Assessing the role of bacterial plasmid replication in a competition model of sensitive and resistant bacteria to antibiotics

Eduardo Ibargüen-Mondragón; Miller Cerón Gómez; Edith M. Burbano-Rosero; Eduardo Ibargüen-Mondragón; Miller Cerón Gómez; Edith M. Burbano-Rosero

doi:10.3934/math.2021549

AIMS Mathematics

2021, Volume 6, Issue 9: 9446-9467. doi: 10.3934/math.2021549

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Research article

Assessing the role of bacterial plasmid replication in a competition model of sensitive and resistant bacteria to antibiotics

1.
Research Group on Mathematical Biology and Applied Mathematics (GIBIMMA), Department of Mathematics, University of Narño, Pasto, Clle 18-Cra 50, Colombia
2.
Research Group on Mathematical Biology and Applied Mathematics (GIBIMMA), Department of Biology, University of Narño, Pasto, Clle 18-Cra 50, Colombia

Received: 27 March 2021 Accepted: 25 May 2021 Published: 23 June 2021
MSC : 32D23, 93D20

Antibiotic resistance is one of the top 10 public health problems that most affects humanity. In recent decades, plasmid-mediated antibiotic resistance (PMAR) has increased. However, due to the lack of knowledge about the biology of plasmids, there are gaps in the role played by them within antibiotic resistance. In this sense, properties that agree with the biological phenomenon and have contributed to the understanding of PMAR have been discovered from mathematical modeling. In this work, we focus on the role that the plasmid replication rate plays in the elimination or spread of bacteria both sensitive and resistant to antibiotics. Qualitative analysis reveals the existence of a free-bacteria equilibrium point, a resistant equilibrium point, and two coexistence equilibrium points (high and low bacterial load). If each bacterium (sensitive or resistant) produces at most one new bacterium, the infection will be controlled or eliminated. If each bacterium (sensitive or resistant) produces more than one bacteria, several scenarios of bacterial progression are presented that depend on the plasmid replication rate. The results suggest that plasmid replication is essential for the outcome of bacterial infection at the local level.
- bacteria,
- antibiotic resistance,
- plasmids,
- ordinary differential,
- equations stability,
- Hopf bifurcation
Citation: Eduardo Ibargüen-Mondragón, Miller Cerón Gómez, Edith M. Burbano-Rosero. Assessing the role of bacterial plasmid replication in a competition model of sensitive and resistant bacteria to antibiotics[J]. AIMS Mathematics, 2021, 6(9): 9446-9467. doi: 10.3934/math.2021549

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Abstract

Antibiotic resistance is one of the top 10 public health problems that most affects humanity. In recent decades, plasmid-mediated antibiotic resistance (PMAR) has increased. However, due to the lack of knowledge about the biology of plasmids, there are gaps in the role played by them within antibiotic resistance. In this sense, properties that agree with the biological phenomenon and have contributed to the understanding of PMAR have been discovered from mathematical modeling. In this work, we focus on the role that the plasmid replication rate plays in the elimination or spread of bacteria both sensitive and resistant to antibiotics. Qualitative analysis reveals the existence of a free-bacteria equilibrium point, a resistant equilibrium point, and two coexistence equilibrium points (high and low bacterial load). If each bacterium (sensitive or resistant) produces at most one new bacterium, the infection will be controlled or eliminated. If each bacterium (sensitive or resistant) produces more than one bacteria, several scenarios of bacterial progression are presented that depend on the plasmid replication rate. The results suggest that plasmid replication is essential for the outcome of bacterial infection at the local level.

References

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