2011, 8(1): 171-182. doi: 10.3934/mbe.2011.8.171

A note on the use of influenza vaccination strategies when supply is limited

1. 

Mathematical, Computational and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, United States, United States

2. 

Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287

Received  June 2010 Revised  September 2010 Published  January 2011

The 2009 A (H1N1) influenza pandemic was rather atypical. It began in North America at the start of the spring and in the following months, as it moved south, efforts to develop a vaccine that would mitigate the potential impact of a second wave were accelerated. The world's limited capacity to produce an adequate vaccine supply over just a few months resulted in the development of public health policies that "had" to optimize the utilization of limited vaccine supplies. Furthermore, even after the vaccine was in production, extensive delays in vaccine distribution were experienced for various reasons. In this note, we use optimal control theory to explore the impact of some of the constraints faced by most nations in implementing a public health policy that tried to meet the challenges that come from having access only to a limited vaccine supply that is never 100% effective.
Citation: Sunmi Lee, Romarie Morales, Carlos Castillo-Chavez. A note on the use of influenza vaccination strategies when supply is limited. Mathematical Biosciences & Engineering, 2011, 8 (1) : 171-182. doi: 10.3934/mbe.2011.8.171
References:
[1]

F. Brauer, Z. Feng and C. Castillo Chavez, Discrete epidemic models,, Mathematical Biosciences and Engineering, 7 (2010), 1.  doi: 10.3934/mbe.2010.7.1.  Google Scholar

[2]

G. Chowell, C. E. Ammon, N. W. Hengartner and J. M. Hyman, Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions,, Journal of Theoretical Biology, 241 (2006), 193.  doi: 10.1016/j.jtbi.2005.11.026.  Google Scholar

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G. Chowell, C. Viboud, X. Wang, S. Bertozzi and M. Miller, Adaptive vaccination strategies to mitigate pandemic influenza: Mexico as a case study,, Public Library of Science, 4 (2009).   Google Scholar

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G. Chowell, M. A. Miller and C. Viboud, Seasonal influenza in the United States, France and Australia: Transmission and prospects for control,, Epidemiology and Infection, 136 (2007), 1.   Google Scholar

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R. Gani, H. Hughes, D. Fleming, T. Grifin, J. Medlock and S. Leach, Potential impact of antiviral use during influenza pandemic,, Emerg. Infect. Dis., 11 (2005), 1355.   Google Scholar

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E. Hansen and T. Day, Optimal control of epidemics with limited resources,, Journal of Mathematical Biology, (2010), 1.   Google Scholar

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E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model,, Discrete and Continuous Dynamical Systems Series, 2 (2002), 473.  doi: 10.3934/dcdsb.2002.2.473.  Google Scholar

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S. Lee, G. Chowell and C. Castillo-Chavez, Optimal control of influenza pandemics: The role of antiviral treatment and isolation,, Journal Theoretical Biology, 265 (2010), 136.  doi: 10.1016/j.jtbi.2010.04.003.  Google Scholar

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I. M. Longini Jr., M. E. Halloran, A. Nizam and Y. Yang, Containing pandemic influenza with antiviral agents,, American Journal of Epidemiology, 159 (2004), 623.  doi: 10.1093/aje/kwh092.  Google Scholar

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N. E. Basta, D. L. Chao, E. Halloran, L. Matrajt and I. M. Longini, Jr., Strategies for Pandemic and Seasonal Influenza Vaccination of Schoolchildren in the United States,, American Journal of Epidemiolofy, 170 (2009), 679.  doi: 10.1093/aje/kwp237.  Google Scholar

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Health and Wellness, H1N1 Vaccine approved in Canada: 10/21/2009,, Available online: \url{http://www.associatedcontent.com/article/2311287/h1n1_vaccine\_approved_in_canada.html?cat=5}., ().   Google Scholar

[24]

The Wall Street Journal US, Pregnant Women, Kids to Get Vaccine First: 07/30/2009,, Available online: \url{http://online.wsj.com/article/SB124887563173290207.html}., ().   Google Scholar

[25]

World Health Organization, Update on A(H1N1) pandemic and seasonal vaccine availability: 07/07/2009,, Available online: \url{http://www.who.int/immunization/sage/3.MPK-SAGE_7_July.pdf}., ().   Google Scholar

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show all references

References:
[1]

F. Brauer, Z. Feng and C. Castillo Chavez, Discrete epidemic models,, Mathematical Biosciences and Engineering, 7 (2010), 1.  doi: 10.3934/mbe.2010.7.1.  Google Scholar

[2]

G. Chowell, C. E. Ammon, N. W. Hengartner and J. M. Hyman, Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions,, Journal of Theoretical Biology, 241 (2006), 193.  doi: 10.1016/j.jtbi.2005.11.026.  Google Scholar

[3]

G. Chowell, C. Viboud, X. Wang, S. Bertozzi and M. Miller, Adaptive vaccination strategies to mitigate pandemic influenza: Mexico as a case study,, Public Library of Science, 4 (2009).   Google Scholar

[4]

G. Chowell, M. A. Miller and C. Viboud, Seasonal influenza in the United States, France and Australia: Transmission and prospects for control,, Epidemiology and Infection, 136 (2007), 1.   Google Scholar

[5]

O. Diekmann and J. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation,", Wiley, (2000).   Google Scholar

[6]

W. H. Fleming and R. W. Rishel, "Deterministic and Stochastic Optimal Control,", Applications of Mathematics, (1975).   Google Scholar

[7]

R. Gani, H. Hughes, D. Fleming, T. Grifin, J. Medlock and S. Leach, Potential impact of antiviral use during influenza pandemic,, Emerg. Infect. Dis., 11 (2005), 1355.   Google Scholar

[8]

E. Hansen and T. Day, Optimal control of epidemics with limited resources,, Journal of Mathematical Biology, (2010), 1.   Google Scholar

[9]

E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model,, Discrete and Continuous Dynamical Systems Series, 2 (2002), 473.  doi: 10.3934/dcdsb.2002.2.473.  Google Scholar

[10]

S. Lee, G. Chowell and C. Castillo-Chavez, Optimal control of influenza pandemics: The role of antiviral treatment and isolation,, Journal Theoretical Biology, 265 (2010), 136.  doi: 10.1016/j.jtbi.2010.04.003.  Google Scholar

[11]

S. Lenhart and J. T. Workman, "Optimal Control Applied to Biological Models,", Chapman & Hall, (2007).   Google Scholar

[12]

I. M. Longini Jr., M. E. Halloran, A. Nizam and Y. Yang, Containing pandemic influenza with antiviral agents,, American Journal of Epidemiology, 159 (2004), 623.  doi: 10.1093/aje/kwh092.  Google Scholar

[13]

C. E. Mills, J. M. Robins and M. Lipsitch, Transmissibility of 1918 pandemic influenza,, Nature, 432 (2004), 904.  doi: 10.1038/nature03063.  Google Scholar

[14]

N. E. Basta, D. L. Chao, E. Halloran, L. Matrajt and I. M. Longini, Jr., Strategies for Pandemic and Seasonal Influenza Vaccination of Schoolchildren in the United States,, American Journal of Epidemiolofy, 170 (2009), 679.  doi: 10.1093/aje/kwp237.  Google Scholar

[15]

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes,", Wiley, (1962).   Google Scholar

[16]

P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Mathematical Biosciences, 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[17]

World Health Organization (WHO), Current WHO phase of pandemic alert for Pandemic (H1N1) 2009: Access 08/11/2009,, Available online: \url{http://www.who.int/csr/disease/swineflu/phase/en/index.html}., ().   Google Scholar

[18]

World Health Organization (WHO), World now at the start of 2009 influenza pandemic: Update 06/11/2009,, Available online: \url{http://www.who.int/mediacentre/news/statements/2009/h1n1_pandemic_phase6_20090611/en/index.html}., ().   Google Scholar

[19]

Terra Mexico, Mexico. Revelan que virus de influenza humana circulaba desde marzo: 05/05/2009 [In Spanish],, Available online: \url{http://hygimia69.blogspot.com/2009/05/mexico-revelan-que-virus-de-influenza.html}., ().   Google Scholar

[20]

Fox news, 40 Million Doses of H1N1 Vaccine Will Be Burned: Update 01/07/2010,, Available online: \url{http://www.foxnews.com/story/0, ().   Google Scholar

[21]

CTV News, Canada to lend Mexico 5M doses of H1N1 vaccine: Update 01/06/2010,, Available online: \url{http://www.ctv.ca/servlet/ArticleNews/story/CTVNews/20100106/mexico_vaccine_100106/20100106}., ().   Google Scholar

[22]

Health and Wellness, H1N1 Vaccines available in Canada earlier than expected: 10/19/2009,, Available online: \url{http://www.associatedcontent.com/article/2303283/h1n1_vaccines_available_in_canada_earlier.html}., ().   Google Scholar

[23]

Health and Wellness, H1N1 Vaccine approved in Canada: 10/21/2009,, Available online: \url{http://www.associatedcontent.com/article/2311287/h1n1_vaccine\_approved_in_canada.html?cat=5}., ().   Google Scholar

[24]

The Wall Street Journal US, Pregnant Women, Kids to Get Vaccine First: 07/30/2009,, Available online: \url{http://online.wsj.com/article/SB124887563173290207.html}., ().   Google Scholar

[25]

World Health Organization, Update on A(H1N1) pandemic and seasonal vaccine availability: 07/07/2009,, Available online: \url{http://www.who.int/immunization/sage/3.MPK-SAGE_7_July.pdf}., ().   Google Scholar

[26]

Science Insider, The Challenge of Getting Swine Flu Vaccine to Poor Nations: 11/03/2009,, Available online: \url{ http://news.sciencemag.org/scienceinsider/2009/11/the-challenge-o.html}., ().   Google Scholar

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