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Optimal Control for a Discrete Time Influenza Model

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Advances in Computational Biology

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 232))

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Abstract

We formulated a discrete time model in order to study optimal control strategies for a single influenza outbreak. In our model, we divided the population into four classes: susceptible, infectious, treated, and recovered individuals. The total population was divided into subgroups according to activity or susceptibility levels. The goal was to determine how treatment doses should be distributed in each group in order to reduce the final epidemic size. The case of limited resources is considered by including an isoperimetric constraint. We found that the use of antiviral treatment resulted in reductions in the cumulative number of infected individuals. We proposed to solve the problem by using the primal-dual interior-point method that enforces epidemiological constraints explicitly.

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Author information

Authors and Affiliations

  1. Departamento de Matematicas, Universidad Autónoma de Occidente, Cali, Colombia

    Paula Andrea Gonzalez Parra

  2. Computer Science Department, The University of Texas at El Paso, El Paso, TX, 79968-0514, USA

    Martine Ceberio

  3. Department of Applied Mathematics, Kyung Hee University, Yongin, 446-701, Republic of Korea

    Sunmi Lee

  4. Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ, 85287, USA

    Carlos Castillo-Chavez

Authors
  1. Paula Andrea Gonzalez Parra
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  2. Martine Ceberio
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  3. Sunmi Lee
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  4. Carlos Castillo-Chavez
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Corresponding author

Correspondence to Paula Andrea Gonzalez Parra .

Editor information

Editors and Affiliations

  1. University of Caldas, Manizales, Colombia

    Luis F. Castillo

  2. Cenicafé - Centro Nacional de Investigaciones del Café en Colombia, Chinchiná, Colombia

    Marco Cristancho

  3. University of Caldas, Manizales, Colombia

    Gustavo Isaza

  4. BIOS - Centro Bioinformática y Biologia Computacional de Colombia, Manizales, Colombia

    Andrés Pinzón

  5. Department of Computer Science School of Science, University of Salamanca, Salamanca, Spain

    Juan Manuel Corchado Rodríguez

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© 2014 Springer International Publishing Switzerland

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Parra, P.A.G., Ceberio, M., Lee, S., Castillo-Chavez, C. (2014). Optimal Control for a Discrete Time Influenza Model. In: Castillo, L., Cristancho, M., Isaza, G., Pinzón, A., Rodríguez, J. (eds) Advances in Computational Biology. Advances in Intelligent Systems and Computing, vol 232. Springer, Cham. https://doi.org/10.1007/978-3-319-01568-2_33

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  • DOI: https://doi.org/10.1007/978-3-319-01568-2_33

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01567-5

  • Online ISBN: 978-3-319-01568-2

  • eBook Packages: EngineeringEngineering (R0)

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