Stability of an HTLV-HIV coinfection model with multiple delays and CTL-mediated immunity.

IF 4.1 3区 数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-05-25 DOI:10.1186/s13662-021-03416-7
N H AlShamrani
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引用次数: 2

Abstract

In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected CD 4 + T cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system.

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具有多重延迟和ctl介导免疫的HTLV-HIV共感染模型的稳定性
在文献中,已经制定和发展了几个数学模型来描述人类免疫缺陷病毒(HIV)或人类嗜t淋巴病毒I型(HTLV-I)单感染的宿主内动力学。在本文中,我们制定并分析了一种考虑细胞毒性T淋巴细胞(ctl)反应的HTLV-HIV共感染的新的宿主内动力学模型。未感染的cd4 + T细胞可通过两种机制被HIV感染,即游离细胞感染和细胞间感染。另一方面,HTLV-I有两种传播方式,(i)水平传播,通过被感染的细胞直接接触,(ii)垂直传播,通过活跃的htlv感染细胞的有丝分裂。众所周知,细胞内时间延迟在宿主内病毒动力学中起着重要作用。在这项工作中,我们考虑了六种类型的分布式时滞。我们研究解的基本性质。然后,根据阈值参数计算模型的稳态。此外,我们还利用Lyapunov方法研究了稳态的全局稳定性。我们进行了数值模拟来说明和支持我们的理论结果。此外,我们还讨论了多时滞对系统稳态稳定性的影响。
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4-8 weeks
期刊介绍: The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
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