Bacterial Competition in the Presence of a Virus in a Chemostat

Amer Hassan Albargi and Miled El Hajji ()
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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

Mathematics, 2023, vol. 11, issue 16, 1-17

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.

Keywords: chemostat; competition; virus; coexistence; local stability; uniform persistence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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