Mathematical model of the interaction of pathogenic bacteria and bacteriophages

Resumen

We present a mathematical model employing ordinary differential equations to model the interaction dynamics between bacterial pathogens and Bacteriophages. Our model incorporates a non-linear function with inhibitory effects to describe the infection dynamics within these populations. By utilizing the Lyapunov theory and the second additive compound matrix, we analyze the stability of the model. Additionally, a global sensitivity analysis is conducted to identify the most influential parameters. Parameter estimation is performed using growth data of Escherichia coli (E. coli) bacteria in the presence of Coliphages, which are bacteriophages targeting E. coli, at various levels of multiplicity of infection. Our findings reveal a critical threshold that determines whether bacteriophage concentration will lead to coexistence with the bacterium or extinction of the phages. The coexistence equilibrium is found to be locally asymptotically stable, while the phages extinction equilibrium is globally asymptotically stable, contingent upon the magnitude of this threshold. Furthermore, our analysis indicates that the infection rate of bacteria and the half-saturation phage density significantly influence the dynamics of the model. Importantly, our parameter estimation demonstrates the effectiveness of all multiplicities of infection in eliminating infected bacteria, albeit with smaller multiplicities resulting in a higher residual population of bacteriophages post-elimination.