Modeling and Analysis of a Fractional Visceral Leishmaniosis with Caputo and Caputo–Fabrizio derivatives

Almutairi, Dalal Khalid; Abdoon, Mohamed A.; Salih Yousuf Mohamed Salih,; Shahinaz A.Elsamani,; Guma, Fathelrhman EL; Berir, Mohammed

doi:10.46481/jnsps.2023.1453

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…The disease has been observed in various parts of the country, including the Darfur region in western Sudan, the Nuba Mountains in Kordofan, and along the banks of the White Nile, among others [19]. However, it is the eastern region that has experienced the highest incidence of VL, making it a focal point for public health efforts due to the significant concern it poses in those areas [4]. Despite considerable intervention programs aimed at controlling and eliminating VL, particularly in the eastern region.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the Impact of Control Strategies on VisceralLeishmaniasis: A Mathematical Modeling Perspective

EL Gumaa,

A. Abdoon,

Qazza

et al. 2024

Eur. J. Pure Appl. Math.

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Visceral Leishmaniasis remains a significant public health challenge in eastern Sudan despite extensive control efforts. This study employs MCMC Bayesian inference techniques to fit a mathematical model for studying visceral Leishmaniasis transmission dynamics with interventions. The research focuses on evaluation of control programs to adapt to the dynamic nature of visceralLeishmaniasis transmission. We analyze 22 years of cumulative visceral Leishmaniasis cases from eastern Sudan, an endemic region for visceral Leishmaniasis, and assessed the effectiveness of interventions implemented thus far. The results reveal that visceral Leishmaniasis is prevalent, with reported cases representing less than 20% of community infections. Improved surveillance and diagnostics are necessary for accurately estimating the disease burden. The effectiveness of intervention strategies for vector control for reducing VL transmission in the region is found to be limited. Furthermore, the model predicts visceral Leishmaniasis cases will continue to increase in the near future, underscoring the need adaptable initiatives to reduce the disease burden.

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Section: Introductionmentioning

confidence: 99%

Analyzing the Impact of Control Strategies on VisceralLeishmaniasis: A Mathematical Modeling Perspective

EL Gumaa,

A. Abdoon,

Qazza

et al. 2024

Eur. J. Pure Appl. Math.

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“…Additionally, they have been instrumental in deriving solutions for intricate mathematical models like the generalized Zakharov equation and initial value problems involving generalized fractional derivatives [25,31]. Furthermore, recent studies [5,14,15,44,46] have expanded upon these methodologies, presenting numerical solutions, comparative studies, and applications encompassing symmetric attractors, electric circuits, image encryption, and stability analyses in control systems and image processing. The adaptability and versatility of these methods continue to pave the way for advancements in multidisciplinary fields, illustrating their profound impact on diverse technological landscapes.…”

Section: Introductionmentioning

confidence: 99%

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

Boulehmi

2024

Eur. J. Pure Appl. Math.

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This study aims to use a novel scheme for the Atangana-Baleanu Caputo fractional derivative (ABC-FD) to solve the fractional Bernoulli equation and the fractional R ̈ossler model. Furthermore, the suggested technique is compared to Runge-Kutta Fourth Order (RK4). The proposed method is efficacious and generates solutions that are indistinguishable from the approx-imate solutions generated by the RK4 method. Therefore, we can adapt the approach to various systems and develop results that are more accurate. On top of that, the new technique (ABC-FD) can identify chaotic situations. Consequently, this approach can be used to enhance the performance of other systems. In the future, this technique can be employed to determine the numerical solution for a multitude of models applicable in the fields of science and engineering.

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“…For instance, Caputo defined a fractional derivative with a singular kernel and nonlocal behavior. Almutairi et al [18] followed the Laplace Adomian decomposition…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of visceral leishmaniasis dynamics using fractional‐order operators: A comparative study

Abdulkream Alharbi,

A. Abdoon,

Saadeh

et al. 2024

Math Methods in App Sciences

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An in‐depth understanding of the mechanism concerning the parasitic disease called visceral leishmaniasis (VL) remains challenging. Thus, we modeled the dynamics of this illness using two fractional‐order operators, including Caputo–Fabrizio and Atangana–Baleanu. In the proposed dynamical model, the endemic and disease‐free equilibrium points were considered the symmetrical components. The fractional Euler method was applied to simulate the developed model, thus determining the equilibrium points' stability. The numerical simulation results were compared with the measured data to validate the model. The results obtained from the optimum fractional operator disclosed the minimum absolute and relative errors. The primary outcome of our study is the successful application of fractional‐order operators, specifically the Atangana–Baleanu operators with = 0.98, in modeling the dynamics of VL. Notably, the numerical simulation results, validated against real data from Sudan, demonstrated that the Atangana–Baleanu operators with = 0.98 yielded the best performance, with minimum absolute and relative errors. This underscores the precision of our fractional calculus‐based dynamical model in predicting VL dynamics compared to the classical framework, particularly for fractional‐order values of = 0.99 and = 0.98.

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Modeling and Analysis of a Fractional Visceral Leishmaniosis with Caputo and Caputo–Fabrizio derivatives

Cited by 9 publications

References 26 publications

Analyzing the Impact of Control Strategies on VisceralLeishmaniasis: A Mathematical Modeling Perspective

Analyzing the Impact of Control Strategies on VisceralLeishmaniasis: A Mathematical Modeling Perspective

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

Modeling and analysis of visceral leishmaniasis dynamics using fractional‐order operators: A comparative study

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