Modeling the effect of tobacco smoking on the in-host dynamics of HIV/AIDS (original) (raw)
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Modeling tobacco smoking effect on HIV antiretroviral therapy
Journal of Mathematical and Computational Science, 2017
In this paper, we formulate a mathematical model to study how tobacco smoking affects antiretroviral therapy. The model is based on the fact that smoking induces metabolism of ARVs and HIV patient addiction to smoking affects adherence to drugs. Equilibrium states and effective reproduction number R e f are computed. Conditions for equilibria stability are derived. The model shows that in the absence of tobacco smoking and HIV, disease free equilibrium is stable when R e f < 1 and in the presence of tobacco smoking and HIV, endemic equilibrium is stable when R e f > 1. The analysis shows that tobacco smoking decreases the efficacy of antiretroviral therapy and this effect is critical when smoking induces metabolism of antiretroviral drugs by 30% to 70%. Even if a HIV infected smoker remains adherent to therapy, still the effect of tobacco smoking on drugs' efficacy is inevitable. For management of HIV epidemic and its therapy, abstinence from smoking by HIV patients is recommended.
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.
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.
Mathematical Models of the Complete Course of HIV Infection and AIDS
Mathematical models of HIV infection are important to our understanding of AIDS. However, most models do not predict both the decrease in CD4 þ T cells and the increase in viral load seen over the course of infection. By including terms for continuous loss of CD4 þ T cells and incorporating alteration in viral clearance and viral production, two new models have been created that accurately predict the dynamics of the disease. The first model is a clearance rate reduction model and is based on a 10% per year decrease in both viral clearance and CD4 þ T cell levels. A macrophage reservoir model incorporating the observation that macrophage viral production increases up to 1000 fold in the presence of opportunistic infections that become increasingly common as disease progresses. Both viral clearance and macrophage reservoir models predict the expected decrease in T cell levels and rise in viral load observed at the onset of AIDS.
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.
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.
Ogunniran, M. A. Pub.1, 2018
In this work, we formulated a mathematical model to study the interaction between HIV/AIDS and Cluster of Differentiation 4 cells (CD4 + T), incorporating the roles of Cytotoxic T-lymphocytes (CTLs) cells and antiretroviral therapy. The proliferation of CD4 + T cells was considered to follow the logistic growth pattern. The presence of HIV in the CD4 + T cells stimulates the recruitment of CD4 + T and CTL cells. The recruitment of uninfected CD4 + T and CTL immune cells fall purely as an exponential function of time in the presence of HIV. The basic reproduction number 0 R was obtained using the next generation matrix method. We adopted the Jacobian stability criterion and the Lyaponuv second method of stability to establish the local and global stabilities of the equilibrium states and show that HIV can be eliminated from CD4 + T cells when 0 1 R but will continue to persist within CD4 + T cells when 0 1 R . Early medication therapy was observed to reduce viral load and increase the number of CTL cells, while CD4 + T cells is kept above the AIDS bar. A high initial viral load was noticed to induce rapid decline in the number of CD4 + T cells. To keep a healthy system, we recommended that the CTL and uninfected CD4 + T cells population should be maintained by reducing viral load through early medication therapy and cloning of CTL cells within infected human, which fights and kills infected cells.
Modeling the dynamics of HIV and T cells during primary infection
Nonlinear Analysis: Real World Applications, 2010
A mathematical model for the dynamics of HIV primary infection is proposed and analysed for the stability of infected state. Further, as there is a time delay for infected CD4 + T cells to become actively infected, a model is proposed to consider this time delay. The local stability of the delay model is discussed and results are shown numerically. It is found that the delay has no effect on the dynamics of HIV in the proposed model.
Modelling coupled within host and population dynamics of R_5R5andR 5 andR5andX_4$$ X 4 HIV infection
Journal of Mathematical Biology, 2017
Most existing models have considered the immunological processes occurring within the host and the epidemiological processes occurring at population level as decoupled systems. We present a new model using continuous systems of non linear ordinary differential equations by directly linking the within host dynamics capturing the interactions between Langerhans cells, CD4 + T-cells, R5 HIV and X4 HIV and the without host dynamics of a basic compartmental HIV/AIDS model. The model captures the biological theories of the cells that take part in HIV transmission. The study incorporates in its analysis the differences in time scales of the fast within host dynamics and the slow without host dynamics. In the mathematical analysis, important thresholds, the reproduction numbers, were computed which are useful in predicting the progression of the infection both within the host and without the host. The study results showed that the model exhibits four within host equilibrium points inclusive of three endemic equilibria whose effects translate into different scenarios at the population level. All the endemic equilibria were shown to be globally stable using Lyapunov functions and this is an important result in linking the within host dynamics to the population dynamics, because the disease free equilibrium point ceases to exist. The effects of linking were observed on the endemic equilibrium points of both the within host and population dynamics. Linking the two dynamics was shown to increase in the viral load within the host and increase in the epidemic levels in the population dynamics.
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.