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Role of Media and Effects of Infodemics and Escapes in the Spatial Spread of Epidemics: A Stochastic Multi-Region Model with Optimal Control Approach

Author

Listed:
  • Fadwa El Kihal

    (Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Casablanca 20000, Morocco)

  • Imane Abouelkheir

    (Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Casablanca 20000, Morocco)

  • Mostafa Rachik

    (Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Casablanca 20000, Morocco)

  • Ilias Elmouki

    (Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Casablanca 20000, Morocco)

Abstract

Mass vaccination campaigns play major roles in the war against epidemics. Such prevention strategies cannot always reach their goals significantly without the help of media and awareness campaigns used to prevent contacts between susceptible and infected people. Feelings of fear, infodemics, and misconception could lead to some fluctuations of such policies. In addition to the vaccination strategy, the movement restriction approach is essential because of the factor of mobility or travel. However, anti-epidemic border measures may also be disturbed if some infected travelers manage to escape and infiltrate into a safer region. In this paper, we aim to study infection dynamics related to the spatial spread of an epidemic in interconnected regions in the presence of random perturbations caused by the three above-mentioned reasons. Therefore, we devise a stochastic multi-region epidemic model in which contacts between susceptible and infected populations, vaccination-based and movement restriction optimal control approaches are all assumed to be unpredictable, and then, we discuss the effectiveness of such policies. In order to reach our goal, we employ a stochastic maximum principle version for noised systems, state and prove the sufficient and necessary conditions of optimality, and finally provide the numerical results obtained using a stochastic progressive-regressive schemes method.

Suggested Citation

  • Fadwa El Kihal & Imane Abouelkheir & Mostafa Rachik & Ilias Elmouki, 2019. "Role of Media and Effects of Infodemics and Escapes in the Spatial Spread of Epidemics: A Stochastic Multi-Region Model with Optimal Control Approach," Mathematics, MDPI, vol. 7(3), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:304-:d:217036
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    References listed on IDEAS

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    3. Zhao, Yanan & Jiang, Daqing & O’Regan, Donal, 2013. "The extinction and persistence of the stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4916-4927.
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    6. Yuan, Xinpeng & Xue, Yakui & Liu, Maoxing, 2013. "Analysis of an epidemic model with awareness programs by media on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 1-11.
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