A numerical study on the dynamics of SIR epidemic model through Genocchi wavelet collocation method

Area of Science:

• Epidemiology
• Mathematical Biology
• Numerical Analysis

Background:

• Mathematical models are crucial for understanding disease spread and public health.
• Fractional-order differential equations are increasingly used to model complex, non-local phenomena in disease dynamics.

Purpose of the Study:

• To apply the Genocchi wavelet collocation method to solve the SIR (Susceptible-Infectious-Recovered) epidemic model of arbitrary fractional order.
• To investigate the dynamical behavior of the SIR model using a Caputo fractional derivative.
• To demonstrate the efficiency and accuracy of the proposed numerical method.

Main Methods:

• The Genocchi wavelet collocation method was employed to transform the fractional-order nonlinear ordinary differential equations into algebraic equations.
• This approach merges operational matrices with collocation techniques for efficient computation.
• Numerical solutions were generated and compared with established methods like Runge-Kutta and residual power series.

Main Results:

• The Genocchi wavelet collocation method provides precise and reliable results for fractional-order SIR models.
• The method is computationally efficient, requiring fewer resources than traditional techniques.
• Graphical representations of numerical outcomes for various fractional orders illustrate the model's dynamics.

Conclusions:

• The Genocchi wavelet collocation method is a highly effective and accurate technique for analyzing nonlinear complications in epidemic and biological models.
• This approach offers a simpler, faster, and parameter-free alternative for studying complex real-world disease dynamics.
• The study validates the utility of fractional calculus in epidemiological modeling and provides a robust numerical tool.