Analysis of deterministic and stochastic mathematical models with resistant bacteria and bacteria debris for bacteriophage dynamics

Abstract

Bacteriophages, more colloquially known as phages, are viruses that kill bacteria. Phages are used to treat bacterial infections. In this paper, an underlying deterministic bacteriophage model is extended with the objective of investigating bacteria-phage dynamics taking into account resistant bacteria and bacteria debris, and is analyzed. In addition, this extended model accounts for multiple phage attachment and phage loss due to attachment to latently and actively infected bacteria. Based on this extended deterministic model, two new stochastic models, a continuous-time Markov chain (CTMC) model and an Itô stochastic differential equation (SDE) model were derived and analyzed. Numerical examples illustrate some of the dynamics of the bacteriophage interaction when resistant bacteria are present.