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Mathematical Analysis of a Bacterial Competition in a Continuous Reactor in the Presence of a Virus

Author

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  • Abdulrahman Ali Alsolami

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Miled El Hajji

    (ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvédère, Tunis El Manar University, Tunis 1068, Tunisia
    Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

Abstract

In this paper, we discuss the competition of two species for a single essential growth-limiting nutriment with viral infection that affects only the first species. Although the classical models without viral infection suggest competitive exclusion, this model exhibits the stable coexistence of both species. We reduce the fourth-dimension proposed model to a three-dimension one. Thus, the coexistence of the two competing species is demonstrated using the theory of uniform persistence applied to the three-variable reduced system. We prove that there is no coexistence of both species without the presence of the virus and the satisfaction of some assumptions on the growth rates of species. Finally, we give some numerical simulations to confirm the obtained theoretical findings.

Suggested Citation

  • Abdulrahman Ali Alsolami & Miled El Hajji, 2023. "Mathematical Analysis of a Bacterial Competition in a Continuous Reactor in the Presence of a Virus," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:883-:d:1063170
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    References listed on IDEAS

    as
    1. Wade, M.J. & Harmand, J. & Benyahia, B. & Bouchez, T. & Chaillou, S. & Cloez, B. & Godon, J.-J. & Moussa Boudjemaa, B. & Rapaport, A. & Sari, T. & Arditi, R. & Lobry, C., 2016. "Perspectives in mathematical modelling for microbial ecology," Ecological Modelling, Elsevier, vol. 321(C), pages 64-74.
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    Cited by:

    1. Miled El Hajji & Dalal M. Alshaikh & Nada A. Almuallem, 2023. "Periodic Behaviour of an Epidemic in a Seasonal Environment with Vaccination," Mathematics, MDPI, vol. 11(10), pages 1-20, May.
    2. Amer Hassan Albargi & Miled El Hajji, 2023. "Bacterial Competition in the Presence of a Virus in a Chemostat," Mathematics, MDPI, vol. 11(16), pages 1-17, August.

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