ABSTRACT
We propose a mathematical model based in ordinary differential equations between bacterial pathogen and Bacteriophages to describe the infection dynamics of these populations, for which we use a nonlinear function with an inhibitory effect. We study the stability of the model using the Lyapunov theory and the second additive compound matrix and perform a global sensitivity analysis to elucidate the most influential parameters in the model, besides we make a parameter estimation using growth data of Escherichia coli (E.coli) bacteria in presence of Coliphages (bacteriophages that infect E.coli) with different multiplicity of infection. We found a threshold that indicates whether the bacteriophage concentration will coexist with the bacterium (the coexistence equilibrium) or become extinct (phages extinction equilibrium), the first equilibrium is locally asymptotically stable while the other is globally asymptotically stable depending on the magnitude of this threshold. Beside we found that the dynamics of the model is particularly affected by infection rate of bacteria and Half-saturation phages density. Parameter estimation show that all multiplicities of infection are effective in eliminating infected bacteria but the smaller one leaves a higher number of bacteriophages at the end of this elimination.
Subject(s)
Bacteriophages , Escherichia coli , Coliphages , Bacteria , Models, TheoreticalABSTRACT
Introducción: La resistencia a los antimicrobianos (RAM) es un problema de salud pública que manifiesta la disminuida eficacia de estos agentes en la prevención y tratamiento de una proporción cada vez más amplia de patologías. Los actinomicetos son un grupo bacteriano importante de productores de metabolitos activos contra patógenos. Objetivo: Aislar actinomicetos del bosque tropical de Nariño, con potencial producción de metabolitos inhibitorios contra bacterias multidrogo-resistentes. Materiales y métodos: Se tomaron muestras de suelo de Bosque Tropical Húmedo de la Reserva Natural del Río Ñambí, se analizaron microbiológica y molecularmente. Se estimuló la producción in vitro de metabolitos secundarios y evaluó el efecto inhibitorio de estos extractos contra las bacterias multidrogo-resistentes Escherichia coli y Staphylococcus aureus. Resultados: Se obtuvieron 11 aislados presuntivos, se confirmó que cuatro de ellos correspondieron al género Streptomyces sp. Las pruebas de inhibición contra bacterias multidrogo-resistentes E. coli y S. aureus, permitieron verificar que el aislado P3772 fue el más eficiente en la inhibición de los patógenos. Conclusiones: Todos los actinomicetos evaluados presentan actividad antibacteriana contra al menos una de las bacterias patógenas estudiadas; destacando el aislado P3772, que inhibe a E. coli y S. aureus. Se espera caracterizar los compuestos vinculados a la actividad antibacteriana.
Introduction: Antimicrobial resistance (AR) is a public health problem that reveals the diminished efficacy of these agents in the prevention and treatment of an increasingly larger number of pathologies. Actinomycetes are an important bacterial producer group of metabolites that are active against pathogens. Objective: To isolate actinomycetes from the tropical forest of Nariño (Colombia), which have the potential to produce inhibitory metabolites against multi-drug resistant bacteria. Materials and methods: Soil samples were taken from the Humid Tropical Forest of the Río Ńambí Natural Reserve and analyzed through microbiological and molecular assays. In vitro production of secondary metabolites was first stimulated, followed by the assessment of the inhibitory effect of these extracts against multi-drug resistant Escherichia coli and Staphylococcus aureus. Results: 11 presumptive isolates were obtained, confirming that four of them corresponded to the Streptomyces sp. genus. The bacterial isolate P3772 was identified as the one with the highest inhibitory effect against multi-drug resistant E. coli and S. aureus. Conclusions: All the actinomycetes evaluated presented antibacterial activity. The isolate P3772 stands out, which inhibited both E. coli and S. aureus. The compounds associated with this antibacterial activity will be characterized in future studies.