Global stability analysis of HIV-1 infection model with three time delays

Stochastic model of the dynamics of HIV-1 infection describing the interaction of target cells and viral particles in the lymphatic nodes and their movement between the lymphatic nodes is constructed. The lymphatic system is represented as a graph, vertices of which are the lymphatic nodes and edges are the lymphatic vessels. The novelty of the model consists in the description of populations of cells and viral particles in terms of a multidimensional birth and death process with the random point-distributions. The random pointdistributions describe the duration of the transition of cells and viral particles between the lymph nodes and the duration of the stages of their development. The durations of transitions of viral particles and cells between the lymphatic nodes are not random and based on the rate of lymph flow. The durations of the developmental stages of infected target cells are assume to be constant. The graph theory for the formalization and compact representation of the model is used. An algorithm for modelling the dynamics of the studied populations is constructed basing on the Monte-Carlo method. The results of computational experiments for a system consisting of five lymphatic nodes are presented. *

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“…Following [2,4,6,10], we introduce the set of assumptions that determine dynamics of HIV-1 infection:…”

Section: Moreover Let S Denotes the Cell Source In Bone Marrow And Lmentioning

confidence: 99%

“…Mostly, these models are divided into deterministic and stochastic one. Deterministic models take the form of the systems of delay differential equations [3,4]. The equations of such models describe concentration of target cells, infected cells, viral particles, etc.…”

Section: Introductionmentioning

confidence: 99%

Stochastic compartmental model of HIV-1 infection

Loginov

Pertsev

2020

ITM Web Conf.

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“…To understand how models are currently used to represent the progression of this disease, we considered 40 recent models of within-host dynamics, all of which are expressed as nonlinear systems of differential equations. Of these models, one used stochastic differential equations Wang, Liu, Xu & Zhang (2015) and eight used delayed differential equations (Huang et al (2016) , Alshorman et al (2016), Pitchaimani & Monica (2015), Sahani (2016), Balasubramaniam et al (2015), Elaiw & Almuallem (2016)). In addition, the focus of several of these papers was somewhat different from ours.…”

Section: Of 32mentioning

confidence: 99%

A mathematical model of HIV dynamics treated with a population of gene-edited haematopoietic progenitor cells exhibiting threshold phenomenon

Ratti

Nanda

Eszterhas

et al. 2019

Mathematical Medicine and Biology: A Journal of the IMA

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The use of gene-editing technology has the potential to excise the CCR5 gene from haematopoietic progenitor cells, rendering their differentiated CD4-positive (CD4+) T cell descendants HIV resistant. In this manuscript, we describe the development of a mathematical model to mimic the therapeutic potential of gene editing of haematopoietic progenitor cells to produce a class of HIV-resistant CD4+ T cells. We define the requirements for the permanent suppression of viral infection using gene editing as a novel therapeutic approach. We develop non-linear ordinary differential equation models to replicate HIV production in an infected host, incorporating the most appropriate aspects found in the many existing clinical models of HIV infection, and extend this model to include compartments representing HIV-resistant immune cells. Through an analysis of model equilibria and stability and computation of $R_0$ for both treated and untreated infections, we show that the proposed therapy has the potential to suppress HIV infection indefinitely and return CD4+ T cell counts to normal levels. A computational study for this treatment shows the potential for a successful ‘functional cure’ of HIV. A sensitivity analysis illustrates the consistency of numerical results with theoretical results and highlights the parameters requiring better biological justification. Simulations of varying level production of HIV-resistant CD4+ T cells and varying immune enhancements as the result of these indicate a clear threshold response of the model and a range of treatment parameters resulting in a return to normal CD4+ T cell counts.

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“…In Ref. [13], the authors considered the therapy of reverse transcriptase inhibitors (RTIs) drugs which have different drug efficacy on CD4+ T cells, to block conversion of uninfected cells to infected cells. In Refs [14,15], protease inhibitor (PI) drugs therapy was designed to intervene replication of the virus, make the newly produced virus noninfectious.…”

Section: Introductionmentioning

confidence: 99%

A stochastic model of HIV infection incorporating combined therapy of HAART driven by Lévy jumps

2019

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A stochastic HIV infection model of virus-to-cell transmission is proposed, incorporating the antiretroviral drug therapy by introducing efficacy parameters of RTI and PI drugs, considering the Lévy noise for the inherent stochastic biochemical processes. First, we discuss the model existence of a global positive solution and, by applying Itô's formula, establish a sufficient condition for the extinction of infected CD4 + T-cells and virus particles. Then, for proving the persistence in mean, a special method is investigated to handle the model. It is obtained that ifR 1 > 1 the infected CD4 + T-cells and virus particles will be persistent in mean. Finally, some numerical simulations are carried out to show the effects of inherent stochastic fluctuation.

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Global stability analysis of HIV-1 infection model with three time delays

Cited by 25 publications

References 57 publications

Stochastic compartmental model of HIV-1 infection

Stochastic compartmental model of HIV-1 infection

A mathematical model of HIV dynamics treated with a population of gene-edited haematopoietic progenitor cells exhibiting threshold phenomenon

A stochastic model of HIV infection incorporating combined therapy of HAART driven by Lévy jumps

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