{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T10:46:05Z","timestamp":1761561965685,"version":"3.41.2"},"reference-count":26,"publisher":"Emerald","issue":"3","license":[{"start":{"date-parts":[[2015,3,2]],"date-time":"2015-03-02T00:00:00Z","timestamp":1425254400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,3,2]]},"abstract":"<jats:sec>\n               <jats:title content-type=\"abstract-heading\">Purpose<\/jats:title>\n               <jats:p> \u2013 The purpose of this paper is to use analytical method and optimization tools to suggest time-optimal vaccination program for a basic SIR epidemic model with mass action contact rate when supply is limited. <\/jats:p>\n            <\/jats:sec>\n            <jats:sec>\n               <jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title>\n               <jats:p> \u2013 The Lagrange Multiplier Method and Pontryagin\u2019s Maximum Principle are used to explore optimal control strategy and obtain analytical solution for the control system to minimize the total cost of disease with boundary constraint. The numerical simulation is done with Matlab using the sequential linear programming method to illustrate the impact of parameters. <\/jats:p>\n            <\/jats:sec>\n            <jats:sec>\n               <jats:title content-type=\"abstract-heading\">Findings<\/jats:title>\n               <jats:p> \u2013 The result highlighted that the optimal control strategy is Bang-Bang control \u2013 to vaccinate with maximal effort until either all of the resources are used up or epidemic is over, and the optimal strategies and total cost of vaccination are usually dependent on whether there is any constraint of resource, however, the optimal strategy is independent on the relative cost of vaccination when the supply is limited. <\/jats:p>\n            <\/jats:sec>\n            <jats:sec>\n               <jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title>\n               <jats:p> \u2013 The research indicate a practical view that the enhancement of daily vaccination rate is critical to make effective initiatives to prevent epidemic from out breaking and reduce the costs of control. <\/jats:p>\n            <\/jats:sec>\n            <jats:sec>\n               <jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title>\n               <jats:p> \u2013 The analysis of the time-optimal application of outbreak control is of clear practical value and the introducing of resource constraint in epidemic control is of realistic sense, these are beneficial for epidemiologists and public health officials.<\/jats:p>\n            <\/jats:sec>","DOI":"10.1108\/k-05-2014-0103","type":"journal-article","created":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T07:38:40Z","timestamp":1427269120000},"page":"475-486","source":"Crossref","is-referenced-by-count":5,"title":["Optimal vaccination policy and cost analysis for epidemic control in resource-limited settings"],"prefix":"10.1108","volume":"44","author":[{"given":"Kuan","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ermei","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinggao","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"key":"key2020122523025101200_b1","doi-asserted-by":"crossref","unstructured":"Abakuks, A.\n                (1974), \u201cOptimal immunisation policies for epidemics\u201d, \n                  Advances in Applied Probability\n               , Vol. 6 No. 3, pp. 494-511.","DOI":"10.2307\/1426230"},{"key":"key2020122523025101200_b2","doi-asserted-by":"crossref","unstructured":"Behncke, H.\n                (2000), \u201cOptimal control of deterministic epidemics\u201d, \n                  Optimal Control Applications and Methods\n               , Vol. 21 No. 6, pp. 269-285.","DOI":"10.1002\/oca.678"},{"key":"key2020122523025101200_b3","doi-asserted-by":"crossref","unstructured":"Bridges, C.B.\n               , \n                  Kuehnert, M.J.\n                and \n                  Hall, C.B.\n                (2003), \u201cTransmission of influenza: implications for control in health care settings\u201d, \n                  Clinical Infectious Diseases\n               , Vol. 37 No. 8, pp. 1094-1101.","DOI":"10.1086\/378292"},{"key":"key2020122523025101200_b4","unstructured":"Bryson, A.E.\n                (1975), \n                  Applied Optimal Control-Optimization, Estimation and Control\n               , CRC Press, Boca Raton, Florida."},{"key":"key2020122523025101200_b5","doi-asserted-by":"crossref","unstructured":"Carrat, F.\n               , \n                  Luong, J.\n               , \n                  Lao, H.\n               , \n                  Sall\u00e9, A.V.\n               , \n                  Lajaunie, C.\n                and \n                  Wackernagel, H.\n                (2006), \u201cA \u2018small-world-like\u2019 model for comparing interventions aimed at preventing and controlling influenza pandemics\u201d, \n                  BMC Medicine\n               , Vol. 4 No. 3, pp. 26-40.","DOI":"10.1186\/1741-7015-4-26"},{"key":"key2020122523025101200_b6","unstructured":"Castilho, C.\n                (2006), \u201cOptimal control of an epidemic through educational campaigns\u201d, \n                  Electronic Journal of Differential Equations\n               , Vol. 2006 No. 125, pp. 1-11."},{"key":"key2020122523025101200_b7","doi-asserted-by":"crossref","unstructured":"Cauchemez, S.\n               , \n                  Carrat, F.\n               , \n                  Viboud, C.\n               , \n                  Valleron, A.J.\n                and \n                  Boelle, P.Y.\n                (2004), \u201cA Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data\u201d, \n                  Statistics in Medicine\n               , Vol. 23 No. 22, pp. 3469-3487.","DOI":"10.1002\/sim.1912"},{"key":"key2020122523025101200_b8","doi-asserted-by":"crossref","unstructured":"Elderd, B.D.\n               , \n                  Dukic, V.M.\n                and \n                  Dwyer, G.\n                (2006), \u201cUncertainty in predictions of diseases spread and public health responses to bioterrorism and emerging diseases\u201d, \n                  Proceedings of the National Academy of Sciences\n               , Vol. 103 No. 42, pp. 15639-15697.","DOI":"10.1073\/pnas.0600816103"},{"key":"key2020122523025101200_b9","doi-asserted-by":"crossref","unstructured":"Hansen, E.\n                and \n                  Day, T.\n                (2011), \u201cOptimal control of epidemics with limited resources\u201d, \n                  Journal of Mathematical Biology\n               , Vol. 62 No. 3, pp. 423-451.","DOI":"10.1007\/s00285-010-0341-0"},{"key":"key2020122523025101200_b10","doi-asserted-by":"crossref","unstructured":"Hill, A.N.\n                and \n                  Longini, I.M. Jr\n                (2003), \u201cThe critical vaccination fraction for heterogeneous epidemic models\u201d, \n                  Mathematical Biosciences\n               , Vol. 181 No. 1, pp. 85-106.","DOI":"10.1016\/S0025-5564(02)00129-3"},{"key":"key2020122523025101200_b11","unstructured":"Hull, D.\n                (2003), \n                  Optimal Control Theory for Applications\n               , Springer, Berlin, Heidelberg, New York, NY."},{"key":"key2020122523025101200_b12","unstructured":"Kamien, M.I.\n                and \n                  Schwartz, N.L.\n                (2012), \n                  Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management\n               , Courier Dover Publications, New York, NY."},{"key":"key2020122523025101200_b200","unstructured":"Kermark, W.O.\n                and \n                  Mckendrick, A.G.\n                (1927), \u201cContributions to the mathematical theory of epidemics I\u201d, \n                  Proceedings of the Royal Society A\n               , Vol. 115, No. 5, pp. 700-721."},{"key":"key2020122523025101200_b14","doi-asserted-by":"crossref","unstructured":"Lipsitch, M.\n               , \n                  Cohen, T.\n               , \n                  Cooper, B.\n               , \n                  Robins, J.M.\n               , \n                  Ma, S.\n               , \n                  James, L.\n                and \n                  Murray, M.\n                (2003), \u201cTransmission dynamics and control of severe acute respiratory syndrome\u201d, \n                  Science\n               , Vol. 300 No. 5627, pp. 1966-1970.","DOI":"10.1126\/science.1086616"},{"key":"key2020122523025101200_b15","doi-asserted-by":"crossref","unstructured":"Magombedze, G.\n               , \n                  Mukandavire, Z.\n               , \n                  Chiyaka, C.\n                and \n                  Musuka, G.\n                (2009), \u201cOptimal control of a sex-structured HIV\/AIDS model with condom use\u201d, \n                  Mathematical Modelling and Analysis\n               , Vol. 14 No. 4, pp. 483-494.","DOI":"10.3846\/1392-6292.2009.14.483-494"},{"key":"key2020122523025101200_b16","doi-asserted-by":"crossref","unstructured":"Mills, C.E.\n               , \n                  Robins, J.M.\n                and \n                  Lipsitch, M.\n                (2004), \u201cTransmissibility of 1918 pandemic influenza\u201d, \n                  Nature\n               , Vol. 432 No. 7019, pp. 904-906.","DOI":"10.1038\/nature03063"},{"key":"key2020122523025101200_b17","doi-asserted-by":"crossref","unstructured":"Morton, R.\n                and \n                  Wickwire, K.H.\n                (1974), \u201cOn the optimal control of a deterministic epidemic\u201d, \n                  Advances in Applied Probability\n               , Vol. 6 No. 4, pp. 622-635.","DOI":"10.2307\/1426183"},{"key":"key2020122523025101200_b18","doi-asserted-by":"crossref","unstructured":"Okosun, K.O.\n               , \n                  Makinde, O.D.\n                and \n                  Takaidza, I.\n                (2013), \u201cAnalysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV\/AIDS epidemic\u201d, \n                  Journal of Biological Physics\n               , Vol. 39 No. 1, pp. 99-121.","DOI":"10.1007\/s10867-012-9288-2"},{"key":"key2020122523025101200_b19","unstructured":"Pontryagin, L.S.\n                (1987), \n                  Mathematical Theory of Optimal Processes\n               , CRC Press, Boca Raton, Florida."},{"key":"key2020122523025101200_b20","doi-asserted-by":"crossref","unstructured":"Riley, S.\n               , \n                  Fraser, C.\n               , \n                  Donnelly, C.A.\n               , \n                  Ghani, A.C.\n               , \n                  Abu-Raddad, L.J.\n               , \n                  Hedley, A.J.\n                and \n                  Anderson, R.M.\n                (2003), \u201cTransmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health intervention\u201d, \n                  Science\n               , Vol. 300 No. 5627, pp. 1961-1966.","DOI":"10.1126\/science.1086478"},{"key":"key2020122523025101200_b21","doi-asserted-by":"crossref","unstructured":"Riley, S.\n                and \n                  Ferguson, N.M.\n                (2007), \u201cSmallpox transmission and control: spatial dynamics in Great Britain\u201d, \n                  Proceedings of the National Academy of Sciences\n               , Vol. 103 No. 33, pp. 12637-12642.","DOI":"10.1073\/pnas.0510873103"},{"key":"key2020122523025101200_b22","doi-asserted-by":"crossref","unstructured":"Rodrigues, H.S.\n               , \n                  Monteiro, M.T.T.\n                and \n                  Torres, D.F.M.\n                (2014), \u201cVaccination models and optimal control strategies to dengue\u201d, \n                  Mathematical Biosciences\n               , Vol. 247, pp. 1-12.","DOI":"10.1016\/j.mbs.2013.10.006"},{"key":"key2020122523025101200_b23","doi-asserted-by":"crossref","unstructured":"Sethi, S.P.\n                (1978), \u201cOptimal quarantine programmes for controlling an epidemic spread\u201d, \n                  Journal of the Operational Research Society\n               , Vol. 29 No. 3, pp. 265-268.","DOI":"10.1057\/jors.1978.55"},{"key":"key2020122523025101200_b24","doi-asserted-by":"crossref","unstructured":"Tanner, M.W.\n               , \n                  Sattenspiel, L.\n                and \n                  Ntaimo, L.\n                (2008), \u201cFinding optimal vaccination strategies under parameter uncertainty using stochastic programming\u201d, \n                  Mathematical Biosciences\n               , Vol. 215 No. 2, pp. 144-151.","DOI":"10.1016\/j.mbs.2008.07.006"},{"key":"key2020122523025101200_b25","doi-asserted-by":"crossref","unstructured":"Wickwire, K.H.\n                (1975), \u201cOptimal isolation policies for deterministic and stochastic epidemics\u201d, \n                  Mathematical Biosciences\n               , Vol. 26 No. 3, pp. 325-346.","DOI":"10.1016\/0025-5564(75)90020-6"},{"key":"key2020122523025101200_b26","doi-asserted-by":"crossref","unstructured":"Zhou, Y.\n               , \n                  Yang, K.\n               , \n                  Zhou, K.\n                and \n                  Liang, Y.\n                (2014), \u201cOptimal vaccination policies for an SIR model with limited resources\u201d, \n                  Acta Biotheoretica\n               , Vol. 62 No. 2, pp. 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