Abstract
Bacteriophages or phages (viruses of bacteria) play numerous roles in shaping the diversity of bacterial communities within the human gut. Either a phage-infected bacterial cell immediately starts a lysis mechanisms (virulent/lytic infection), or it enters a stable state within the host as a prophage (lysogeny), until a trigger event, called Spontaneous Prophage Induction (SPI), allows the lysis phenomenon. We develop an approach to address the role of SPI within phage-bacteria interactions and the influence of lysogeny on the success of phage therapy. This is based on a model structure in terms of time since infection. Our analysis suggests that SPI allows lysogen bacteria to have a competitive advantage over their non-lysogenic counterparts. Moreover, the model exhibits the bistability phenomenon such that, depending on the initial conditions, the dynamic can either converge towards a purely temperate state (only lysogens and temperate phages persist) or a purely lytic state (only nonlysogens and virulent phages persist). We also highlight the existence of SPI's critical values leading to the coexistence of all states through periodic oscillations. Finally, the model suggests that efficient bacteria control through phage therapy can be achieved by minimizing lysogens' offspring.