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Mathematics 2019, 7(3), 304; https://doi.org/10.3390/math7030304

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

Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Casablanca 20000, Morocco
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Received: 23 January 2019 / Revised: 19 February 2019 / Accepted: 6 March 2019 / Published: 25 March 2019
(This article belongs to the Special Issue Mathematical Models in Epidemiology)
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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. View Full-Text
Keywords: multi-region epidemic model; stochastic model; media coverage; infodemics; misconception; vaccination; stochastic optimal control; stochastic multi-points boundary value problems multi-region epidemic model; stochastic model; media coverage; infodemics; misconception; vaccination; stochastic optimal control; stochastic multi-points boundary value problems
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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El Kihal, F.; Abouelkheir, I.; Rachik, M.; Elmouki, I. 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 2019, 7, 304.

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