Mutual inhibition in presence of a virus in continuous culture

Salah Alsahafi; Stephen Woodcock; Salah Alsahafi; Stephen Woodcock

doi:10.3934/mbe.2021162

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3258-3273. doi: 10.3934/mbe.2021162

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Mutual inhibition in presence of a virus in continuous culture

Salah Alsahafi ^,,
Stephen Woodcock

University of Technology Sydney, School of Mathematical and Physical Sciences, Australia

Academic Editor: Rosana Rodríguez-López

Received: 02 March 2021 Accepted: 06 April 2021 Published: 12 April 2021

In this paper, we consider two species competing for a limiting substrate such that each species impedes the growth of the other one (Mutual inhibition) in presence of a virus inhibiting one bacterial species. A system of ordinary differential equations is proposed as a mathematical model for this competition. A detailed local qualitative analysis of the system is carried out. We proved that for a general nonlinear growth rates, the Competitive Exclusion Principle still valid, that at least one species goes extinct. For some cases where we have two locally stable equilibrium points, initial species concentrations are important in determining which is the winning species. Obtained results were confirmed by some numerical simulations using Matlab software.
- chemostat,
- competition,
- reversible inhibition,
- virus,
- local analysis,
- competitive Exclusion Principle
Citation: Salah Alsahafi, Stephen Woodcock. Mutual inhibition in presence of a virus in continuous culture[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3258-3273. doi: 10.3934/mbe.2021162

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Abstract

In this paper, we consider two species competing for a limiting substrate such that each species impedes the growth of the other one (Mutual inhibition) in presence of a virus inhibiting one bacterial species. A system of ordinary differential equations is proposed as a mathematical model for this competition. A detailed local qualitative analysis of the system is carried out. We proved that for a general nonlinear growth rates, the Competitive Exclusion Principle still valid, that at least one species goes extinct. For some cases where we have two locally stable equilibrium points, initial species concentrations are important in determining which is the winning species. Obtained results were confirmed by some numerical simulations using Matlab software.

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