Dynamic Analysis Of Some Kinds Of HIV Models With Saturation Incidence

HIV primarily infects host T lymphocytes,which are the main drivers of the immune response.HIV gradually depletes T lymphocytes,leading to a loss of T cell and immune cell function,and leaving the host T cell susceptible to infection.In order to better investigate the biological significance of this,many scholars have developed HIV models by considering various factors.In this thesis,we have developed several models of HIV infection dynamics with saturation rates,analyzed the dynamics of the models,and investigated the effects of factors such as saturation recovery rate and infection delay on the HIV dynamics models.Chapter 1 is an introductory section,which describes the background and significance of HIV research and lists the required mathematical theoretical knowledge.Chapter 2 develops a dynamics model of HIV infection with saturation incidence and recovery rates.Firstly,the non-negativity and boundedness of the solution are demonstrated;secondly,the basic regeneration number is defined and the conditions for the existence of equilibrium points are obtained;thirdly,the stability of disease-free equilibrium points and positive equilibrium points are investigated by means of the Hurwitz criterion,the construction of positive definite Lyapunov functions and the La Salle invariant set principle;finally,the accuracy of the results is verified by numerical simulations,and the stability of the equilibrium point is obtained.Chapter 3 considers the dynamics of HIV infection with saturation incidence and delay of infection.Firstly,the existence of Hopf bifurcation at disease-free equilibrium points and positive equilibrium points are discussed through Hopf bifurcation existential;secondly,through center manifold theory and normal form theory,we give analysis of the positive equilibrium in the direction of the Hopf bifurcation and stability;finally,numerical simulations are carried out by Matlab software to obtain images of the bifurcation cycle solutions and to give sufficient conditions for the system to generate bifurcation.Chapter 4 summarises the main work in this thesis and provides an outlook for future work.