In this paper,dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated.The model involves the concentrations of uninfected cells,infected cells,free viru...In this paper,dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated.The model involves the concentrations of uninfected cells,infected cells,free virus,CTL response cells,and antibody antibody response cells.There are three delays in the model:the intracellular delay,virus replication delay and the antibody delay.The basic reproductive number of viral infection,the antibody immune reproductive number,the CTL immune reproductive number,the CTL immune competitive reproductive number and the antibody immune competitive reproductive number are derived.By means of Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions for the stability of each equilibrium is established.The results show that the intracellular delay and virus replication delay do not impact upon the stability of each equilibrium,but when the antibody delay is positive,Hopf bifurcation at the antibody response and the interior equilibrium will exist by using the antibody delay as a bifurcation parameter.Numerical simulations are carried out to justify the analytical results.展开更多
In this paper,the dynamical behaviors for a five-dimensional virus infection model with Latently Infected Cells and Beddington-DeAngelis incidence are investigated.In the model,four delays which denote the latently in...In this paper,the dynamical behaviors for a five-dimensional virus infection model with Latently Infected Cells and Beddington-DeAngelis incidence are investigated.In the model,four delays which denote the latently infected delay,the intracel-lular delay,virus production period and CTL response delay are considered.We define the basic reproductive number and the CTL immune reproductive number.By using Lyapunov functionals,LaSalle's invariance principle and linearization method,the threshold conditions on the stability of each equilibrium are established.It is proved that when the basic reproductive number is less than or equal to unity,the infection-free equilibrium is globally asy mptot ically stable;when the CTL immune repro-ductive number is less than or equal to unity and the basic reproductive number is greater than unity,the immune free infection equilibrium is globally asymptotically stable;when the CTL immune reproductive number is greater than unity and immune response delay is equal to zero,the immune infection equilibrium is globally asymptotically stable.The results show that immune response delay may destabilize the steady state of infection and lead to Hopf bifurcation.The existence of the Hopf bifurcation is discussed by using immune response delay as a bifurcation parameter.Numerical simulations are carried out to justify the analytical results.展开更多
基金The work was supported by NSF of China(11201002)Natural Science Foundation of Universities in Anhui Province(KJ2017A815).
文摘In this paper,dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated.The model involves the concentrations of uninfected cells,infected cells,free virus,CTL response cells,and antibody antibody response cells.There are three delays in the model:the intracellular delay,virus replication delay and the antibody delay.The basic reproductive number of viral infection,the antibody immune reproductive number,the CTL immune reproductive number,the CTL immune competitive reproductive number and the antibody immune competitive reproductive number are derived.By means of Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions for the stability of each equilibrium is established.The results show that the intracellular delay and virus replication delay do not impact upon the stability of each equilibrium,but when the antibody delay is positive,Hopf bifurcation at the antibody response and the interior equilibrium will exist by using the antibody delay as a bifurcation parameter.Numerical simulations are carried out to justify the analytical results.
基金This work is supported by the National Science Foundation of China[No.11201002]the Major Project of Natural Science Foundation of Anhui Province[No.KJ2017A815]We would like to thank the anonymous referees and the edi-tor for very helpful suggestions and comments,which have improved the quality of our study.
文摘In this paper,the dynamical behaviors for a five-dimensional virus infection model with Latently Infected Cells and Beddington-DeAngelis incidence are investigated.In the model,four delays which denote the latently infected delay,the intracel-lular delay,virus production period and CTL response delay are considered.We define the basic reproductive number and the CTL immune reproductive number.By using Lyapunov functionals,LaSalle's invariance principle and linearization method,the threshold conditions on the stability of each equilibrium are established.It is proved that when the basic reproductive number is less than or equal to unity,the infection-free equilibrium is globally asy mptot ically stable;when the CTL immune repro-ductive number is less than or equal to unity and the basic reproductive number is greater than unity,the immune free infection equilibrium is globally asymptotically stable;when the CTL immune reproductive number is greater than unity and immune response delay is equal to zero,the immune infection equilibrium is globally asymptotically stable.The results show that immune response delay may destabilize the steady state of infection and lead to Hopf bifurcation.The existence of the Hopf bifurcation is discussed by using immune response delay as a bifurcation parameter.Numerical simulations are carried out to justify the analytical results.
