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Abstract
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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 Poincaré–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.
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Keywords
phage therapy model, stability, Hopf bifurcation,
Poincaré–Andronov–Hopf bifurcation theorem, numerical
simulations
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Mathematical Subject Classification
Primary: 37M20
Secondary: 34C23, 34D20
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Milestones
Received: 31 December 2022
Revised: 13 October 2023
Accepted: 12 November 2023
Published: 21 December 2023
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