Quasineutral dynamics shape coexistence and clearance in a model of in 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 summary Bacteriophages—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.