Bacterial Competition in the Presence of a Virus in a Chemostat
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 a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3530 |
| _version_ | 1797583980411748352 |
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| author | Amer Hassan Albargi Miled El Hajji |
| author_facet | Amer Hassan Albargi Miled El Hajji |
| author_sort | Amer Hassan Albargi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T23:45:53Z |
| format | Article |
| id | doaj.art-b6731c4405814292891cf47be940e076 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:45:53Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b6731c4405814292891cf47be940e0762023-11-19T02:03:23ZengMDPI AGMathematics2227-73902023-08-011116353010.3390/math11163530Bacterial Competition in the Presence of a Virus in a ChemostatAmer Hassan Albargi0Miled El Hajji1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaENIT-LAMSIN, Tunis El Manar University, BP. 37, Tunis-Belvédère, Tunis 1002, TunisiaWe 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.https://www.mdpi.com/2227-7390/11/16/3530chemostatcompetitionviruscoexistencelocal stabilityuniform persistence |
| spellingShingle | Amer Hassan Albargi Miled El Hajji Bacterial Competition in the Presence of a Virus in a Chemostat Mathematics chemostat competition virus coexistence local stability uniform persistence |
| title | Bacterial Competition in the Presence of a Virus in a Chemostat |
| title_full | Bacterial Competition in the Presence of a Virus in a Chemostat |
| title_fullStr | Bacterial Competition in the Presence of a Virus in a Chemostat |
| title_full_unstemmed | Bacterial Competition in the Presence of a Virus in a Chemostat |
| title_short | Bacterial Competition in the Presence of a Virus in a Chemostat |
| title_sort | bacterial competition in the presence of a virus in a chemostat |
| topic | chemostat competition virus coexistence local stability uniform persistence |
| url | https://www.mdpi.com/2227-7390/11/16/3530 |
| work_keys_str_mv | AT amerhassanalbargi bacterialcompetitioninthepresenceofavirusinachemostat AT miledelhajji bacterialcompetitioninthepresenceofavirusinachemostat |