A fractional order Monkeypox model with protected travelers using the fixed point theorem and Newton polynomial interpolation

Adom-Konadu, Agnes; Bonyah, Ebenezer; Sackitey, Albert Lanor; Anokye, Martin; Asamoah, Joshua Kiddy K.

doi:10.1016/j.health.2023.100191

Cited by 7 publications

(2 citation statements)

References 39 publications

(44 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fractional calculus, with its numerous attributes and practical applications in engineering and physics, has captured the attention of scientists worldwide. Utilizing a fractional-order system model is essential for observing hereditary characteristics, memory, and crossover behavior [39]. This operator exhibits both fractional calculus properties and a form of self-similarity or fractal-like behavior.…”

Section: Introductionmentioning

confidence: 99%

Mathematical insights of social media addiction: fractal-fractional perspectives

Nadeem Anjam,

Tabassum,

Arshad

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

The excessive use of social media has become a growing concern in the current century, with dependence on these platforms developing into a complex behavioral addiction. Addressing this issue requires the employment of well-directed and inclusive efforts. In pursuit of continuous development in existent strategies, this article presents a non-linear deterministic mathematical model that encapsulates the dynamics of social media addiction within a population. The proposed model incorporates the fractal-fractional order derivative in the sense of the Caputo operator. The objectives of this research are attained by groping the dynamics of the social media addiction model through the stratification of the population into five compartments: susceptible individuals, exposed individuals, addicted individuals, recovery individuals, and those who have quit using social media. The validity of the devised model is established by proving the existence and uniqueness of the solution within the framework of the fixed-point theory. The Ulam-Hyer's stability is established through nonlinear functional analysis, perturbing the problem with a small factor. Utilizing the Adam Bashforth numerical scheme, we obtain numerical solutions, which we validate through MATLAB simulations. \textcolor{red}{Additionally, we explore the application of artificial neural networks (ANNs) to approximate solutions, presenting a significant innovation in this domain. We propose the adoption of this novel method for solving integral equations that elucidate the dynamics of social media addiction, surpassing traditional numerical methods. Numerical results are illustrated across various fractional orders and fractal dimensions, with comparisons made against integer orders. Our study indicates that ANN outperforms the Adams-Bashforth algorithm, offering a dependable approach to problem-solving.} Throughout the article, we underscore the competitive advantage of our proposed strategy, providing a more nuanced understanding of the complex dynamics outlined in the model.

show abstract

Section: Introductionmentioning

confidence: 99%

Mathematical insights of social media addiction: fractal-fractional perspectives

Nadeem Anjam,

Tabassum,

Arshad

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Fractional calculus has garnered significant attention from the global scientific community, thanks to its diverse features and practical applications across physics and engineering. It is essential to use a fractional-order system model to observe memory, crossover behavior, and hereditary features in systems [29]. This operator enables more effective modeling of complex systems with memory-dependent dynamics, finding applications in health surveillance and COVID-19 modeling.…”

Section: Introductionmentioning

confidence: 99%

Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis

Anjam,

Turki Alqahtani,

Alharthi

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics.

show abstract

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

Manivel,

Venkatesh,

Arunkumar

et al. 2024

Advcd Theory and Sims

View full text Add to dashboard Cite

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

show abstract

A fractional order Monkeypox model with protected travelers using the fixed point theorem and Newton polynomial interpolation

Cited by 7 publications

References 39 publications

Mathematical insights of social media addiction: fractal-fractional perspectives

Mathematical insights of social media addiction: fractal-fractional perspectives

Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis

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

Contact Info

Product

Resources

About