An analysis of a stochastic model for bacteriophage systems

• Published in: Mathematical biosciences Vol. 241; no. 1; pp. 99 - 108
• Main Authors: Bardina, X., Bascompte, D., Rovira, C., Tindel, S.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.01.2013; Elsevier
• Subjects: Animals; Bacteria; Bacterial Infections - prevention & control; Bacterial Infections - therapy; Bacteriolysis; Bacteriophage; Bacteriophages - physiology; Brownian motion; Competition systems; Humans; Large deviations; Mathematical Concepts; Mathematics; Models, Biological; Probability; Stochastic Processes; Systems Biology; Brownian motion; Large deviations; Bacteriophage; Competition systems
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2012.09.009

► We model a bacteriophage therapies consisting in inoculating a (benign) virus in order to kill the bacteria known to be responsible of a certain disease. ► The model is a kind of predator–prey equation with delay and with noise that will appear when collecting data from laboratory tests. ► In a reasonable time the system is not far from its stable equilibrium. ► We have produced a concentration type result around the equilibrium. In this article, we analyze a system modeling bacteriophage treatments for infections in a noisy context. In the small noise regime, we show that after a reasonable amount of time the system is close to a bacteria free equilibrium (which is a relevant biologic information) with high probability. Mathematically speaking, our study hinges on concentration techniques for delayed stochastic differential equations.