The Impact of Prophage on the Equilibria and Stability of Phage and Host

Abstract

In this paper, we present a bacteriophage model that includes prophage, that is, phage genomes that are incorporated into the host cell genome. The general model is described by an 18-dimensional system of ordinary differential equations. This study focuses on asymptotic behaviour of the model, and thus the system is reduced to a simple six-dimensional model, involving uninfected host cells, infected host cells and phage. We use dynamical system theory to explore the dynamic behaviour of the model, studying in particular the impact of prophage on the equilibria and stability of phage and host. We employ bifurcation and stability theory, centre manifold and normal form theory to show that the system has multiple equilibrium solutions which undergo a series of bifurcations, finally leading to oscillating motions. Numerical simulations are presented to illustrate and confirm the analytical predictions. The results of this study indicate that in some parameter regimes, the host cell population may drive the phage to extinction through diversification, that is, if multiple types of host emerge; this prediction holds even if the phage population is likewise diverse. This parameter regime is restricted, however, if infecting phage are able to recombine with prophage sequences in the host cell genome.