THE IMPACT OF MEMORY EFFECT AND NONLOCALLITY IN COVID-19 WORLD DATA USING HYBRID FRACTIONAL ORDER COMPARTMENTAL MODEL AND NEURAL NETWORKS

Abstract

Background:
This study investigates the impact of memory effects and nonlocality on COVID-19 World Data. The primary objective is to explore the dynamics of the pandemic using a hybrid fractional order compartmental model combined with neural networks.
Methods:
The research employs a hybrid fractional order compartmental model alongside an artificial neural network. Key procedures include stability analysis of equilibrium points, the development of a Disease Informed Neural Network (DINN) by integrating the fractional order model with neural networks, and the application of Laplace Transforms to expedite fractional derivative computations during neural network training.
Results:
The study identifies optimal fractional order values: α_1=0.7899, α_2=0.8636,α_3= 0.8496 , and α_4=0.8591. The disease transmission parameters are determined as ρ=0.1730,δ=0.0466, and ω=0.0018. Numerical simulations are conducted, which visually compare the hybrid fractional order compartmental model and neural network results against real COVID-19 World Data across all compartments.
Conclusion:
The paper concludes that the developed model effectively captures the dynamics of COVID-19, emphasizing the role of memory and nonlocal effects in disease transmission. The insights gained from plotting dynamic model behaviors, including minimum and maximum solutions, contribute to a comprehensive understanding of disease transmission and inform potential interventions.