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  1. AU="Elhia, Mohamed"
  2. AU="Pavlov, Youri I"

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  1. Article: Set-Valued Control to COVID-19 Spread with Treatment and Limitation of Vaccination Resources.

    Boujallal, Lahoucine / Elhia, Mohamed

    Iranian journal of science and technology. Transaction A, Science

    2022  Volume 46, Issue 3, Page(s) 829–838

    Abstract: In this paper, we consider an SEIR model that describes the dynamics of the COVID-19 pandemic. Subject to this model with vaccination and treatment as controls, we formulate a control problem that aims to reduce the number of infectious individuals to ... ...

    Abstract In this paper, we consider an SEIR model that describes the dynamics of the COVID-19 pandemic. Subject to this model with vaccination and treatment as controls, we formulate a control problem that aims to reduce the number of infectious individuals to zero. The novelty of this work consists of considering a more realistic control problem by adding mixed constraints to take into account the limited vaccines supply. Furthermore, to solve this problem, we use a set-valued approach combining a Lyapunov function defined in the sense of viability theory with some results from the set-valued analysis. The expressions of the control variables are given via continuous selection of an adequately designed feedback map. The main result of our study shows that even though there are limits of vaccination resources, the combination of treatment and vaccination strategies can significantly reduce the number of exposed and infectious individuals. Some numerical simulations are proposed to show the efficiency of our set-valued approach and to validate our theoretical results.
    Language English
    Publishing date 2022-05-08
    Publishing country Iran
    Document type Journal Article
    ZDB-ID 2444103-X
    ISSN 1028-6276 ; 0360-1307
    ISSN 1028-6276 ; 0360-1307
    DOI 10.1007/s40995-022-01295-5
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article: A novel control set-valued approach with application to epidemic models.

    Boujallal, Lahoucine / Elhia, Mohamed / Balatif, Omar

    Journal of applied mathematics & computing

    2020  Volume 65, Issue 1-2, Page(s) 295–319

    Abstract: This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we ... ...

    Abstract This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations that model the temporal evolution of disease spread. The set of initial data, from which the number of infected people decrease to zero, is generated by a new type of Lyapunov functions defined in the sense of viability theory. The associated controls are provided via selections of adequately designed feedback map. The existence of such selections is improved by using Micheal selection theorem. Finally, an application to the SIRS epidemic model, with numerical simulations, is given to show the efficiency of our approach. To the best of our knowledge, our work is the first one that used a set-valued approach based on the viability theory to deal with an epidemic control problem.
    Keywords covid19
    Language English
    Publishing date 2020-07-13
    Publishing country Germany
    Document type Journal Article
    ZDB-ID 2424171-4
    ISSN 1865-2085 ; 1598-5865
    ISSN (online) 1865-2085
    ISSN 1598-5865
    DOI 10.1007/s12190-020-01392-x
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article: Fractional optimal control problem for an age-structured model of COVID-19 transmission.

    Khajji, Bouchaib / Kouidere, Abdelfatah / Elhia, Mohamed / Balatif, Omar / Rachik, Mostafa

    Chaos, solitons, and fractals

    2021  Volume 143, Page(s) 110625

    Abstract: The aim of this study is to model the transmission of COVID-19 and investigate the impact of some control strategies on its spread. We propose an extension of the classical SEIR model, which takes into account the age structure and uses fractional-order ... ...

    Abstract The aim of this study is to model the transmission of COVID-19 and investigate the impact of some control strategies on its spread. We propose an extension of the classical SEIR model, which takes into account the age structure and uses fractional-order derivatives to have a more realistic model. For each age group
    Language English
    Publishing date 2021-01-02
    Publishing country England
    Document type Journal Article
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110625
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Article: A novel control set-valued approach with application to epidemic models

    Boujallal, Lahoucine / Elhia, Mohamed / Balatif, Omar

    J Appl Math Comput

    Abstract: This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we ... ...

    Abstract This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations that model the temporal evolution of disease spread. The set of initial data, from which the number of infected people decrease to zero, is generated by a new type of Lyapunov functions defined in the sense of viability theory. The associated controls are provided via selections of adequately designed feedback map. The existence of such selections is improved by using Micheal selection theorem. Finally, an application to the SIRS epidemic model, with numerical simulations, is given to show the efficiency of our approach. To the best of our knowledge, our work is the first one that used a set-valued approach based on the viability theory to deal with an epidemic control problem.
    Keywords covid19
    Publisher WHO
    Document type Article
    Note WHO #Covidence: #641115
    Database COVID19

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