Optimal strategies of social distancing and vaccination against seasonal influenza

  • Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 August 2013
  • MSC : Primary: 49J15, 62P10.

  • Optimal control strategies for controlling seasonal influenza transmission in the US are of high interest, because of the significant epidemiological and economic burden of influenza. To evaluate optimal strategies of vaccination and social distancing, we used an age-structured dynamic model of seasonal influenza. We applied optimal control theory to identify the best way of reducing morbidity and mortality at a minimal cost. In combination with the Pontryagins maximum principle, we calculated time-dependent optimal policies of vaccination and social distancing to minimize the epidemiological and economic burden associated with seasonal influenza. We computed optimal age-specific intervention strategies and analyze them under various costs of interventions and disease transmissibility. Our results show that combined strategies have a stronger impact on the reduction of the final epidemic size. Our results also suggest that the optimal vaccination can be achieved by allocating most vaccines to preschool-age children (age under five) followed by young adults (age 20-39) and school age children (age 6-19). We find that the optimal vaccination rates for all age groups are highest at the beginning of the outbreak, requiring intense effort at the early phase of an epidemic. On the other hand, optimal social distancing of clinical cases tends to last the entire duration of an outbreak, and its intensity is relatively equal for all age groups. Furthermore, with higher transmissibility of the influenza virus (i.e. higher R0), the optimal control strategy needs to include more efforts to increase vaccination rates rather than efforts to encourage social distancing. Taken together, public health agencies need to consider both the transmissibility of the virus and ways to encourage early vaccination as well as voluntary social distancing of symptomatic cases in order to determine optimal intervention strategies against seasonal influenza.

    Citation: Eunha Shim. Optimal strategies of social distancing and vaccination against seasonal influenza[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1615-1634. doi: 10.3934/mbe.2013.10.1615

    Related Papers:

  • Optimal control strategies for controlling seasonal influenza transmission in the US are of high interest, because of the significant epidemiological and economic burden of influenza. To evaluate optimal strategies of vaccination and social distancing, we used an age-structured dynamic model of seasonal influenza. We applied optimal control theory to identify the best way of reducing morbidity and mortality at a minimal cost. In combination with the Pontryagins maximum principle, we calculated time-dependent optimal policies of vaccination and social distancing to minimize the epidemiological and economic burden associated with seasonal influenza. We computed optimal age-specific intervention strategies and analyze them under various costs of interventions and disease transmissibility. Our results show that combined strategies have a stronger impact on the reduction of the final epidemic size. Our results also suggest that the optimal vaccination can be achieved by allocating most vaccines to preschool-age children (age under five) followed by young adults (age 20-39) and school age children (age 6-19). We find that the optimal vaccination rates for all age groups are highest at the beginning of the outbreak, requiring intense effort at the early phase of an epidemic. On the other hand, optimal social distancing of clinical cases tends to last the entire duration of an outbreak, and its intensity is relatively equal for all age groups. Furthermore, with higher transmissibility of the influenza virus (i.e. higher R0), the optimal control strategy needs to include more efforts to increase vaccination rates rather than efforts to encourage social distancing. Taken together, public health agencies need to consider both the transmissibility of the virus and ways to encourage early vaccination as well as voluntary social distancing of symptomatic cases in order to determine optimal intervention strategies against seasonal influenza.


    加载中
    [1] Oxford University Press, Oxford, 1991.
    [2] Optimal Control Application Methods, 21 (2000), 269-285.
    [3] Bull World Health Organization, 90 (2012), 264-271.
    [4] $2^{nd}$ edition, Texts in Applied Mathematics, 40, Springer, New York, 2012.
    [5] Am. J. Epidemiol, 162 (2005), 1-8.
    [6] Value Health, 14 (2011), 800-811.
    [7] PLoS One, 4 (2009), e8164.
    [8] Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2000.
    [9] BMC Infect. Dis., 7 (2007).
    [10] Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975.
    [11] Proc. Natl. Acad. Sci. USA, 104 (2007), 5692-5697.
    [12] Hum. Vaccin. Immunother., 8 (2012), 21-28.
    [13] Emerg. Infect. Dis., 12 (2006), 1671-1681.
    [14] Math. Biosci., 235 (2012), 1-7.
    [15] PLoS One, 5 (2010), e12777.
    [16] Math. Biosci. Eng., 8 (2011), 183-197.
    [17] JAMA, 272 (1994), 1661-1665.
    [18] Ann. Intern. Med., 123 (1995), 518-527.
    [19] PLoS One, 6 (2011), e22087.
    [20] Med. J. Aust., 185 (2006), S35-8.
    [21] Br. Med. Bull., 92 (2009), 33-42.
    [22] J. R. Soc. Interface, 8 (2011), 661-670.
    [23] BMC Public Health, 9 (2009).
    [24] J. Theor. Biol., 265 (2010), 136-150.
    [25] Bull. Math. Biol., 74 (2012), 958-980.
    [26] Math. Biosci. Eng., 8 (2011), 171-182.
    [27] BMC Med., 7 (2009).
    [28] Chapman & Hall/CRC Mathematical and Computational Biology Series, Chapman & Hall/CRC, Boca Raton, FL, 2007.
    [29] BMC Infect. Dis., 10 (2010).
    [30] Am. J. Epidemiol., 161 (2005), 303-306.
    [31] Int. J. Infect. Dis., 8 (2004), 227-235.
    [32] Science, 325 (2009), 1705-1708.
    [33] BMC Public Health, 11 (2011), S11.
    [34] PLoS One, 3 (2008), e1839.
    [35] Vaccine, 25 (2007), 5086-5096.
    [36] Vaccine, 26 (2008), 3742-3749.
    [37] Euro. Surveill., 14 (2009), 19227.
    [38] Interscience Publishers John Wiley & Sons, Inc., New York-London, 1962.
    [39] Math. Biosci. Eng., 8 (2011), 141-170.
    [40] BMC Public Health, 11 (2011), S4.
    [41] Arch. Intern. Med., 165 (2005), 265-272.
    [42] Acta Biotheor, 59 (2011), 1-28.
    [43] JAMA, 292 (2004), 1333-1340.
    [44] JAMA, 289 (2003), 179-186.
    [45] Math. Biosci., 240 (2012), 241-249.
    [46] J. R. Soc. Interface, 9 (2012), 304-312.
    [47] PLoS One, 5 (2010), e10520.
    [48] Math. Biosci., 180 (2002), 29-48.
    [49] Am. J. Epidemiol., 160 (2004), 509-516.
    [50] Am. J. Epidemiol., 164 (2006), 936-944.
    [51] Vaccine, 23 (2005), 1284-1293.
    [52] Exp. Biol. Med. (Maywood), 236 (2011), 955-961.
    [53] Math. Biosci., 211 (2008), 166-185.
    [54] Available from: http://www.census.gov/population/international/data/idb/region.php.
    [55] (2009). Available from: http://www.cdc.gov/h1n1flu/vaccination/pdf/A-Wortley-H1N1-sample-clinic.pdf.
    [56] MMWR Recomm. Rep., 58(RR-10) (2009), 1-8.
    [57] MMWR Recomm. Rep., 47(RR-15) (1998), 1-14.
  • Reader Comments
  • © 2013 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(1620) PDF downloads(606) Cited by(32)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog