Stability and Dynamic of HIV-1 Mathematical Model with Logistic Target Cell Growth, Treatment Rate, Cure Rate and Cell-to-cell Spread

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

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Modeling Cell-to-Cell Spread of HIV-1 with Nonlocal Infections

Complexity ◽

10.1155/2018/2139290 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 11

Author(s):

Xiaoting Fan ◽

Yi Song ◽

Wencai Zhao

Keyword(s):

Reproduction Number ◽

Reaction Diffusion ◽

Threshold Dynamics ◽

Delayed Reaction ◽

Heterogeneous Model ◽

Host Environment ◽

Reaction Diffusion Model ◽

Globally Attractive ◽

Cell Spread ◽

Hiv 1

This paper is devoted to develop a nonlocal and time-delayed reaction-diffusion model for HIV infection within host cell-to-cell viral transmissions. In a bounded spatial domain, we study threshold dynamics in terms of basic reproduction number R0 for the heterogeneous model. Our results show that if R0<1, the infection-free steady state is globally attractive, implying infection becomes extinct, while if R0>1, virus will persist in the host environment.

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Requirement for an Intact T-Cell Actin and Tubulin Cytoskeleton for Efficient Assembly and Spread of Human Immunodeficiency Virus Type 1

Journal of Virology ◽

10.1128/jvi.01469-06 ◽

2007 ◽

Vol 81 (11) ◽

pp. 5547-5560 ◽

Cited By ~ 134

Author(s):

Clare Jolly ◽

Ivonne Mitar ◽

Quentin J. Sattentau

Keyword(s):

Human Immunodeficiency Virus ◽

T Cells ◽

Plasma Membrane ◽

T Cell ◽

Immunodeficiency Virus ◽

Fixed Cell ◽

Cell Spread ◽

Hiv 1 ◽

Cell Cell

ABSTRACT Human immunodeficiency virus type 1 (HIV-1) infection of CD4+ T cells leads to the production of new virions that assemble at the plasma membrane. Gag and Env accumulate in the context of lipid rafts at the inner and outer leaflets of the plasma membrane, respectively, forming polarized domains from which HIV-1 buds. HIV-1 budding can result in either release of cell-free virions or direct cell-cell spread via a virological synapse (VS). The recruitment of Gag and Env to these plasma membrane caps in T cells is poorly understood but may require elements of the T-cell secretory apparatus coordinated by the cytoskeleton. Using fixed-cell immunofluorescence labeling and confocal microscopy, we observed a high percentage of HIV-1-infected T cells with polarized Env and Gag in capped, lipid raft-like assembly domains. Treatment of infected T cells with inhibitors of actin or tubulin remodeling disrupted Gag and Env compartmentalization within the polarized raft-like domains. Depolymerization of the actin cytoskeleton reduced Gag release and viral infectivity, and actin and tubulin inhibitors reduced Env incorporation into virions. Live- and fixed-cell confocal imaging and assay of de novo DNA synthesis by real-time PCR allowed quantification of HIV-1 cell-cell transfer. Inhibition of actin and tubulin remodeling in infected cells interfered with cell-cell spread across a VS and reduced new viral DNA synthesis. Based on these data, we propose that HIV-1 requires both actin and tubulin components of the T-cell cytoskeleton to direct its assembly and budding and to elaborate a functional VS.

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Functional Mapping of Regions Involved in the Negative Imprinting of Virion Particle Infectivity and in Target Cell Protection by Interferon-Induced Transmembrane Protein 3 against HIV-1

Journal of Virology ◽

10.1128/jvi.01716-18 ◽

2018 ◽

Vol 93 (2) ◽

Cited By ~ 6

Author(s):

Romain Appourchaux ◽

Mathilde Delpeuch ◽

Li Zhong ◽

Julien Burlaud-Gaillard ◽

Kevin Tartour ◽

...

Keyword(s):

Target Cell ◽

Transmembrane Protein ◽

Regulatory Role ◽

Target Cells ◽

Restriction Factors ◽

Cell Protection ◽

Differential Behavior ◽

Antiviral Activities ◽

Divergent Behavior ◽

Hiv 1

ABSTRACT The interferon-induced transmembrane proteins (IFITMs) are a family of highly related antiviral factors that affect numerous viruses at two steps: in target cells by sequestering incoming viruses in endosomes and in producing cells by leading to the production of virions that package IFITMs and exhibit decreased infectivity. While most studies have focused on the former, little is known about the regulation of the negative imprinting of virion particle infectivity by IFITMs and about its relationship with target cell protection. Using a panel of IFITM3 mutants against HIV-1, we have explored these issues as well as others related to the biology of IFITM3, in particular virion packaging, stability, the relation to CD63/multivesicular bodies (MVBs), the modulation of cholesterol levels, and the relationship between negative imprinting of virions and target cell protection. The results that we have obtained exclude a role for cholesterol and indicate that CD63 accumulation does not directly relate to an antiviral behavior. We have defined regions that modulate the two antiviral properties of IFITM3 as well as novel domains that modulate protein stability and that, in so doing, influence the extent of its packaging into virions. The results that we have obtained, however, indicate that, even in the context of an IFITM-susceptible virus, IFITM3 packaging is not sufficient for negative imprinting. Finally, while most mutations concomitantly affect target cell protection and negative imprinting, a region in the C-terminal domain (CTD) exhibits a differential behavior, potentially highlighting the regulatory role that this domain may play in the two antiviral activities of IFITM3. IMPORTANCE IFITM proteins have been associated with the sequestration of incoming virions in endosomes (target cell protection) and with the production of virion particles that incorporate IFITMs and exhibit decreased infectivity (negative imprinting of virion infectivity). How the latter is regulated and whether these two antiviral properties are related remain unknown. By examining the behavior of a large panel of IFITM3 mutants against HIV-1, we determined that IFITM3 mutants are essentially packaged into virions proportionally to their intracellular levels of expression. However, even in the context of an IFITM-susceptible virus, IFITM3 packaging is not sufficient for the antiviral effects. Most mutations were found to concomitantly affect both antiviral properties of IFITM3, but one CTD mutant exhibited a divergent behavior, possibly highlighting a novel regulatory role for this domain. These findings thus advance our comprehension of how this class of broad antiviral restriction factors acts.

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