Global Analysis of a Fractional‐Order Hepatitis B Virus Model Under Immune Response in the Presence of Cytokines

Advanced Theory and Simulations, Год журнала: 2024, Номер 7(12)

Опубликована: Авг. 26, 2024

Abstract This research proposes and investigates an epidemiological model to study the dynamic behaviors of Hepatitis B virus (HBV) under immune response cytokine influence. The model's stability, positivity, boundedness, equilibria are analyzed using Lyapunov functional methods Routh–Hurwitz criterion Caputo fractional derivative. evaluates nucleoside analogues interferon treatments, determining critical drug efficiencies. Equilibria, including infection‐free endemic states, fundamental reproduction number, , predict disease elimination. Numerical simulations utilize Adams method L1 scheme, capturing memory traces as order changes. Results show scheme effectively captures traces, providing empirical support for theoretical findings. Furthermore, Ulam–Hyers stability is treated according equilibrium point, which describes relationships between functions. Notably, findings yielded profound insights. They revealed that HBV system remains locally asymptotic stable at disease‐free point when . At same time, illustrated a correlation rate infection rise in infected individuals, indicating feasibility eradicating managing infections through multifaceted approach various measures such vaccination effective administration protocols. proposed framework can guide medical professionals decision‐makers developing strategies limit eliminate spread population.

Язык: Английский

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Analytical analysis and bifurcation of pine wilt dynamical transmission with host vector and nonlinear incidence using sustainable fractional approach

Partial Differential Equations in Applied Mathematics, Год журнала: 2024, Номер 11, С. 100830 - 100830

Опубликована: Июль 22, 2024

To study the dynamical system, it is necessary to formulate a mathematical model comprehend dynamics of diseases that are prevalent around world by using fractional calculus. A developed with hypothesis created adding control and asymptomatic variables observe rate change pine wilt ABC operator used turn into ordered for continuous monitoring. The Boundedness uniqueness investigated bounded findings Banach space, which key properties such an epidemic model. newly system examined both qualitatively quantitatively determine its stable position, verification flip bifurcation has been made systems. Derived reproductive numbers next-generation technique as well sensitivity each involved parameter verified. Atangana–Toufik scheme employed find solution different values, advanced tools reliable solutions. Simulations have see real behavior effects disease battels in community. Also, identify situation spread after employing due treatment. Such type investigation will be useful investigating helpful developing strategies based on our justified outcomes.

Язык: Английский

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Fractional order forestry resource conservation model featuring chaos control and simulations for toxin activity and human-caused fire through modified ABC operator

Mathematics and Computers in Simulation, Год журнала: 2024, Номер 227, С. 282 - 302

Опубликована: Авг. 14, 2024

Язык: Английский

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A Mathematical Model of the Dynamics of the Transmission of Monkeypox Disease Using Fractional Differential Equations

Advanced Theory and Simulations, Год журнала: 2024, Номер 7(9)

Опубликована: Июнь 22, 2024

Abstract This study presents a comprehensive analysis of the dynamics Mpox viral transmission using compartmental mathematical model. The model incorporates impact immunization, isolation, and hospitalization on disease management, as well interaction between humans rodents. Through numerical simulations, highlights effectiveness isolation in mitigating emphasizes significance modeling simulation techniques understanding dynamics. utilization Caputo's fractional differential equation human dynamical is shown to be effective regulating all compartments. Sensitivity conducted identify most influential parameters virus transmission. findings contribute valuable insights for public health strategies provide foundation further research control management.

Язык: Английский

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Deciphering two-dimensional calcium fractional diffusion of membrane flux in neuron

Journal of Applied Mathematics and Computing, Год журнала: 2024, Номер 70(5), С. 4133 - 4156

Опубликована: Май 24, 2024

Язык: Английский

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Mathematical modeling of the Coronavirus (Covid-19) transmission dynamics using classical and fractional derivatives

Discrete and Continuous Dynamical Systems - B, Год журнала: 2024, Номер 30(1), С. 289 - 329

Опубликована: Июнь 28, 2024

This study focuses on formulating and analysing a COVID-19 transmission dynamics model using integer fractional-order derivatives in the Caputo sense. The considers two doses of vaccination, confinement, treatment with limited resources. control reproduction number is computed asymptotic stability analysis disease-free equilibrium proved. We also prove existence at least one endemic whenever $ \mathcal{R}_c>1 $. Using real data from Germany, we calibrate our models by performing parameter estimations. find that approximately equal to 1.90, which implies disease remains Germany. perform global sensitivity computing partial rank correlation coefficients (PRCC) between \mathcal{R}_c (respectively compartments infected individuals) each parameter. By fixing vaccine coverage 70%, observe it might be more effective increase efficacy than increasing numbers vaccinated people. After that, formulate corresponding fractional sense, proving positivity, boundedness, existence, uniqueness solutions. calculate model, DFE, point. numerical simulations, for long-term forecasting, seems better use derivative range \varphi\in (0,0.87] just ordinary derivatives. Indeed, this parameter, daily detected cases are closer those classical predicts.

Язык: Английский

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Mathematical Modeling of Malaria Epidemic Dynamics with Enlightenment and Therapy Intervention Using the Laplace-Adomian Decomposition Method and Caputo Fractional Order

Franklin Open, Год журнала: 2024, Номер 8, С. 100147 - 100147

Опубликована: Авг. 24, 2024

Язык: Английский

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Analyzing the dynamics of human papillomavirus transmission via fractal and fractional dimensions under Mittag-Leffler Law

Modeling Earth Systems and Environment, Год журнала: 2024, Номер unknown

Опубликована: Окт. 8, 2024

Язык: Английский

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Stability and BI-RADS 4 subcategories mitigate on cancer risk dynamics with fractional operators: A case study analysis

Alexandria Engineering Journal, Год журнала: 2024, Номер 109, С. 41 - 57

Опубликована: Сен. 3, 2024

In this paper, we present a mathematical model to lower the probability of breast cancer risk Breast Imaging Reporting and Data Systems (BI-RADS) 4 subcategories with fractal fractional operator. This method improves evaluation quality, creates straightforward concepts for early detection cancer, outcomes can be tracked easily by using BI-RADS-4 data at Near East University Hospital. It uses Banach fixed point theorem nonlinear functional analysis confirms boundedness uniqueness solutions. Sensitivity was performed on parameters, advanced numerical techniques were used develop Also, reveals disease-free endemic equilibrium points, indicating local global asymptotic stability. Chaos control in regulated linear responses approach bring system stabilize according its points equilibrium. The growing procedure yields more effective similar than rotting technique, which happens quickly lowest orders. Using Lagrange polynomial insight into fractal-fractional operator, conducted simulations presented comparative graphical form classical non-integer derivatives. comparison integer results highlighted importance accurate parameters simulation. Moreover, it suggests that operator-included models help reveal significant decisions managing such real-life problems. Numerical absorption features derivative generalized Mittag-Leffler kernel. approximation solution allows different order dimension between 0 1, changing determined diagnosis, quitting smoking, higher lactation rates, ongoing care reduce risk. Our findings are critical researchers, policymakers, health practitioners combating preventing contributing worldwide public initiatives. • is intended standardize reporting imaging. Model tested 42 BI-RADS patients NEU Hospital, demonstrating converging characteristics. analysis. Disease-free performed,

Язык: Английский

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Dynamical Behavior of a Diabetes Model with Complications Using Fractional Operator

Опубликована: Янв. 1, 2025

Язык: Английский

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