Abstract: In this paper, an HIV-1 infection model with saturation incidence and time delay due to the CTL immune response is investigated. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcation at the CTL-activated infection equilibrium are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, it is shown that the infection-free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity. When the immune response reproductive ratio is less than unity and the basic reproductive ratio is greater than unity, the CTL-inactivated infection equilibrium of the system is globally asymptotically stable. [Copyright &y& Elsevier]
Abstract: In this paper, we study a delayed six-dimensional human immunodeficiency virus (HIV) model with Cytotoxic T Lymphocytes (CTLs) immune response. Our model describes the interaction of HIV with two target cells: CD4+ T cells and macrophages. We derive that the global asymptotic attractivity of the model is completely determined by the basic reproduction number and the immune reproduction number for the viral infection. By constructing Lyapunov functionals, we have shown that the infection-free equilibrium , the immune-free equilibrium and the chronic-infection equilibrium are globally asymptotically attractive when and , respectively. [Copyright &y& Elsevier]
Abstract: In this paper, the dynamical behavior of a virus dynamics model with CTL immune response is studied. Sufficient conditions for the asymptotical stability of a disease-free equilibrium, an immune-free equilibrium and an endemic equilibrium are obtained. We prove that there exists a threshold value of the infection rate b beyond which the endemic equilibrium bifurcates from the immune-free one. Still for increasing b values, the endemic equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore’s condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings. [Copyright &y& Elsevier]