Mathematical modeling on bacterial resistance to multiple antibiotics caused by spontaneous mutations

• Published in: BioSystems Vol. 117; pp. 60 - 67
• Main Authors: Ibargüen-Mondragón, Eduardo, Mosquera, Saulo, Cerón, Miller, Burbano-Rosero, Edith Mariela, Hidalgo-Bonilla, Sandra P., Esteva, Lourdes, Romero-Leitón, Jhoana P.
• Format: Journal Article
• Language: English
• Published: Ireland Elsevier Ireland Ltd 01.03.2014
• Subjects: Anti-Bacterial Agents - pharmacology; Antibiotics; Bacteria; Bacterial Physiological Phenomena - drug effects; Bacterial Physiological Phenomena - genetics; Bacterial resistance; Cell Survival - drug effects; Cell Survival - genetics; Computer Simulation; Drug Resistance, Bacterial - drug effects; Drug Resistance, Bacterial - genetics; Equilibrium solutions; Microbial Viability - drug effects; Microbial Viability - genetics; Models, Genetic; Mutation - drug effects; Mutation - genetics; Ordinary differential equations; Ordinary differential equations; Primary: 34D23, 93D20; Equilibrium solutions; Bacterial resistance; Antibiotics; Secondary: 65L05
• ISSN: 0303-2647; 1872-8324
• DOI: 10.1016/j.biosystems.2014.01.005

•We model the interaction between sensitive and resistant bacteria to multiple antibiotics.•We consider the most basic mechanisms of acquisition of bacterial resistance to antibiotics.•Conditions that determine outcome of bacterial elimination or progression are established. We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is 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.