Fractal-fractional SIRS epidemic model with temporary immunity using Atangana-Baleanu derivative

Abstract

The basic SIRS deterministic model is one of the powerful and important compartmental modeling frameworks that serve as the foundation for a variety of epidemiological models and investigations. In this study, a nonlinear Atangana-Baleanu fractal-fractional SIRS epidemiological model is proposed and analysed. The model’s equilibrium points (disease-free and endemic) are studied for local asymptotic stability. The existence of the model’s solution and its uniqueness, as well as the Hyers-Ulam stability analysis, are established. Numerical solutions and phase portraits for the fractal-fractional model are generated using a recently constructed and effective Newton polynomial-based iterative scheme for nonlinear dynamical fractal-fractional model problems. Our numerical simulations demonstrate that fractal-fractional dynamic modeling is a very useful and appropriate mathematical modeling tool for developing and studying epidemiological models.