Sobre la resistencia bacteriana hacia
antibióticos de acción bactericida y
bacteriostática

JHOANA P. ROMERO L. ^{a, *}, EDUARDO IBARGÜEN MONDRAGÓN ^b

^a Universidad de Antioquia, Instituto de Matemáticas, Medellín, Colombia.
^b Universidad de Nariño, Departamento de Matemáticas y Estadística, Pasto, Colombia.

Resumen En este artículo se formula un modelo matemático simple que describe la interacción entre bacterias sensibles y resistentes a múltiples antibióticos de acción bactericida y bacteriostática de forma simultánea, en el supuesto de que la adquisición de resistencia bacteriana se da a través de mutaciones espontáneas y adquiridas por la exposición a diferentes antibióticos. El análisis cualitativo revela la existencia de un equilibrio libre de bacterias, un equilibrio solo con bacterias resistentes y un equilibrio endémico donde coexisten ambas poblaciones de bacterias.

Palabras claves: Soluciones de equilibrio, resistencia bacteriana, antibióticos.
MSC2010: 34D23, 93D20, 65L05.

On bacterial resistance to bactericidal and
bacteriostatic antibiotics

Abstract In this work we formulate a simple mathematical model that describes the population dynamics of bacteria exposed simultaneously to multiple bactericidal and bacteriostatic antibiotics, assuming that resistance is acquired through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.

Keywords: Equilibrium solutions, bacterial resistance, antibiotics.

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^*Autor para correspondencia: E-mail :jpatirom3@gmail.com.
Recibido: 20 de enero de 2014, Aceptado: 26 de marzo de 2014.
Para citar este artículo: J. Romero, E. Ibargüen, Sobre la resistencia bacteriana hacia antibióticos de acción
bactericida y bacteriostática, Rev. Integr. Temas Mat. 32 (2014), no. 1, 101-116.