# American Institute of Mathematical Sciences

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
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##### References:
 [1] Erika Asano, Louis J. Gross, Suzanne Lenhart, Leslie A. Real. Optimal control of vaccine distribution in a rabies metapopulation model. Mathematical Biosciences & Engineering, 2008, 5 (2) : 219-238. doi: 10.3934/mbe.2008.5.219 [2] Folashade B. Agusto, Abba B. Gumel. Theoretical assessment of avian influenza vaccine. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 1-25. doi: 10.3934/dcdsb.2010.13.1 [3] Eunha Shim. Prioritization of delayed vaccination for pandemic influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 95-112. doi: 10.3934/mbe.2011.8.95 [4] Olivia Prosper, Omar Saucedo, Doria Thompson, Griselle Torres-Garcia, Xiaohong Wang, Carlos Castillo-Chavez. Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 141-170. doi: 10.3934/mbe.2011.8.141 [5] Majid Jaberi-Douraki, Seyed M. Moghadas. Optimal control of vaccination dynamics during an influenza epidemic. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1045-1063. doi: 10.3934/mbe.2014.11.1045 [6] Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control & Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185 [7] Julien Arino, Chris Bauch, Fred Brauer, S. Michelle Driedger, Amy L. Greer, S.M. Moghadas, Nick J. Pizzi, Beate Sander, Ashleigh Tuite, P. van den Driessche, James Watmough, Jianhong Wu, Ping Yan. Pandemic influenza: Modelling and public health perspectives. Mathematical Biosciences & Engineering, 2011, 8 (1) : 1-20. doi: 10.3934/mbe.2011.8.1 [8] Alexander Arguchintsev, Vasilisa Poplevko. An optimal control problem by parabolic equation with boundary smooth control and an integral constraint. Numerical Algebra, Control & Optimization, 2018, 8 (2) : 193-202. doi: 10.3934/naco.2018011 [9] Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 [10] Bruno Buonomo, Eleonora Messina. Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: A theoretical study. Mathematical Biosciences & Engineering, 2012, 9 (3) : 539-552. doi: 10.3934/mbe.2012.9.539 [11] Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129 [12] Sofia O. Lopes, Fernando A. C. C. Fontes, Maria do Rosário de Pinho. On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems. Discrete & Continuous Dynamical Systems, 2011, 29 (2) : 559-575. doi: 10.3934/dcds.2011.29.559 [13] Térence Bayen, Alain Rapaport, Fatima-Zahra Tani. Optimal periodic control for scalar dynamics under integral constraint on the input. Mathematical Control & Related Fields, 2020, 10 (3) : 547-571. doi: 10.3934/mcrf.2020010 [14] Hassen Aydi, Ayman Kachmar. Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II. Communications on Pure & Applied Analysis, 2009, 8 (3) : 977-998. doi: 10.3934/cpaa.2009.8.977 [15] Rodolfo Acuňa-Soto, Luis Castaňeda-Davila, Gerardo Chowell. A perspective on the 2009 A/H1N1 influenza pandemic in Mexico. Mathematical Biosciences & Engineering, 2011, 8 (1) : 223-238. doi: 10.3934/mbe.2011.8.223 [16] Diána H. Knipl, Gergely Röst. Modelling the strategies for age specific vaccination scheduling during influenza pandemic outbreaks. Mathematical Biosciences & Engineering, 2011, 8 (1) : 123-139. doi: 10.3934/mbe.2011.8.123 [17] Ting Kang, Qimin Zhang, Haiyan Wang. Optimal control of an avian influenza model with multiple time delays in state and control variables. Discrete & Continuous Dynamical Systems - B, 2021, 26 (8) : 4147-4171. doi: 10.3934/dcdsb.2020278 [18] Zhen-Zhen Tao, Bing Sun. Galerkin spectral method for elliptic optimal control problem with $L^2$-norm control constraint. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021220 [19] K. F. Cedric Yiu, S. Y. Wang, K. L. Mak. Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains. Journal of Industrial & Management Optimization, 2008, 4 (1) : 81-94. doi: 10.3934/jimo.2008.4.81 [20] Raimund Bürger, Gerardo Chowell, Pep Mulet, Luis M. Villada. Modelling the spatial-temporal progression of the 2009 A/H1N1 influenza pandemic in Chile. Mathematical Biosciences & Engineering, 2016, 13 (1) : 43-65. doi: 10.3934/mbe.2016.13.43

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