Optimal strategies of social distancing and vaccination against seasonal influenza

Mathematical Biosciences and Engineering

Volumn 10, Issue 5-6, 2013, Pages 1615-1634

  Shim, Eunha ^a  

^a The University of Tulsa   (United States)

Author keywords

Influenza; Optimal control theory; Social distancing; Vaccination

Indexed keywords

INFLUENZA VACCINE;

ADOLESCENT; ADULT; ARTICLE; BASIC REPRODUCTION NUMBER; CHILD; DISEASE TRANSMISSION; EPIDEMIC; EPIDEMIOLOGY; HUMAN; INFANT; INFLUENZA; MIDDLE AGED; PATIENT CARE; PRESCHOOL CHILD; PROBABILITY; SEASON; THEORETICAL MODEL; TIME; UNITED STATES; YOUNG ADULT;

ADOLESCENT; ADULT; BASIC REPRODUCTION NUMBER; CHILD; CHILD, PRESCHOOL; DISEASE OUTBREAKS; EPIDEMIOLOGY; HUMANS; INFANT; INFLUENZA VACCINES; INFLUENZA, HUMAN; MIDDLE AGED; MODELS, THEORETICAL; PATIENT ISOLATION; PROBABILITY; SEASONS; TIME FACTORS; UNITED STATES; YOUNG ADULT;

EID: 84884483256     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2013.10.1615     Document Type: Article

References (57)

1. R. M. Anderson and R. M. May, "Infectious Diseases of Humans," Oxford University Press, Oxford, 1991.
2. H. Behnke, Optimal control of deterministic epidemics, Optimal Control Application Meth-ods, 21 (2000), 269-285.
3. K. J. Bolton, J. M. McCaw, R. Moss, R. S. Morris, S. Wang, A. Burma, B. Darma, D. Narangerel, P. Nymadawa and J. McVernon, Likely effectiveness of pharmaceutical and non-pharmaceutical interventions for mitigating influenza virus transmission in Mongolia, Bull World Health Organization, 90 (2012), 264-271.
4. F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epi-demiology," 2nd edition, Texts in Applied Mathematics, 40, Springer, New York, 2012.
5. J. S. Brownstein, K. P. Kleinman and K. D. Mandl, Identifying pediatric age groups for influenza vaccination using a real-time regional surveillance system, Am. J. Epidemiol, 162 (2005), 1-8.
6. K. M. Clements, J. Chancellor, K. Nichol, K. DeLong and D. Thompson, Cost-effectiveness of a recommendation of universal mass vaccination for seasonal influenza in the United States, Value Health, 14 (2011), 800-811.
7. G. Chowell, C. Viboud, X. Wang, S. M. Bertozzi and M. A. Miller, Adaptive vaccination strategies to mitigate pandemic influenza: Mexico as a case study, PLoS One, 4 (2009), e8164.
8. O. Diekmann and J. Heesterbeek, "Mathematical Epidmeiology of Infectious Diseases: Model Building, Analysis and Interpretation," Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2000.
9. H. P. Duerr, S. O. Brockmann, I. Piechotowski, M. Schwehm and M. Eichner, Influenza pandemic intervention planning using InfluSim: Pharmaceutical and non-pharmaceutical in-terventions, BMC Infect. Dis., 7 (2007).
10. W. H. Fleming and R. W. Rishel, "Deterministic and Stochastic Optimal Control," Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975.
11. A. P. Galvani, T. C. Reluga and G. B. Chapman, Long-standing influenza vaccination policy is in accord with individual self-interest but not with the utilitarian optimum, Proc. Natl. Acad. Sci. USA, 104 (2007), 5692-5697. (Pubitemid 47175742)
12. R. Gasparini, D. Amicizia, P. L. Lai and D. Panatto, Clinical and socioeconomic impact of seasonal and pandemic influenza in adults and the elderly, Hum. Vaccin. Immunother., 8 (2012), 21-28.
13. R. J. Glass, L. M. Glass, W. E. Beyeler and H. J. Min, Targeted social distancing design for pandemic influenza, Emerg. Infect. Dis., 12 (2006), 1671-1681. (Pubitemid 44674242)
14. J. Glasser, Z. Feng, A. Moylan, S. Del Valle and C. Castillo-Chavez, Mixing in age-structured population models of infectious diseases, Math. Biosci., 235 (2012), 1-7.
15. J. Glasser, D. Taneri, Z. Feng, J. H. Chuang, P. Tll, W. Thompson, M. McCauley and J. Alexander, Evaluation of targeted influenza vaccination strategies via population modeling, PLoS One, 5 (2010), e12777.
16. P. A. Gonzalez-Parra, S. Lee, L. Velazquez and C. Castillo-Chavez, A note on the use of optimal control on a discrete time model of influenza dynamics, Math. Biosci. Eng., 8 (2011), 183-197.
17. T. M. Govaert, C. T. Thijs, N. Masurel, M. J. Sprenger, G. J. Dinant and J. A. Knot-tnerus, The efficacy of influenza vaccination in elderly individuals. A randomized double-blind placebo-controlled trial, JAMA, 272 (1994), 1661-1665. (Pubitemid 24359136)
18. P. A. Gross, A. W. Hermogenes, H. S. Sacks, J. Lau and R. A. Levandowski, The efficacy of influenza vaccine in elderly persons. A meta-analysis and review of the literature, Ann. Intern. Med., 123 (1995), 518-527.
19. N. Halder, J. K. Kelso and G. J. Milne, Cost-effective strategies for mitigating a future influenza pandemic with H1N1 2009 characteristics, PLoS One, 6 (2011), e22087.
20. J. S. Horvath, M. McKinnon and L. Roberts, The Australian response: Pandemic influenza preparedness, Med. J. Aust., 185 (2006), S35-8. (Pubitemid 44823404)
21. M. J. Keeling and L. Danon, Mathematical modelling of infectious diseases, Br. Med. Bull., 92 (2009), 33-42.
22. M. J. Keeling and P. J. White, Targeting vaccination against novel infections: Risk, age and spatial structure for pandemic influenza in Great Britain, J. R. Soc. Interface, 8 (2011), 661-670.
23. J. K. Kelso, G. J. Milne and H. Kelly, Simulation suggests that rapid activation of social distancing can arrest epidemic development due to a novel strain of influenza, BMC Public Health, 9 (2009).
24. S. Lee, G. Chowell and C. Castillo-Chavez, Optimal control for pandemic influenza: The role of limited antiviral treatment and isolation, J. Theor. Biol., 265 (2010), 136-150.
25. S. Lee, M. Golinski and G. Chowell, Modeling optimal age-specific vaccination strategies against pandemic influenza, Bull. Math. Biol., 74 (2012), 958-980.
26. S. Lee, R. Morales and C. Castillo-Chavez, A note on the use of influenza vaccination strate-gies when supply is limited, Math. Biosci. Eng., 8 (2011), 171-182.
27. V. J. Lee, D. C. Lye and A. Wilder-Smith, Combination strategies for pandemic influenza response - a systematic review of mathematical modeling studies, BMC Med., 7 (2009).
28. S. Lenhart and J. T. Workman, "Optimal Control Applied to Biological Models," Chapman & Hall/CRC Mathematical and Computational Biology Series, Chapman & Hall/CRC, Boca Raton, FL, 2007.
29. F. Lin, K. Muthuraman and M. Lawley, An optimal control theory approach to non-pharma-ceutical interventions, BMC Infect. Dis., 10 (2010).
30. I. M. Longini, Jr. and M. E. Halloran, Strategy for distribution of influenza vaccine to high-risk groups and children, Am. J. Epidemiol., 161 (2005), 303-306. (Pubitemid 40256201)
31. A. M. McBean and P. L. Hebert, New estimates of influenza-related pneumonia and influenza hospitalizations among the elderly, Int. J. Infect. Dis., 8 (2004), 227-235. (Pubitemid 38953678)
32. J. Medlock and A. P. Galvani, Optimizing influenza vaccine distribution, Science, 325 (2009), 1705-1708.
33. G. N. Mercer, S. I. Barry and H. Kelly, Modelling the effect of seasonal influenza vaccination on the risk of pandemic influenza infection, BMC Public Health, 11 (2011), S11.
34. S. M. Moghadas, C. S. Bowman, G. Rst and J. Wu, Population-wide emergence of antiviral resistance during pandemic influenza, PLoS One, 3 (2008), e1839.
35. N. A. Molinari, I. R. Ortega-Sanchez, M. L. Messonnier, W. W. Thompson, P. M. Wortley, E. Weintraub and C. B. Bridges, The annual impact of seasonal influenza in the US: Measuring disease burden and costs, Vaccine, 25 (2007), 5086-5096. (Pubitemid 46879994)
36. S. D. Mylius, T. J. Hagenaars, A. K. Lugnr and J. Wallinga, Optimal allocation of pandemic influenza vaccine depends on age, risk and timing, Vaccine, 26 (2008), 3742-3749.
37. H. Nishiura, C. Castillo-Chavez, M. Safan and G. Chowell, Transmission potential of the new influenza A(H1N1) virus and its age-specificity in Japan, Euro. Surveill., 14 (2009), 19227.
38. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathe-matical Theory of Optimal Processes," Interscience Publishers John Wiley & Sons, Inc., New York-London, 1962.
39. O. Prosper, O. Saucedo, D. Thompson, G. Torres-Garcia, X. Wang and C. Castillo-Chavez, Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 in-fluenza, Math. Biosci. Eng., 8 (2011), 141-170.
40. E. Shim, L. A. Meyers and A. P. Galvani, Optimal H1N1 vaccination strategies based on self-interest versus group interest, BMC Public Health, 11 (2011), S4.
41. L. Simonsen, T. A. Reichert, C. Viboud, W. C. Blackwelder, R. J. Taylor and M. A. Miller, Impact of influenza vaccination on seasonal mortality in the US elderly population, Arch. Intern. Med., 165 (2005), 265-272. (Pubitemid 40216277)
42. J. M. Tchuenche, S. A. Khamis, F. B. Agusto and S. C. Mpeshe, Optimal control and sen-sitivity analysis of an influenza model with treatment and vaccination, Acta Biotheor, 59 (2011), 1-28.
43. W. W. Thompson, D. K. Shay, E. Weintraub, L. Brammer, C. B. Bridges, N. J. Cox and K. Fukuda, Influenza-associated hospitalizations in the United States, JAMA, 292 (2004), 1333-1340. (Pubitemid 39223224)
44. W. W. Thompson, D. K. Shay, E. Weintraub, L. Brammer, N. Cox, L. J. Anderson and K. Fukuda, Mortality associated with influenza and respiratory syncytial virus in the United States, JAMA, 289 (2003), 179-186. (Pubitemid 36068705)
45. S. Towers and Z. Feng, Social contact patterns and control strategies for influenza in the elderly, Math. Biosci., 240 (2012), 241-249.
46. J. Truscott, C. Fraser, S. Cauchemez, A. Meeyai, W. Hinsley, C. A. Donnelly, A. Ghani and N. Ferguson, Essential epidemiological mechanisms underpinning the transmission dynamics of seasonal influenza, J. R. Soc. Interface, 9 (2012), 304-312.
47. A. R. Tuite, D. N. Fisman, J. C. Kwong and A. L. Greer, Optimal pandemic influenza vaccine allocation strategies for the Canadian population, PLoS One, 5 (2010), e10520.
48. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. (Pubitemid 35304346)
49. J. Wallinga and P. Teunis, Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures, Am. J. Epidemiol., 160 (2004), 509-516. (Pubitemid 39215626)
50. J. Wallinga, P. Teunis and M. Kretzschmar, Using data on social contacts to estimate age-spe-cific transmission parameters for respiratory-spread infectious agents, Am. J. Epidemiol., 164 (2006), 936-944. (Pubitemid 44729833)
51. D. Weycker, J. Edelsberg, M. E. Halloran, I. M. Longini, Jr., A. Nizam, V. Ciuryla and G. Oster, Population-wide benefits of routine vaccination of children against influenza, Vaccine, 23 (2005), 1284-1293. (Pubitemid 40126532)
52. J. T. Wu and B. J. Cowling, The use of mathematical models to inform influenza pandemic preparedness and response, Exp. Biol. Med. (Maywood), 236 (2011), 955-961.
53. P. Zhang and P. M. Atkinson, Modelling the effect of urbanization on the transmission of an infectious disease, Math. Biosci., 211 (2008), 166-185. (Pubitemid 50009478)
54. U.S. Census Bureau, International Data Base. Available from: http://www.census.gov/population/international/data/idb/region.php.
55. Centers For Disease Control and Prevention, Large-scale vaccination clinic output and staffing estimates: An example, (2009). Available from: www.cdc.gov/h1n1flu/vaccination/pdf/A-Wortley-H1N1-sample-clinic.pdf.
56. Centers For Disease Control and Prevention, Use of influenza A (H1N1) 2009 monovalent vaccine. Recommendations of the Advisory Committee on Immunization Practices (ACIP), 2009, MMWR Recomm. Rep., 58(RR-10) (2009), 1-8.
57. Centers For Disease Control and Prevention, Preventing emerging infectious diseases: A strategy for the 21st century. Overview of the updated CDC plan, MMWR Recomm. Rep., 47(RR-15) (1998), 1-14.