],"editor":[{"given":"Anandakumar","family":"Haldorai","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":56,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["10.1155\/2024\/5531062"],"URL":"https:\/\/doi.org\/10.1155\/2024\/5531062","archive":["Portico"],"relation":{},"ISSN":["1687-9724","1687-9732"],"issn-type":[{"type":"print","value":"1687-9724"},{"type":"electronic","value":"1687-9732"}],"subject":[],"published":{"date-parts":[[2024,1]]},"assertion":[{"value":"2024-01-30","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-08-14","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-08-30","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5531062"}}