Global properties and bifurcation analysis of an HIV-1 infection model with two target cells

Liu, Yongqi; Liu, Xuanliang

doi:10.1007/s40314-017-0523-0

Cited by 6 publications

(4 citation statements)

References 33 publications

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“…These models included two compartments of infection, but did not describe the asymptotical viral dynamics after transplantation of the liver. Qesmi et al [17] proposed a mathematical model of ordinary differential equations to describe the dynamics of the HBV/HCV and its interaction with both liver and blood cells based on [4,13], and found that the system undergoes either a transcritical or a backward bifurcation. Wodarz and Jansen [23] proposed a model containing infected cells, non-acitived antigen presenting cells (APCs), acitived APCs and CTL, and analysed its complex dynamics.…”

Section: Introductionmentioning

confidence: 99%

Threshold dynamics of a HCV model with virus to cell transmission in both liver with CTL immune response and the extrahepatic tissue

Feng

2020

Journal of Biological Dynamics

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Section: Introductionmentioning

confidence: 99%

Threshold dynamics of a HCV model with virus to cell transmission in both liver with CTL immune response and the extrahepatic tissue

Feng

2020

Journal of Biological Dynamics

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“…As a result, more accurate drug efficacy can be determined when using the HIV model with two classes of target cells. Recently, many efforts have been devoted to the analysis of various mathematical models of HIV dynamics with two categories of target cells (see, e.g., [29][30][31][32][33][34][35][36][37]). However, in these papers, the production and removal rates of the HIV particles and cells are given by linear functions; moreover, only one or two classes of infected cells are considered.…”

Section: Introductionmentioning

confidence: 99%

Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays

Ełaiw

Elnahary

2019

Mathematics

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This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4 + T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The model is incorporated with distributed time delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The effect of antibody on HIV infection is analyzed. The production and removal rates of the ten compartments of the model are given by general nonlinear functions which satisfy reasonable conditions. Nonnegativity and ultimately boundedness of the solutions are proven. Using the Lyapunov method, the global stability of the equilibria of the model is proven. Numerical simulations of the system are provided to confirm the theoretical results. We have shown that the antibodies can play a significant role in controlling the HIV infection, but it cannot clear the HIV particles from the plasma. Moreover, we have demonstrated that the intracellular time delay plays a similar role as the Highly Active Antiretroviral Therapies (HAAT) drugs in eliminating the HIV particles.

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“…In this case, HIV has two resources and then coexistence of HIV and HTLV-I can be occurred even when the immune system is inactive. HIV mono-infection models with two classes of target cells have been studied in several works, (see e.g., [10] and [6,11,[13][14][15][16]34]) Therefore, our model can be extended to take into account the second class of target cells for HIV, macrophages. We leave this extension for future works.…”

Section: Equilibrium Pointmentioning

confidence: 99%

Global stability of HIV/HTLV co-infection model with CTL-mediated immunity

Ełaiw¹,

AlShamrani²

2022

DCDS-B

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Mathematical modeling of human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) mono-infections has received considerable attention during the last decades. These two viruses share the same way of transmission between individuals; through direct contact with certain contaminated body fluids. Therefore, a person can be co-infected with both viruses. In the present paper, we construct and analyze a new HIV/HTLV-I co-infection model under the effect of Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD4 + T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing (active) HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by two routes of transmission, virus-to-cell (VTC) and cell-to-cell (CTC). Both active and silent HIV-infected cells can infect the susceptible CD4 + T cells by CTC mechanism. On the other side, HTLV-I has only one mode of transmission via direct cell-to-cell contact. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We calculate all possible equilibria and define the key threshold parameters which govern the existence and stability of all equilibria of the model. We explore the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have discussed the influence of CTL immune response on the co-infection dynamics. We have presented numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we evaluate the effect of HTLV-I infection on the HIV dynamics and vice versa.

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Global properties and bifurcation analysis of an HIV-1 infection model with two target cells

Cited by 6 publications

References 33 publications

Threshold dynamics of a HCV model with virus to cell transmission in both liver with CTL immune response and the extrahepatic tissue

Threshold dynamics of a HCV model with virus to cell transmission in both liver with CTL immune response and the extrahepatic tissue

Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays

Global stability of HIV/HTLV co-infection model with CTL-mediated immunity

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