Bifurcation analysis of a phage-bacteria interaction model with prophage induction

Area of Science:

• Mathematical Biology
• Ecology
• Microbiology

Background:

• Phages interact with bacteria through lytic and lysogenic cycles.
• Prophage induction is a key factor in phage-bacteria dynamics.
• Understanding these interactions is crucial for controlling bacterial infections.

Purpose of the Study:

• To investigate conditions for phage-mediated bacterial environment purification.
• To determine if phages can trigger bacterial outbreaks.
• To analyze phage-bacteria dynamics using a mathematical model.

Main Methods:

• Developed a predator-prey model incorporating phage life cycles.
• Derived the basic offspring number (N0) as a threshold parameter.
• Applied Lyapunov-LaSalle techniques and center manifold approximation for stability analysis.
• Investigated transcritical and Hopf bifurcations.

Main Results:

• Identified three equilibria: unstable, phage-free (PFE), and environment-persistent (EPE).
• PFE is globally asymptotically stable when N0 < 1.
• EPE is locally stable when N0 > 1, with periodic solutions arising via Hopf bifurcation for N0 > 1.
• High N0 leads to bacterial population decline, while low N0 can cause periodic outbreaks.

Conclusions:

• Phage presence can purify environments at high N0.
• Periodic solutions at low N0 may explain recurrent bacterial outbreaks.
• The model provides insights into phage therapy and bacterial infection dynamics.