A Bacteriophage Therapy Model In Vivo With Time Delay

The growing problem of antibiotic resistance has led to renewed interest in bacteriophage therapy as a potential alternative to antibiotics for the treatment of drug-resistant bacteria.Considering the latency time delay in the process of bacteriophage treatment,this thesis introduce the dynamic modelling method and establish a bacteriophage therapy in vivo model with time delay as bacteria-bacteriophage-the host innate immune cell model,aiming to reveal the effect of time delay on the mechanism of bacteriophage therapy.Theoretical analyses characterize the existence and stability conditions of equilibrium points are given by the qualitative theory of delay differential equations.Next,we study the existence of Hopf bifurcation based on Beretta and Kuang’s geometric discriminant criterion.Consequently,we discuss the direction and stability of the Hopf bifurcation around the positive equilibrium point by means of the center manifold and the normal form theory.Numerically,it shows that the system has complex dynamical behaviours by using Matlab software,which includes Hopf bifurcation,stability switch and bistable phenomenon.Moreover,the simulation results verify the correctness of the theory.The results obtained in this thesis provide a theoretical basis for the design of optimal scheme for bacteriophage therapy.