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Optimal Control of Heterogeneous Mutating Viruses

Author

Listed:
  • Elena Gubar

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii Prospekt 35, Petergof, Saint-Petersburg 198504, Russia
    These authors contributed equally to this work.)

  • Vladislav Taynitskiy

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii Prospekt 35, Petergof, Saint-Petersburg 198504, Russia
    These authors contributed equally to this work.)

  • Quanyan Zhu

    (Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA
    These authors contributed equally to this work.)

Abstract

Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results.

Suggested Citation

  • Elena Gubar & Vladislav Taynitskiy & Quanyan Zhu, 2018. "Optimal Control of Heterogeneous Mutating Viruses," Games, MDPI, vol. 9(4), pages 1-18, December.
    • Handle: RePEc:gam:jgames:v:9:y:2018:i:4:p:103-:d:190387
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    References listed on IDEAS

    as
    1. Rota Bulò, Samuel & Bomze, Immanuel M., 2011. "Infection and immunization: A new class of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 71(1), pages 193-211, January.
    2. Declan Butler, 2012. "Flu surveillance lacking," Nature, Nature, vol. 483(7391), pages 520-522, March.
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    Citations

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    Cited by:

    1. Guiyun Liu & Jieyong Chen & Zhongwei Liang & Zhimin Peng & Junqiang Li, 2021. "Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs," Mathematics, MDPI, vol. 9(9), pages 1-16, April.
    2. Elena Gubar & Laura Policardo & Edgar J. Sanchez Carrera & Vladislav Taynitskiy, 2021. "Optimal Lockdown Policies driven by Socioeconomic Costs," Papers 2105.08349, arXiv.org.
    3. Xiyun Zhang & Zhongyuan Ruan & Muhua Zheng & Jie Zhou & Stefano Boccaletti & Baruch Barzel, 2022. "Epidemic spreading under mutually independent intra- and inter-host pathogen evolution," Nature Communications, Nature, vol. 13(1), pages 1-13, December.
    4. Elena Gubar & Vladislav Taynitskiy & Denis Fedyanin & Ilya Petrov, 2023. "Quarantine and Vaccination in Hierarchical Epidemic Model," Mathematics, MDPI, vol. 11(6), pages 1-17, March.
    5. Quanyan Zhu & Elena Gubar & Eitan Altman, 2022. "Preface to Special Issue on Dynamic Games for Modeling and Control of Epidemics," Dynamic Games and Applications, Springer, vol. 12(1), pages 1-6, March.

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