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Neural Networks Simulation of Distributed SEIR System

Author

Listed:
  • Tibor Kmet

    (Department of Informatics, J. Selye University, Bratislavská Cesta 3322, 945 01 Komárno, Slovakia)

  • Maria Kmetova

    (Department of Mathematics, Faculty of Natural Sciences and Informatics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia)

  • Ladislav Végh

    (Department of Informatics, J. Selye University, Bratislavská Cesta 3322, 945 01 Komárno, Slovakia)

Abstract

In this paper, a neural network-based optimal control synthesis is presented for distributed optimal control problems. We deal with solutions of systems controlled by parabolic differential equations with control and state constraints and discrete time delays. The given optimal control problem is transformed into a discrete nonlinear problem and then implemented into a feed-forward adaptive critic neural network. We propose a new algorithm to reach optimal control and an optimal trajectory using a feed-forward neural network. We present a concrete application of this simulation method on the SEIR (Susceptible—Exposed—Infectious—Recovered) optimal control problem of a distributed system for disease control. The results show that the adaptive-critic-based neural network approach is suitable for the solution of optimal distributed control problems with delay in state and control variables subject to control-state constraints and simulates the spread of disease in the SEIR system.

Suggested Citation

  • Tibor Kmet & Maria Kmetova & Ladislav Végh, 2023. "Neural Networks Simulation of Distributed SEIR System," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2113-:d:1136533
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    References listed on IDEAS

    as
    1. Zhou, Jiaying & Zhao, Yi & Ye, Yong, 2022. "Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).
    2. Meng, Lan & Zhu, Wei, 2022. "Analysis of SEIR epidemic patch model with nonlinear incidence rate, vaccination and quarantine strategies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 489-503.
    3. Giorgio Gnecco, 2012. "A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, January.
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