Mathematical model of interaction Escherichia coli and Coliphages

Area of Science:

• Mathematical Biology
• Microbiology
• Ecology

Background:

• Bacterial pathogens like Escherichia coli (E.coli) pose significant health risks.
• Bacteriophages are viruses that infect bacteria and are being explored as therapeutic agents.
• Understanding the dynamics of bacterial-phage interactions is crucial for developing effective control strategies.

Purpose of the Study:

• To develop and analyze a mathematical model describing the infection dynamics between bacterial pathogens and bacteriophages.
• To investigate the stability of the proposed model using theoretical and computational methods.
• To perform parameter estimation using experimental data of E.coli and Coliphage interactions.

Main Methods:

• Development of a mathematical model using ordinary differential equations to represent bacterial and bacteriophage populations.
• Application of Lyapunov theory and the second additive compound matrix for model stability analysis.
• Global sensitivity analysis to identify influential model parameters.
• Parameter estimation using growth data of E.coli in the presence of Coliphages at varying multiplicities of infection.

Main Results:

• A critical threshold was identified, determining either coexistence equilibrium (bacterial-phage stability) or phage extinction equilibrium.
• The coexistence equilibrium was found to be locally asymptotically stable, while phage extinction was globally asymptotically stable, dependent on the threshold magnitude.
• Model dynamics are significantly influenced by the bacterial infection rate and the half-saturation phage density.
• Parameter estimation indicated that all tested multiplicities of infection effectively reduced infected bacteria, with lower multiplicities resulting in a higher final bacteriophage population.

Conclusions:

• The mathematical model provides insights into bacterial-phage infection dynamics and stability.
• The identified threshold and influential parameters offer a basis for predicting and managing bacterial infections using bacteriophages.
• Experimental validation confirmed the efficacy of bacteriophages in controlling E.coli, with implications for phage therapy strategies.