{"content"=>"TheDynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells.", "i"=>{"content"=>"In Vivo"}} (original) (raw)
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The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells
International Scholarly Research Notices, 2017
The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having 0 < 1. Lastly, the biological dynamics of HIV in vivo infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.
The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells
The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having . Lastly, the biological dynamics of HIV in vivo infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.
Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells
There have been many mathematical models aimed at analysing the in-vivo dynamics of HIV. However, in most cases the attention has been on the inte- raction between the HIV virions and the CD4+ T-cells. This paper brings in the intervention of the CD8+ T-cells in seeking, destroying, and killing the in- fected CD4+ T-cells during early stages of infection. The paper presents and analyses a five-component in-vivo model and applies the results in investigat- ing the in-vivo dynamics of HIV in presence of the CD8+ T-cells. We prove the positivity and the boundedness of the model solutions. In addition, we show that the solutions are biologically meaningful. Both the endemic and vi- rions-free equilibria are determined and their stability investigated. In addi- tion, the basic reproductive number is derived by the next generation matrix method. We prove that the virions-free equilibrium state is locally asymptoti- cally stable if and only if R0 <1 and unstable otherwise. The results show that at acute infection the CD8+ T-cells play a paramount role in reducing HIV viral replication. We also observe that the model exhibits backward and trans-critical bifurcation for some set of parameters for R0 < 1 . This is a clear indication that having R0 <1 is not sufficient condition for virions deple- tion.
Analysis of the dynamics of a mathematical model for HIV infection
Journal of Mathematics and Computer Science, 2020
Mathematical models are essential tools in the study of different infectious diseases. Researchers have developed other in-host models to investigate HIV dynamics in the human body. In this paper, a mathematical model for the HIV infection of CD4 + T cells is analyzed. We consider the proliferation of T cells in this study. It is found that there exist two equilibrium states for this model: Infection-free equilibrium state and infected equilibrium state. Local stability is discussed for both infection-free and infected equilibrium states using Routh-Hurwitz criteria. Also, we calculate the basic reproduction number (R 0) for the model with the help of next generation matrix method. The global stability of the infection-free equilibrium point is discussed using Lyapunov's second method. From the stability analysis, it is found that if basic reproduction number R 0 1, infection of HIV is cleared out, and if R 0 > 1, infection of HIV persists. The conditions for global stability of the infected equilibrium point are derived using a geometric approach. We find a parameter region where the infected equilibrium point is globally stable. We carry out numerical simulations to verify the results. Also, the effects of the proliferation rate of uninfected CD4 + T cells and recovery rate of infected CD4 + T cells in dynamics of the T cells and free virus are studied using numerical simulations. It is found that small variations of these parameters can change the model's whole dynamics, and infection can be controlled by controlling the proliferation rate and improving the recovery rate.
Mathematical Study of the Dynamics of the Development of HIV
Journal of Applied Mathematics and Physics, 2016
Over the history of humankind, they is no disease that has received so much attention as the HIV infection and mathematical models have been applied successfully to the investigation of HIV dynamics. It is, however, of note that, few of these investigations are able to explain the observation that host cell counts reduce while viral load increases as the infection progress. Also, various clinical studies of HIV infection have suggested that high T-cell activation levels are positively correlated with rapid disease development in untreated patients. This activation might be a major reason for the depletion of cells observed in most cases of long-term untreated HIV infection. In this paper, we use a simple mathematical model without treatment to investigate the stability of the system and compare the results with that obtained numerically by the use of MATHCAD. Our model which is a system of differential equations describing the interaction of the HIV and the immune system is divided into three compartments: uninfected CD4T cells, infected CD4Tcells and the virus population. This third compartment includes an extra source of the virus since it is believed that the virus in the blood constitute less than 2% of the total population. We obtain a linearization of the original system, and using Routh-Hurwitz condition for the non-linear system, the critical points are unstable.
Dynamics of an HIV-1 infection model with cell mediated immunity
Communications in Nonlinear Science and Numerical Simulation, 2014
In this paper, we study the dynamics of an improved mathematical model on HIV-1 virus with cell mediated immunity. This new 5-dimensional model is based on the combination of a basic 3-dimensional HIV-1 model and a 4-dimensional immunity response model, which more realistically describes dynamics between the uninfected cells, infected cells, virus, the CTL response cells and CTL effector cells. Our 5-dimensional model may be reduced to the 4-dimensional model by applying a quasi-steady state assumption on the variable of virus. However, it is shown in this paper that virus is necessary to be involved in the modeling, and that a quasi-steady state assumption should be applied carefully, which may miss some important dynamical behavior of the system. Detailed bifurcation analysis is given to show that the system has three equilibrium solutions, namely the infection-free equilibrium, the infectious equilibrium without CTL, and the infectious equilibrium with CTL, and a series of bifurcations including two transcritical bifurcations and one or two possible Hopf bifurcations occur from these three equilibria as the basic reproduction number is varied. The mathematical methods applied in this paper include characteristic equations, Routh-Hurwitz condition, fluctuation lemma, Lyapunov function and computation of normal forms. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions.
Mathematical Modeling Applied to Understand the Dynamical Behavior of HIV Infection
Open Journal of Modelling and Simulation
The study of viral dynamics of HIV/AIDS has resulted in a deep understanding of host-pathogenesis of HIV infection from which numerous mathematical modeling have been derived. Most of these models are based on nonlinear ordinary differential equations. In Bangladesh, the rate of increase of HIV infection comparing with the other countries of the world is not so high. Bangladesh is still considered to be a low prevalent country in the region with prevalence < 1% among MARP (Most at risk populations). In this paper, we have presented the current situation of HIV infection in Bangladesh and also have discussed the mathematical representation of a three-compartmental HIV model with their stability analysis. We have determined the basic reproduction number 0 R and shown the local and global stability at disease free and chronic infected equilibrium points. Also we have shown that if the basic reproduction number 0 1 R ≤ , then HIV infection is cleared from T cell population and it converges to disease free equilibrium point. Whereas if 0 1 R > , then HIV infection persists.
2020
The development of HIV, when evaluated in vivo can be modeled into a system of ordinary differential equations using a deterministic approach. Until now, there is no medicine to cure HIV infection, but there is a treatment that can slow the progression of HIV in the body called Antiretroviral Treatment. The development of HIV, when evaluated in vivo can be modeled into a system of ordinary differential equations using a deterministic approach. In this paper, a mathematical model be formed for the dynamics of HIV in the body with the intervention of Antiretroviral Treatment and take into account the influence of Apoptosis on T-cells. The dynamical system analysis of the model is derived by determining the stability of infectious free equilibrium point and endemic equilibrium point using the Routh-Hurwitz criterion. Numerical simulations are performed to analyze the effects of Antiretroviral Treatment intervention and the impact of Apoptosis on T-cells in inhibiting HIV progression.
Mathematical analysis of the global dynamics of a model for HIV infection of CD4 + T cells
A mathematical model that describes HIV infection of CD4 + T cells is analyzed. Global dynamics of the model is rigorously established. We prove that, if the basic reproduction number R 0 6 1, the HIV infection is cleared from the T-cell population; if R 0 > 1, the HIV infection persists. For an open set of parameter values, the chronic-infection equilibrium P * can be unstable and periodic solutions may exist. We establish parameter regions for which P * is globally stable.
Mathematical Model of HIV-1 Dynamics with T Cell Activation
Journal of Applied Mathematics and Physics, 2020
A deterministic in-host model of HIV-1 that incorporates naive and activated T cells is being investigated. The model represents the dynamics of five subsets of T cells and one class of HIV-1. The virus free and the infection persistent equilibria are found and their stability analysed. With the aid of suitable Lyapunov functionals, we have shown that the model equilibria are globally asymptotically stable under special conditions. The numerical simulation is performed to illustrate both the short term and long term dynamics of HIV-1 infection. The results of simulation are in agreement with published data with regard to CD4+ T cell concentration and the viral load.