The Research On HIV Dynamic Models With Beddington-DeAngelis Incidence And Delays Effect

Since the discovery of HIV in 1981,HIV has been a threat to human health.Ac-cording to statistics,there are currently 75.7 million people infected with HIV world-wide,and 32.7 million people have died of AIDS-related diseases.Therefore,under-standing the HIV virus The infection mechanism plays an important role in preventing and controlling the spread of the virus.This work mainly takes the HIV virus as the research background,and conducts an in-depth study on a type of HIV virus infection model with Beddington-DeAngelis incidence and distribution delay.The main content is summarized as follows,1.In the first part(corresponding to the second section),a kind of HIV virus dynamics model with distributed delay and Beddington-DeAngelis incidence rate is established.First,the positivity,boundedness of the system solution,and the basic reproduction number of the model are obtained.Secondly,the threshold condition for the existence of the positive equilibrium point of the system is established.By con-structing a suitable Lyapunov function,it is obtained that the disease-free equilibrium of the system is globally asymptotically stable when R₀<1.When R₀>1,the endemic equilibrium point is globally asymptotically stable.Finally,the theoretical results are demonstrated through numerical simulation,and the effects of discrete time delay and distributed time delay on the stability of the HIV virus dynamics model are compared.2.The second part(corresponding to the third section),considering that the reason why the HIV virus cannot be eradicated is due to the existence of latent infected cells,because some of the HIV virus does not actively replicate after infecting CD4⁺T cells,But hidden in these latent infected cells,even after antiviral treatment,it can still be reactivated and continue to replicate HIV virus.In order to understand the mechanism of HIV virus infection more deeply,we have established a latent infection in this section cells,Beddington-DeAngelis incidence and distribution delay HIV virus model,obtained the positivity,boundedness of the system solution,and the basic reproduction number of the system.Secondly,established the threshold condition for the existence of the positive equilibrium point of the system.By using The linearization method,Lyapunov functional method,obtained the stability of the equilibrium point.Finally,the impact of the reactivation delay of latent infected cells on the stability of the system is discussed.3.The third part(corresponding to the fourth section),Considering in the presence of latent infected cells,this section conducts a more in-depth study on a type of delayed HIV virus model with latent infection and Beddington-DeAngelis incidence.First,the positive and boundedness of the model solution is obtained,and the basic reproduction number of the model.The stability of the equilibrium point is obtained by constructing a suitable Lyapunov function.Furthermore,with the time delay as the bifurcation parameter,the existence of the Hopf bifurcation of the system is discussed.In the end,the theoretical results are demonstrated through numerical simulation.