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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 4: 761-784. doi: 10.3934/mbe.2014.11.761
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A SEIR model for control of infectious diseases with constraints

  • 1.
    Faculdade de Engenharia da Universidade do Porto, DEEC and ISR-Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto
  • Published: 01 March 2014

  • MSC : Primary: 92D30, 49K15; Secondary: 34A34.

  • Optimal control can be of help to test and compare different vaccination strategies of a certain disease.In this paper we propose the introduction ofconstraints involving state variables on an optimal control problem applied to a compartmental SEIR (Susceptible. Exposed, Infectious and Recovered) model. We study the solution of such problems when mixed state control constraints are used to impose upper bounds on the available vaccines at each instant of time. We also explore the possibility of imposing upper bounds on the number of susceptible individuals with and without limitations on the number of vaccines available. In the case of mere mixed constraints a numerical and analytical study is conducted while in the other two situations only numerical results are presented.

    Citation: M. H. A. Biswas, L. T. Paiva, MdR de Pinho. A SEIR model for control of infectious diseases with constraints[J]. Mathematical Biosciences and Engineering, 2014, 11(4): 761-784. doi: 10.3934/mbe.2014.11.761

    Related Papers:

  • Optimal control can be of help to test and compare different vaccination strategies of a certain disease.In this paper we propose the introduction ofconstraints involving state variables on an optimal control problem applied to a compartmental SEIR (Susceptible. Exposed, Infectious and Recovered) model. We study the solution of such problems when mixed state control constraints are used to impose upper bounds on the available vaccines at each instant of time. We also explore the possibility of imposing upper bounds on the number of susceptible individuals with and without limitations on the number of vaccines available. In the case of mere mixed constraints a numerical and analytical study is conducted while in the other two situations only numerical results are presented.


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    [1] Springer-Verlag. New York, 2001.
    [2] John Wiley, New York, 1983.
    [3] Springer-Verlag, London, 2013.
    [4] SIAM J. Control Optim., 48, (2010), 4500-4524.
    [5] Nonlinear Analysis, 63 (2005), e2591-e2602.
    [6] Set-Valued and Variational Analysis, 17 (2009), 203-2219.
    [7] MdR de Pinho,Hacet. J. Math. Stat., 40 (2011), 287-295.
    [8] Department of Electrical and Electronic Engineering, Imperial College London, London, England, UK, 2010.
    [9] SIAM Review, 37 (1995), 181-218.
    [10] $2^{nd}$ Edition (405 pages), John Wiley, New York, 1980.
    [11] In Mathematical Understanding of Infectious Disease Dynamics (S. Ma and Y. Xia, Eds.), Vol. 16. Chap. 1, pp. 1-61, World Scientific Publishing Co. Pte. Ltd., Singapore, 2008.
    [12] Bulletin of Mathematical Biology, 53 (1991), 35-55.
    [13] J. Optim. Theory Appl., 86 (1995), 649-667.
    [14] SIAM J. Control Optm., 41 (2002), 380-403.
    [15] SIAM Advances in Design and Control, 24, 2012.
    [16] Optim. Control Appl. Meth., 32 (2011), 181-184.
    [17] DIMACS Series in Discrete Mathematics, 75 (2010), 67-81.
    [18] Project Report, 2013, http://paginas.fe.up.pt/~faf/ProjectFCT2009/report.pdf.
    [19] Mathematical Biosciences and Engineering, 8 (2011), 141-170.
    [20] Journal of Applied Mathematics, 2012 (2012), 1-20.
    [21] Springer, New York, 2012.
    [22] Applied Mathematical Modelling, 34 (2010), 2685-2697.
    [23] Birkhäuser, Boston, 2000.
    [24] Mathematical Programming, 106 (2006), 25-57.
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