Stability analysis of the hiv model through incommensurate fractional-order nonlinear system

Daşbaşı, Bahatdin

doi:10.1016/j.chaos.2020.109870

Cited by 21 publications

(4 citation statements)

References 46 publications

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“…Modeling and analysis of HIV dynamics with FODEs have been investigated in many papers (see e.g. [58][59][60]). Clinicians can use the information (in terms of behavior predictions) of fractional-order systems to fit patients' data with the most appropriate nonintegerorder index.…”

Section: Mathematical Modelsmentioning

confidence: 99%

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

AlShamrani

2021

Adv Differ Equ

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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 $\mathrm{CD} 4^{+}\mathrm{T}$ 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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Section: Mathematical Modelsmentioning

confidence: 99%

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

AlShamrani

2021

Adv Differ Equ

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“…Given the fact that the stability theorem of fractional differential equations favors stability analysis and controller synthesis, this motivates us to adopt stability criteria for the field of incommensurate fractional-order nonlinear systems and give sufficient conditions for determining stability [4]. Therefore, modeling of biological dynamics with IFOS is more comprehensive in terms of predicting the behavior of the system [5]. Furthermore, theorems of existence, uniqueness and dependence upon initial conditions according to some special conditions of IFOS are given in [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…There are many recent studies in the literature on the stability of IFOS [8,9,10,11]. In addition, modeling and stability analysis of biological systems by IFOS has been frequently discussed in the literature recently [12,13,5,7,14] and CFOS [15,16,17,18,19,20,21,22,23,24] . In the field of epidemiology, many schemes have been developed to mathematically model various infectious epidemics.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of an Incommensurate Fractional-Order SIR Model

Daşbaşı¹

2021

mmnsa

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In this paper, a fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of an infectious disease is presented. Also, an incommensurate fractional-order differential equations system involving the Caputo meaning fractional derivative is used. The equilibria are calculated and their stability conditions are investigated. Finally, numerical simulations are presented to illustrate the obtained theoretical results.

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“…We refer to [4] for a stability analysis of a Lotka-Volterra predator-prey fractional model with Caputo derivative and different orders of derivative, and to [5] for the case with the same order of derivative. In the framework of epidemic models, we refer to the paper [6], in which an HIV model is analyzed with different orders of fractional derivatives in the Caputo sense.…”

Section: Introductionmentioning

confidence: 99%

Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models

et al. 2021

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We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based on the Caputo derivative, for which we establish existence results of the solutions. Furthermore, we investigate a model based on the Caputo–Fabrizio operator, for which we provide existence of solutions and a study of the equilibria. Both models can be framed in the context of SIS models with time-varying total population, in which the competition between birth and death rates is macroscopically described by the fractional orders of the derivatives. Numerical simulations for both models and a direct numerical comparison are also provided.

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Stability analysis of the hiv model through incommensurate fractional-order nonlinear system

Cited by 21 publications

References 46 publications

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

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

Stability Analysis of an Incommensurate Fractional-Order SIR Model

Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models

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