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Bacterial Competition in the Presence of a Virus in a Chemostat

Author

Listed:
  • Amer Hassan Albargi

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

  • Miled El Hajji

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

Abstract

We derive a mathematical model that describes the competition of two populations in a chemostat in the presence of a virus. We suppose that only one population is affected by the virus. We also suppose that the substrate is continuously added to the bioreactor. We obtain a model taking the form of an “SI” epidemic model using general increasing growth rates of bacteria on the substrate and a general increasing incidence rate for the viral infection. The stability of the steady states was carried out. The system can have multiple steady states with which we can determine the necessary and sufficient conditions for both existence and local stability. We exclude the possibility of periodic orbits and we prove the uniform persistence of both species. Finally, we give some numerical simulations that validate the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3530-:d:1217936
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    References listed on IDEAS

    as
    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. 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.
    Full references (including those not matched with items on IDEAS)

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