An analysis of a stochastic model for bacteriophage systems

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.

► 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.