Numerical Approach for Solving a Fractional-Order Norovirus Epidemic Model with Vaccination and Asymptomatic Carriers

Abstract

This paper explored the impact of population symmetry on the spread and control of a norovirus epidemic. The study proposed a mathematical model for the norovirus epidemic that takes into account asymptomatic infected individuals and vaccination effects using a non-singular fractional operator of Atanganaa–Baleanu Caputo (ABC). Fixed point theory, specifically Schauder and Banach’s fixed point theory, was used to investigate the existence and uniqueness of solutions for the proposed model. The study employed MATLAB software to generate simulation results and demonstrate the effectiveness of the fractional order q. A general numerical algorithm based on Adams–Bashforth and Newton’s Polynomial method was developed to approximate the solution. Furthermore, the stability of the proposed model was analyzed using Ulam–Hyers stability techniques. The basic reproductive number was calculated with the help of next-generation matrix techniques. The sensitivity analysis of the model parameters was performed to test which parameter is the most sensitive for the epidemic. The values of the parameters were estimated with the help of least square curve fitting tools. The results of the study provide valuable insights into the behavior of the proposed model and demonstrate the potential applications of fractional calculus in solving complex problems related to disease transmission.

Keywords

• Mittag–Leffler kernel
• fractional norovirus epidemic model
• ABC-fractional derivative
• iterative solution
• numerical scheme