In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is inve...In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle＇s invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.展开更多
A general nonlinear mathematical model for the viral infection with humoral immunity and two distributed delays is proposed and analyzed. Two bifurcation parameters, the basic reproduction number, R0 and the humoral i...A general nonlinear mathematical model for the viral infection with humoral immunity and two distributed delays is proposed and analyzed. Two bifurcation parameters, the basic reproduction number, R0 and the humoral immunity number, R1 are derived. We established a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. Utilizing Lyapunov functions and LaSalle＇s invariance principle, the global asymptotic stability of all equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior.展开更多
In this paper, we propose a nonlinear virus dynamics model that describes the interac- tions of the virus, uninfected target cells, multiple stages of infected cells and B cells and includes multiple discrete delays. ...In this paper, we propose a nonlinear virus dynamics model that describes the interac- tions of the virus, uninfected target cells, multiple stages of infected cells and B cells and includes multiple discrete delays. We assume that the incidence rate of infection and removal rate of infected cells are given by general nonlinear functions. The model can be seen as a generalization of several humoral immunity viral infection model presented in the literature. We derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to establish the existence and global stability of the three equilibria of the model. We study the globa! asymptotic stability of the equilibria by using Lyapunov method. We perform some numerical simulations for the model with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.展开更多
In this study, we consider two target-cell limited models with saturation type infec- tion rate and intracellular delay： one without self-proliferation and the other with self- proliferation of activated CD4＋T cells...In this study, we consider two target-cell limited models with saturation type infec- tion rate and intracellular delay： one without self-proliferation and the other with self- proliferation of activated CD4＋T cells. We discuss about the local and global behavior of both the systems in presence and absence of intracellular delay. It is shown that the endemic equilibrium of a target-cell limited model would be unstable in presence and absence of intraeellular delay only when self-proliferation of activated CD4＋T cell is considered. Otherwise, all positive solutions converge to the endemic equilibrium or disease-free equilibrium depending on whether the basic reproduction ratio is greater than or less than unity. Our study suggests that amplitude of oscillation is negatively correlated with the constant input rate of CD4＋T cell when intracellular delay is absent or low. However, they are positively correlated if the delay is too high. Amplitude of oscillation, on the other hand, is always positively correlated with the proliferation rate of CD4＋T cell for all delay. Our mathematical and simulation analysis also suggest that there are many potential contributors who are responsible for the variation of CD4＋T cells and virus particles in the blood plasma of HIV patients.展开更多
文摘In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle＇s invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.
文摘A general nonlinear mathematical model for the viral infection with humoral immunity and two distributed delays is proposed and analyzed. Two bifurcation parameters, the basic reproduction number, R0 and the humoral immunity number, R1 are derived. We established a set of conditions on the general functions which are sufficient to determine the global dynamics of the model. Utilizing Lyapunov functions and LaSalle＇s invariance principle, the global asymptotic stability of all equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior.
文摘In this paper, we propose a nonlinear virus dynamics model that describes the interac- tions of the virus, uninfected target cells, multiple stages of infected cells and B cells and includes multiple discrete delays. We assume that the incidence rate of infection and removal rate of infected cells are given by general nonlinear functions. The model can be seen as a generalization of several humoral immunity viral infection model presented in the literature. We derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to establish the existence and global stability of the three equilibria of the model. We study the globa! asymptotic stability of the equilibria by using Lyapunov method. We perform some numerical simulations for the model with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.
基金supported by the National Natural Science Foundation of China(Nos.11371368,11071254)the Natural Science Foundation of Hebei Province of China(No.A2014506015)the Natural Science Foundation for Young Scientists of Hebei Province,China(No.A2013506012)
文摘In this study, we consider two target-cell limited models with saturation type infec- tion rate and intracellular delay： one without self-proliferation and the other with self- proliferation of activated CD4＋T cells. We discuss about the local and global behavior of both the systems in presence and absence of intracellular delay. It is shown that the endemic equilibrium of a target-cell limited model would be unstable in presence and absence of intraeellular delay only when self-proliferation of activated CD4＋T cell is considered. Otherwise, all positive solutions converge to the endemic equilibrium or disease-free equilibrium depending on whether the basic reproduction ratio is greater than or less than unity. Our study suggests that amplitude of oscillation is negatively correlated with the constant input rate of CD4＋T cell when intracellular delay is absent or low. However, they are positively correlated if the delay is too high. Amplitude of oscillation, on the other hand, is always positively correlated with the proliferation rate of CD4＋T cell for all delay. Our mathematical and simulation analysis also suggest that there are many potential contributors who are responsible for the variation of CD4＋T cells and virus particles in the blood plasma of HIV patients.
基金Supported by the National Natural Science Foundation of China(11371048)the Plan Project of Science and Technology of Beijing Municipal Education Committee(KM201610016018)the Central Support Local Projects(21147515602)
