Quasineutral dynamics shape coexistence and clearance in a model ofin vitro phage-bacteria interactions

Phage therapy, which uses viruses that infect bacteria to target and lyse specific bacterial pathogens, has re-emerged as a promising strategy to combat antibiotic-multiresistant bacteria. Advances in metagenomics and synthetic biology, together with systems biology approaches combining mathematical modeling with experimental data, provide excellent opportunities to understand phage-bacteria dynamics. Here we analyze a mathematical model successfully calibrated using in vitro data on the multidrug-resistant bacterium Klebsiella pneumoniae in the presence of the phage vB Kpn 2-P4. The model describes a system with a susceptible bacterial population that can generate phage-resistant mutants. By analyzing the equilibria and bifurcations of the model, we identify a coexistence scenario between phage-resistant bacteria and phages governed by a quasineutral line of equilibria with both stable and unstable segments. Biologically, this quasineutral structure implies that phage-resistant bacteria can persist across a wide range of phage densities without selective pressure favoring a unique outcome, making clearance highly sensitive to additional mortality mechanisms. The clearance of phage-resistant bacteria can be achieved by combining phage activity with an increased death rate of the resistant strains. This process is governed by a global transcritical bifurcation of the quasineutral line. Our model offers mechanistic insight into potential scenarios leading to the complete elimination of phage-resistant bacteria. Author summaryBacteriophages--viruses that infect bacteria--are being reconsidered as alternatives to antibiotics, but bacterial resistance to phages often emerges rapidly. Understanding when phages and bacteria coexist and when resistant bacteria can be eliminated remains a major challenge. In this study, we analyze a mathematical model calibrated with in vitro data describing interactions between bacteria, bacteriophages, and phage-resistant mutants. Using tools from dynamical systems theory, we show that coexistence between phages and resistant bacteria is organized by a quasineutral line of equilibrium states rather than a single stable outcome. This structure explains why long-term dynamics can be highly sensitive to initial conditions without being chaotic. We further identify a bifurcation that leads to the extinction of resistant bacteria when their effective mortality exceeds a critical threshold. Our results provide a mechanistic framework for interpreting resistance-driven outcomes in phage-bacteria systems and highlight how mathematical structure can constrain therapeutic strategies, even in simple experimental settings.