Fractional-order modeling of human behavior in infections: analysis using real data from Liberia

Computer Methods in Biomechanics & Biomedical Engineering, Journal Year: 2025, Volume and Issue: unknown, P. 1 - 15

Published: Jan. 6, 2025

This paper presents a fractional-order model using the Caputo differential operator to study Ebola Virus Disease (EVD) dynamics, calibrated with Liberian data. The demonstrates improved accuracy over integer-order counterparts, particularly in capturing behavioral changes during outbreaks. Stability analysis, Lyapunov functions, and validated numerical method strengthen its mathematical foundation. Simulations highlight utility accurately describing EVD evolution guiding outbreak management. underscores role of interventions epidemic control, offering valuable insights for public health policymaking. research advances infectious disease models enhances strategies mitigating

Language: Английский

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The fractional-order marriage–divorce mathematical model: numerical investigations and dynamical analysis

The European Physical Journal Plus, Journal Year: 2024, Volume and Issue: 139(3)

Published: March 2, 2024

Language: Английский

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Computational analysis of a class of singular nonlinear fractional multi-order heat conduction model of the human head

Scientific Reports, Journal Year: 2024, Volume and Issue: 14(1)

Published: Feb. 12, 2024

Abstract The subject of the article is devoted to development a matrix collocation technique based upon combination fractional-order shifted Vieta–Lucas functions (FSVLFs) and quasilinearization method (QLM) for numerical evaluation fractional multi-order heat conduction model related human head with singularity nonlinearity. operators are adopted in accordance Liouville–Caputo derivative. first utilized order defeat inherent nonlinearity problem, which converted family linearized subequations. Afterward, we use FSVLFs along set nodes as zeros these reach linear algebraic system equations at each iteration. In weighted $$L_2$$ L2 norm, convergence analysis series solution established. We especially assert that expansion form convergent infinity norm $${\mathcal {O}(\frac{1}{K^3})}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">O(1K3) , where K represents number used approximating unknown solution. Diverse computational experiments by running presented combined QLM-FSVLFs conducted using various orders parameters. outcomes indicate produces efficient approximate solutions underlying high-order accuracy, near singular point. Furthermore, methodology residual error employed measure accuracy proposed hybrid algorithm. Comparisons existing models show superiority QLM-FSVLFs, also straightforward implementation.

Language: Английский

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New Generalized Jacobi Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Multi-Term Variable-Order Time-Fractional Diffusion-Wave Equations

Fractal and Fractional, Journal Year: 2024, Volume and Issue: 8(1), P. 68 - 68

Published: Jan. 18, 2024

The current study discusses a novel approach for numerically solving MTVO-TFDWEs under various conditions, such as IBCs and DBCs. It uses class of GSJPs that satisfy the given conditions (IBCs or DBCs). One important parts our method is establishing OMs Ods VOFDs GSJPs. second part using SCM by utilizing these OMs. This algorithm enables extraction precision efficacy in numerical solutions. We provide theoretical assurances treatment’s validating its convergent error investigations. Four examples are offered to clarify approach’s practicability precision; each one, DBCs considered. findings compared those preceding studies, verifying treatment more effective precise than competitors.

Language: Английский

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Stability analysis and numerical evaluations of a COVID-19 model with vaccination

BMC Medical Research Methodology, Journal Year: 2024, Volume and Issue: 24(1)

Published: April 27, 2024

Abstract A novel (nonlinear) mathematical model for the transmission of Coronavirus 19 (COVID-19) with eight compartments and considering impact vaccination is examined in this manuscript. The qualitative behavior system such as boundedness solutions, basic reproduction number, stability equilibrium points investigated detail. Some domestic real data collected from Kerman University Medical Science (KUMC) used to estimate parameters proposed model. We predict dynamical through numerical simulations based on a combined spectral matrix collocation methodology. In respect, we first linearize nonlinear equations by method quasilinearization (QLM). Hence, shifted version Chebyshev polynomials second kind (SCPSK) utilized along domain-splitting strategy acquire solutions over long time interval. uniform convergence upper bound estimation SCPSK bases are proved rigorous manner. Moreover, technique residual error functions testify accuracy QLM-SCPSK method. presented results justify robustness good technique. achieved orders indicate that QLM-SCSK algorithm has exponential rate convergence. Using linearization one hand other hand, enable us behaviour similar disease problems high maximum efficiency an arbitrary domain interest.

Language: Английский

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New Results for Certain Jacobsthal-Type Polynomials

Mathematics, Journal Year: 2025, Volume and Issue: 13(5), P. 715 - 715

Published: Feb. 22, 2025

This paper investigates a class of Jacobsthal-type polynomials (JTPs) that involves one parameter. We present several new formulas for these polynomials, including expressions their derivatives, moments, and linearization formulas. The key idea behind the derivation is based on developing connection formula expresses shifted Chebyshev third kind in terms JTPs. used to deduce inversion Therefore, by utilizing power form representation corresponding formula, we can derive additional them. Additionally, compute some definite integrals polynomials.

Language: Английский

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A mathematical analysis of human papilloma virus (HPV) disease with new perspectives of fractional calculus

Alexandria Engineering Journal, Journal Year: 2025, Volume and Issue: 125, P. 575 - 599

Published: April 23, 2025

Language: Английский

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Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator

Results in Control and Optimization, Journal Year: 2023, Volume and Issue: 13, P. 100332 - 100332

Published: Nov. 7, 2023

The aim of this paper is to analyze a fractional model the Ebola virus. This study important because it contributes our understanding virus transmission dynamics using notion non-local differential operators. We apply recently implemented Atangana-Baleanu-Caputo (ABC) derivative with Mittag-Leffler kernel closely. Picard-Lindelof approach used do comprehensive existence and uniqueness model's solutions. approximate solutions order were obtained numerical technique ABC operator, combination fundamental theorem calculus two-step Lagrange polynomial interpolation. innovative may offer new insights into that not previously explored. Finally, simulations illustrate how control parameters impact specific compartments within model. geometrical representation gives significant information about complexity reliable simulate each compartment at various orders compare them integer-order simulations, highlighting effectiveness modern derivatives. analysis underscores enhanced accuracy non-integer derivatives in capturing dynamics.

Language: Английский

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Novel Approach by Shifted Fibonacci Polynomials for Solving the Fractional Burgers Equation

Fractal and Fractional, Journal Year: 2024, Volume and Issue: 8(7), P. 427 - 427

Published: July 20, 2024

This paper analyzes a novel use of the shifted Fibonacci polynomials (SFPs) to treat time-fractional Burgers equation (TFBE). We first develop fundamental formulas these polynomials, which include their power series representation and inversion formula. establish other new for SFPs, including integer fractional derivatives, in order design collocation approach treating TFBE. These derivative serve as tools that aid constructing operational metrics derivatives SFPs. matrices transform problem its underlying conditions into system nonlinear equations can be treated numerically. An error analysis is analyzed detail. also present three illustrative numerical examples comparisons test our proposed algorithm. results showed algorithm advantageous since highly accurate approximate solutions obtained by choosing few terms retained modes

Language: Английский

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Enhanced shifted Jacobi operational matrices of derivatives: spectral algorithm for solving multiterm variable-order fractional differential equations

Boundary Value Problems, Journal Year: 2023, Volume and Issue: 2023(1)

Published: Nov. 14, 2023

Abstract This paper presents a new way to solve numerically multiterm variable-order fractional differential equations (MTVOFDEs) with initial conditions by using class of modified shifted Jacobi polynomials (MSJPs). As their defining feature, MSJPs satisfy the given conditions. A key aspect our methodology involves construction operational matrices (OMs) for ordinary derivatives (ODs) and (VOFDs) application spectral collocation method (SCM). These constructions enable efficient accurate numerical computation. We establish error analysis convergence proposed algorithm, providing theoretical guarantees its effectiveness. To demonstrate applicability accuracy method, we present five examples. Through these examples, compare results obtained other published results, confirming superiority in terms efficiency. The suggested algorithm yields very agreement between approximate exact solutions, which are shown tables graphs.

Language: Английский

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