Hopf bifurcation analysis of a phage therapy model

We examine the dynamic behavior of a phage therapy model, including nonlinear interactions between bacteria, phages, and the innate immune response. The main goal of this research is to study the existence of Hopf bifurcation and the direction and stability of bifurcating periodic solutions of the phage therapy model. By choosing the killing rate of the innate immune response as a bifurcation parameter, we establish the existence, direction, and stability of Hopf bifurcation at coexistence equilibrium by using the Poincare-Andronov-Hopf bifurcation theorem. Numerically, we investigate the intrinsic growth rate of bacteria, their carrying capacity, and the carrying capacity of the innate immune response by considering them as bifurcation parameters to understand how these parameters affect the system. We numerically examine how the phage parameters (the decay rate, adsorption rate, and burst size of the phage) affect the dynamic behavior of the model.