Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with...Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state.Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E＊ and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.展开更多
In this paper, following a previous paper （[32] Permanence and extinction of a non- autonomous HIV-I model with two time delays, preprint） on the permanence and extinc- tion of a delayed non-autonomous HIV-1 within-...In this paper, following a previous paper （[32] Permanence and extinction of a non- autonomous HIV-I model with two time delays, preprint） on the permanence and extinc- tion of a delayed non-autonomous HIV-1 within-host model, we introduce and investigate a delayed HIV-1 model including maximum homeostatic proliferation rate of CD4＋ T- cells and varying coefficients. By applying the asymptotic analysis theory and oscillation theory, we show： （i） the system will be permanent when the threshold value R. 〉 1, and for this case we also obtain the explicit estimate of the eventual lower bound of the HIV-1 virus load; （ii） the threshold value R＊ 〈 1 implies the extinction of the virus. Furthermore, we obtain that the threshold dynamics is in agreement with that of the corresponding autonomous system, which extends the classic results for the system with constant coefficients. Numerical simulations are also given to illustrate our main results, and in particular, some sensitivity test of R. is established.展开更多
In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. F...In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. Further, the conditions for the existence of Hopf bifurcation are derived by evaluating the characteristic equation. The direction of Hopf bifurcation and stability of bifurcating periodic solutions are determined by employing the center manifold theorem and normal form method. Finally, some of the numerical simulations are carried out to validate the derived theoretical results and main conclusions are included.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 paper, we study the global properties of a human immunodeficiency virus （HIV） infection model with cytotoxic T lymphocytes （CTL） immune response. The model is a six-dimensional that describes the interacti...In this paper, we study the global properties of a human immunodeficiency virus （HIV） infection model with cytotoxic T lymphocytes （CTL） immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4＋ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R0 and the immune response activation number R0. We have proven that if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable （GAS）, if R0≤ 1 〈 R0, then the infected steady state without CTL immune response is GAS, and if R0〉 1, then the infected steady state with CTL immune response is GAS.展开更多
In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium ...In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number： if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infection persists, and the infected equilibrium is globally asymptotically stable.展开更多
文摘Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state.Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E＊ and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.
文摘In this paper, following a previous paper （[32] Permanence and extinction of a non- autonomous HIV-I model with two time delays, preprint） on the permanence and extinc- tion of a delayed non-autonomous HIV-1 within-host model, we introduce and investigate a delayed HIV-1 model including maximum homeostatic proliferation rate of CD4＋ T- cells and varying coefficients. By applying the asymptotic analysis theory and oscillation theory, we show： （i） the system will be permanent when the threshold value R. 〉 1, and for this case we also obtain the explicit estimate of the eventual lower bound of the HIV-1 virus load; （ii） the threshold value R＊ 〈 1 implies the extinction of the virus. Furthermore, we obtain that the threshold dynamics is in agreement with that of the corresponding autonomous system, which extends the classic results for the system with constant coefficients. Numerical simulations are also given to illustrate our main results, and in particular, some sensitivity test of R. is established.
文摘In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. Further, the conditions for the existence of Hopf bifurcation are derived by evaluating the characteristic equation. The direction of Hopf bifurcation and stability of bifurcating periodic solutions are determined by employing the center manifold theorem and normal form method. Finally, some of the numerical simulations are carried out to validate the derived theoretical results and main conclusions are included.
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.
文摘In this paper, we study the global properties of a human immunodeficiency virus （HIV） infection model with cytotoxic T lymphocytes （CTL） immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4＋ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R0 and the immune response activation number R0. We have proven that if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable （GAS）, if R0≤ 1 〈 R0, then the infected steady state without CTL immune response is GAS, and if R0〉 1, then the infected steady state with CTL immune response is GAS.
文摘In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number： if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infection persists, and the infected equilibrium is globally asymptotically stable.
