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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 1: 183-197. doi: 10.3934/mbe.2011.8.183
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A note on the use of optimal control on a discrete time model of influenza dynamics

  • 1.
    Program in Computational Science, The University of Texas at El Paso, El Paso, TX 79968-0514
  • 2.
    Mathematical, Computational and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287
  • 3.
    Program in Computational Science, Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968-0514
  • 4.
    Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287
  • Received: 01 June 2010 Accepted: 29 June 2018 Published: 01 January 2011

  • MSC : Primary: 92B05, 49K21, 93C55; Secondary: 92D40.

  • A discrete time Susceptible - Asymptomatic - Infectious - Treated - Recovered (SAITR) model is introduced in the context of influenza transmission. We evaluate the potential effect of control measures such as social distancing and antiviral treatment on the dynamics of a single outbreak. Optimal control theory is applied to identify the best way of reducing morbidity and mortality at a minimal cost. The problem is solved by using a discrete version of Pontryagin's maximum principle. Numerical results show that dual strategies have stronger impact in the reduction of the final epidemic size.

    Citation: 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[J]. Mathematical Biosciences and Engineering, 2011, 8(1): 183-197. doi: 10.3934/mbe.2011.8.183

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  • A discrete time Susceptible - Asymptomatic - Infectious - Treated - Recovered (SAITR) model is introduced in the context of influenza transmission. We evaluate the potential effect of control measures such as social distancing and antiviral treatment on the dynamics of a single outbreak. Optimal control theory is applied to identify the best way of reducing morbidity and mortality at a minimal cost. The problem is solved by using a discrete version of Pontryagin's maximum principle. Numerical results show that dual strategies have stronger impact in the reduction of the final epidemic size.


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    3. Eunha Shim, Optimal strategies of social distancing and vaccination against seasonal influenza, 2013, 10, 1551-0018, 1615, 10.3934/mbe.2013.10.1615
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  • © 2011 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)
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