A Novel Approach to Modeling COVID-19 Disease and Estimating Model Parameters

This study presents a novel mathematical model for COVID-19 transmission and the impact of vaccination, employing fractional-order ordinary differential equations (ODEs). The model incorporates both direct and indirect transmission pathways. Direct transmission refers to person-to-person spread through droplets, while indirect transmission arises from contact with contaminated objects. The indirect pathway is explicitly modeled by introducing compartments for infectious and clean objects, along with interaction terms reflecting contamination and exposure dynamics. The advantages of fractional-order approaches, including improved prediction accuracy and flexibility in analyzing complex dynamics, are highlighted. The role of vaccination in reducing susceptibility, transmission rates, and symptom severity is explicitly addressed. Reliable data sources, such as the World Health Organization (WHO), Worldometer, and regional health authorities across diverse regions, including North America, Europe, and Asia, are utilized. Using generalized Tikhonov regularization, the model estimates unknown parameters through robust parameter estimation based on daily COVID-19 case data. Stability and equilibrium analyses provide insights into public health implications, demonstrating the effectiveness of interventions such as widespread vaccination and social distancing. The model's robustness in handling noisy data and addressing epidemiological challenges is underscored through comparisons with conventional parameter estimation methods.