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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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An efficient numerical algorithm for solving fractional SIRC model with salmonella bacterial infection.

Rubayyi T Alqahtani1, M A Abdelkawy1,2

  • 1Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh 11564, Saudi Arabia.

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This study presents an efficient numerical method for a fractional SIRC model of Salmonella bacterial infection (FSIRC-MSBI). The fully shifted Jacobi

Keywords:
Caputo fractional derivativeGauss-Radau quadratureShifted Jacobi polynomialsfractional SIRC modelspectral collocation method

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Area of Science:

  • Mathematical Biology
  • Numerical Analysis
  • Infectious Disease Modeling

Background:

  • Fractional differential equations are increasingly used to model complex biological phenomena.
  • The SIRC model is a fundamental epidemiological tool, and its fractional extension (FSIRC) offers enhanced realism.
  • Salmonella bacterial infection (FSIRC-MSBI) presents a significant public health challenge requiring accurate modeling.

Purpose of the Study:

  • To develop and evaluate a novel numerical approach for solving the fractional SIRC model with Salmonella bacterial infection (FSIRC-MSBI).
  • To demonstrate the efficiency, reliability, and accuracy of the proposed numerical method.
  • To explore the potential for spectral accuracy in modeling infectious disease dynamics.

Main Methods:

  • The study employs a fully shifted Jacobi's collocation method for temporal discretization of the FSIRC-MSBI.
  • This numerical technique discretizes the fractional derivatives and solves the resulting system of algebraic equations.
  • Performance is assessed through numerical simulations and comparison with existing methods (implied).

Main Results:

  • The proposed fully shifted Jacobi's collocation method proves to be highly efficient and reliable for the FSIRC-MSBI.
  • Numerical results validate the performance and accuracy of the developed algorithm.
  • The method achieves spectral accuracy, indicating superior convergence properties for the studied model.

Conclusions:

  • The fully shifted Jacobi's collocation method is a superior numerical tool for analyzing fractional infectious disease models like FSIRC-MSBI.
  • This approach offers a robust and accurate means to study the dynamics of Salmonella bacterial infections.
  • The findings pave the way for more precise epidemiological predictions and control strategies.