Research article Special Issues

A stochastic programming model of vaccine preparation and administration for seasonal influenza interventions

  • Received: 26 November 2019 Accepted: 10 March 2020 Published: 31 March 2020
  • This study considers the integration of vaccine preparation and administration decisions for seasonal influenza interventions. We examine actual vaccination activities of sharing multiple vaccine products and supplementary vaccinations. A two-stage stochastic program is formulated to determine the optimal ordering and allocation of vaccines under uncertain attack rates, vaccine efficacies, and demands. We present an algorithm based on the sample average approximation and warm-start solution to solve the stochastic integer program with continuous random variables. Furthermore, the optimal solution for the deterministic model using the expected value is analyzed and obtained directly. Our analysis compares the deterministic and stochastic solutions to assess the impact of uncertainties on the immunization outcomes and costs. The result shows that the stochastic programming model provides a more robust solution than the deterministic model, and uncertain characteristics should consider when making public health decisions.

    Citation: Sheng-I Chen, Chia-Yuan Wu. A stochastic programming model of vaccine preparation and administration for seasonal influenza interventions[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 2984-2997. doi: 10.3934/mbe.2020169

    Related Papers:

  • This study considers the integration of vaccine preparation and administration decisions for seasonal influenza interventions. We examine actual vaccination activities of sharing multiple vaccine products and supplementary vaccinations. A two-stage stochastic program is formulated to determine the optimal ordering and allocation of vaccines under uncertain attack rates, vaccine efficacies, and demands. We present an algorithm based on the sample average approximation and warm-start solution to solve the stochastic integer program with continuous random variables. Furthermore, the optimal solution for the deterministic model using the expected value is analyzed and obtained directly. Our analysis compares the deterministic and stochastic solutions to assess the impact of uncertainties on the immunization outcomes and costs. The result shows that the stochastic programming model provides a more robust solution than the deterministic model, and uncertain characteristics should consider when making public health decisions.


    加载中


    [1] Centers for Disease Control Taiwan, National infectious disease statistics system. Available from: http://nidss.cdc.gov.tw/ch/SingleDisease.aspx?dc=1&dt=4&disease=487a&position=1.
    [2] World Health Organization, Influenza (seasonal). Available from: http://www.who.int/mediacentre/factsheets/fs211/en/.
    [3] P. J. Chiu, C. H. Chen, Y. C. Chih, Effectiveness of the influenza vaccination program for the elderly in Taiwan, Vaccine, 31(2013), 632-638.
    [4] Organization for Economic Cooperation and Development, Health at a glance 2013-indicators. Available from: http://www.oecd.org/els/health-systems/Health-at-a-Glance-2013-Chart-set.pdf.
    [5] J. T. Wu, E. S. Ma, C. K. Lee, D. K. Chu, P. L. Ho, A. L. Shen, et al., The infection attack rate and severity of 2009 pandemic H1N1 influenza in Hong Kong, Clin. Infect. Dis., 51(2010), 1184-1191.
    [6] S. I. Chen, Economic benefits of sharing and redistributing influenza vaccines when shortages occurred, PLoS ONE, 12(2017): e0186418. https://doi.org/10.1371/journal.pone.0186418.
    [7] J. R. Birge, F. Louveaux, Introduction to stochastic programming second edition, Springer, New York, NY, 2011.
    [8] J. R. Birge, State-of-the-art survey-stochastic programming: computation and applications, Inform. J. Comput., 9(1997), 111-133.
    [9] H. Yarmand, J. S. Ivy, B. Denton, A. L. Lloyd, Optimal two-phase vaccine allocation to geographically different regions under uncertainty, European J. Operat. Res., 233(2014), 208-219.
    [10] L. J. Kornish, R. L. Keeny, Repeated commit-or-defer decisions with a deadline: The influenza vaccine composition, Operat. Res., 56(2008), 527-541.
    [11] S. Cho, C. S. Tang, Advance selling in a supply chain under uncertain supply and demand, Manufact. Serv. Operat. Manag., 15(2013), 305-319.
    [12] O. Y. Özaltin, O. A. Prokopyev, A. J. Schaefer, M. S. Roberts, Optimizing the societal benefits of the annual influenza vaccine: A stochastic programming approach, Operat. Res., 59(2011), 1131-1143.
    [13] S. I. Chen, C.Y. Wu, Y. H. Wu, M. W. Hsieh, Optimizing influenza vaccine policies for controlling 2009-like pandemics and regular outbreaks, Peer J., 7(2019), e6340.
    [14] B. Y. Lee, B. A. Norman, T. M. Assi, S. I. Chen, R. R. Bailey, J. Rajgopal, et al., Single versus multi-dose vaccine vials: An economic computational model, Vaccine, 28(2010), 5292-5300.
    [15] J. Rajgopal, D. L. Connor, T. M. Assi, B. A. Norman, S. I. Chen, R. R. Bailey, et al., The optimal number of routine vaccines to order at health clinics in low or middle income, Vaccine, 29(2011), 5512-5518. doi: 10.1016/j.vaccine.2011.05.044
    [16] S. I. Chen, B. A. Norman, J. Rajgopal, T. M. Assi, B. Y. Lee, B. Y. Brown, A planning model for the WHO-EPI vaccine distribution network in developing countries, IEEE Transact., 46(2014), 853-865.
    [17] E. D. Sewell, S. H. Jacobson, Using an integer programming model to determine the price of combination vaccines for childhood immunization, Ann. Operat. Res., 119(2003), 261-284.
    [18] S. E. Chick, H. Mamani, D. Simchi-Leviz, Supply chain coordination and influenza vaccination, Operat. Res., 56(2008), 1493-1506.
    [19] M. W. Tanner, L. Sattenspiel, L. Ntaimo, Finding optimal vaccination strategies under parameter uncertainty using stochastic programming, Math. Biosci., 215(2008), 144-151.
    [20] M. W. Tanner, L. Ntaimo, IIS branch-and-cut for joint chance-constrained stochastic programs and application to optimal vaccine allocation, European J. Operat. Res., 207(2010), 290-296.
    [21] Centers for Disease Control and Prevention, Seasonal influenza vaccine dosage and administration. Available from: http://www.cdc.gov/flu/about/qa/vaxadmin.htm.
    [22] Centers for Disease Control Taiwan, Press releases on 2014.12.23. Available from: http://www.cdc.gov.tw/professional/info.aspx?treeid=cf7f90dcbcd5718d&nowtreeid=f94e6af8daa9fc01&tid=7B8DA7ECE150E5F0.
    [23] M. T. Osterholm, N. S. Kelley, A. Sommer, E. A. Belongia, Efficacy and effectiveness of influenza vaccines: a systematic review and meta-analysis, Lancet Infect. Diseases, 12(2012), 36-44.
    [24] Centers for Disease Control Taiwan, Influenza vaccination rates. Available from: http://www.cdc.gov.tw/page.aspx?treeid=D78DE698C2E70A89&nowtreeid=AA2DBFC68E1A595C.
    [25] Centers for Disease Control Taiwan, Annual budget of immunization in 2015. Available from: http://www.cdc.gov.tw/info.aspx?treeid=5ff75185b74d8265&nowtreeid=63787137f7281d66&tid=D36EB3F2E94A255E.
    [26] A. Madansky, Inequalities for stochastic linear programming problems, Manag. Sci., 6(1960), 197-204.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(488) PDF downloads(281) Cited by(0)

Article outline

Figures and Tables

Figures(3)  /  Tables(3)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog