Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana–Baleanu fractional operator: Real data approach

Xu, Changjin; Liu, Zixin; Pang, Yicheng; Saifullah, Sayed; İnç, Mustafa

doi:10.1016/j.chaos.2022.112662

Cited by 12 publications

(6 citation statements)

References 20 publications

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“…Constructing realistic nonlinear compartmental math- ematical models that are data-driven to better explain the transmission dynamics of epidemics has garnered much attention in the wake of the recent global COVID-19 outbreaks [1][2][3][4][5][6][7][8], including several other important research studies on mathematical modeling with the Caputo and other memory operators, as discussed in [9][10][11][12]. Musa et al [13] propose a novel eight-compartmental deterministic model for the COVID-19 epidemic in Nigeria, which accounts for awareness campaign initiatives and hospitalization control tactics for severe and moderate instances of infections. Infected cumulative instances in Nigeria were used to fit the suggested nonlinear dynamical model from 29 March 2020 to 12 June 2020.…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis of classical and Caputo models for COVID-19 spread: vaccination and stability assessment

Tassaddiq,

Qureshi,

Soomro

et al. 2024

Fixed Point Theory Algorithms Sci Eng

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Several epidemiological models use the Caputo fractional-order differential operator without establishing its significance. This study verifies a Caputo operator-based fractional-order epidemiological model of the SAIVR type. COVID-19 kills. Infection weakens the immune system. The fractional Caputo operator describes COVID-19 immunization. Fundamental system characteristics are determined using fractional calculus. Our analysis included the fractional system’s Hyers–Ulam–Rassias stability and stable states. The uniqueness and existence of fractional Caputo system solutions are explored. The least-squares approach determines system parameters. The Caputo fractional-order α value is optimized to $6.757\text{e}{-}01$ 6.757 e − 01 , indicating that the system best fits real-life medical data for infection. Caputo and classical systems were compared for absolute mean errors. The Box-Whisker chart case summaries show the Caputo operator superiority. When $\alpha \rightarrow 1$ α → 1 , the memory traces and hereditary traits are also observed. Finally, the Caputo fractional framework simulates COVID-19 using strong numerical methods.

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Section: Introductionmentioning

confidence: 99%

Comparative analysis of classical and Caputo models for COVID-19 spread: vaccination and stability assessment

Tassaddiq,

Qureshi,

Soomro

et al. 2024

Fixed Point Theory Algorithms Sci Eng

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“…Researchers are currently using a novel approach to examine the cross-over behaviors caused by these operators. For some detail study, we cite some well known works such as [33][34][35][36]. The interaction between cancerous cells that are not infected with a virus and malignant cells that are infected with it is described in mathematical models for oncolytic virotherapy that are based on piecewise differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

Khan,

Shah,

Debbouche

et al. 2024

Phys. Scr.

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We examine a nonlinear dynamical model that depicts the interaction between cancerous cells and an oncolytic virus. For best modelling the disease, we use the Caputo fractional derivative in piecewise approaches. By employing piecemeal techniques, we treat a compartment in the body that contains infectious and non-infectious cells. More precisely, the solvability and Ulam-Hyers (U-H) stability results are considered using standard concepts. Further, to support our investigation with numerical results, we apply the Euler method to develop an approximation solution. It connected with numerous graphical representations of the system using various arbitrary ordering and varying values of the isolation parameters. Here we remark that the multi-step behavior that certain problems exhibit, is one of important issues naturally. This paper introduces the idea of piecewise derivative with the goal of modeling real-world issues that follow multiples processes. With the help of the used approach, we investigate the cancer disease model and its transmission dynamical behavior with crossover effect.

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“…For example, Rihan and Rajivganthi [28] studied the Hopf bifurcation and stability of a fractional-order delay predator-prey model involving Holling-type III function; Wang et al [29] investigated the bifur-cation phenomenon and stability for a fractional-order delayed predatorprey model owning interspecific competition; Xiao et al [30] discussed controller design of finite-time synchronization in fractional memristive neural network models; Liu et al [31] explored the event-triggered bipartite synchronization issue of coupled fractional-order neural networks. For more concrete contents, one can see [32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation Control of a Fractional-Order Delayed Turbidostat Model via a Novel Extended Hybrid Controller

Xu,

Ou,

Pang

et al. 2023

match

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Building delayed dynamical models to describe the inherent laws of different chemical matters has become a hot theme in recent years. In this current study, we set up a new fractional-order delayed turbidostat model. By using laplace transform, we obtain the characteristic equation of established fractional-order delayed turbidostat model. By selecting the delay as bifurcation parameter and exploring the roots of the corresponding characteristic equation of the involved fractional-order delayed turbidostat model, a novel delay-dependent condition on stability and Hopf bifurcation is acquired. Taking advantage of a novel extended hybrid controller, the stability region and the time of Hopf bifurcation of the established fractional-order delayed turbidostat model are successfully controlled. The role of delay in stabilizing system and controlling Hopf bifurcation is revealed. Matlab experiments are carried out to check the rationality of the acquired key outcomes in this article. The acquired outcomes of this study are completely new and own great theoretical value in dominating concentrations of various chemical matters.

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Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana–Baleanu fractional operator: Real data approach

Cited by 12 publications

References 20 publications

Comparative analysis of classical and Caputo models for COVID-19 spread: vaccination and stability assessment

Comparative analysis of classical and Caputo models for COVID-19 spread: vaccination and stability assessment

Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

Hopf Bifurcation Control of a Fractional-Order Delayed Turbidostat Model via a Novel Extended Hybrid Controller

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