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Optimal Control Problems for a Mathematical Model of the Treatment of Psoriasis

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We consider a mathematical model of the treatment of psoriasis on a finite time interval. The model consists of three nonlinear differential equations describing the interrelationships between the concentrations of T-lymphocytes, keratinocytes, and dendritic cells. The model incorporates two bounded timedependent control functions, one describing the suppression of the interaction between T-lymphocytes and keratinocytes and the other the suppression of the interaction between T-lymphocytes and dendritic cells by medication. For this model, we minimize the weighted sum of the total keratinocyte concentration and the total cost of treatment. This weighted sum is expressed as an integral over the sum of the squared controls. Pontryagin’s maximum principle is applied to find the properties of the optimal controls in this problem. The specific controls are determined for various parameter values in the BOCOP-2.0.5 program environment. The numerical results are discussed.

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  • 03 April 2020

    To the article ���Optimal Control Problems for a Mathematical Model of the Treatment of Psoriasis,��� by N. L. Grigorenko, ��. V. Grigorieva, P. K. Roi, and E. N. Khailov, Vol. 30, No. 4, pp. 352���363, October, 2019.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    N. L. Grigorenko, É. V. Grigorieva & E. N. Khailov

  2. Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata, India

    P. K. Roi

Authors
  1. N. L. Grigorenko
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  2. É. V. Grigorieva
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  3. P. K. Roi
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  4. E. N. Khailov
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Correspondence to N. L. Grigorenko.

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Translated from Prikladnaya Matematika i Informatika, No. 61, 2019, pp. 28–41.

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Grigorenko, N.L., Grigorieva, É.V., Roi, P.K. et al. Optimal Control Problems for a Mathematical Model of the Treatment of Psoriasis. Comput Math Model 30, 352–363 (2019). https://doi.org/10.1007/s10598-019-09461-y

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