An analysis of a stochastic model for bacteriophage systems

Xavier Bardina, David Bascompte, Carles Rovira and Samy Tindel

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona, Spain
Institut Élie Cartan Nancy, B.P. 239, 54506 Vandoeuvre-lès-Nancy Cedex, France.
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona

Abstract

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 sane equilibrium (which is a relevant biologic information) with high probability. Mathematically speaking, our study hinges on concentration techniques for delayed stochastic differential equations.

Keywords: Bacteriophage, competition systems, Brownian motion, large deviations

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