Applying Laplace Adomian decomposition method (LADM) for solving a model of Covid-19

Area of Science:

• Mathematical modeling
• Epidemiology
• Computational mathematics

Background:

• The Covid-19 mathematical model involves nonlinear ordinary differential equations, necessitating approximate analytical solutions.
• Traditional Laplace Adomian decomposition method (LADM) for these models is computationally intensive and complex.
• Existing analytical methods struggle with the inherent complexity of nonlinear epidemiological models.

Purpose of the Study:

• To develop and present a novel, efficient algorithm for solving the Covid-19 mathematical model.
• To combine the Laplace Adomian decomposition method (LADM) with the singularly perturbed vector field (SPVF) method.
• To reduce the computational burden and mathematical complexity associated with approximate solutions.

Main Methods:

• Application of the Laplace Adomian decomposition method (LADM) for approximating solutions.
• Integration of the singularly perturbed vector field (SPVF) method with LADM.
• Development of a new computational algorithm to streamline calculations.
• Comparison of results with numerical simulations for validation.

Main Results:

• The proposed algorithm significantly reduces computer run time and mathematical calculation complexity.
• The method provides reliable approximate analytical power series solutions for the Covid-19 model.
• Validation through comparison with numerical simulations demonstrates the algorithm's effectiveness.
• Graphical representations confirm the reliability and simplicity of the novel approach.

Conclusions:

• The combined LADM-SPVF algorithm offers a more efficient and simpler alternative for solving complex epidemiological models.
• This approach enhances the feasibility of using analytical approximation methods for real-world disease modeling.
• The study highlights the potential of integrating advanced numerical techniques for faster and more accurate predictions.