Investigating the fractional dynamics and sensitivity of an epidemic model with nonlinear convex rate

Abstract

The current study analyzes a fractional compartmental epidemic model for the transmission of infectious disease in a community. This study uses the Caputo derivative as well as Atangana–Baleanu derivative to consider a SIR fractional epidemic model with a convex incidence rate. We demonstrate the existence and uniqueness of solutions by using the idea of fixed-point theory. Comprehensive mathematical approaches show the physical properties of solutions, such as non-negativity and boundedness. The basic reproduction number is evaluated using the next-generation matrix method, determining whether the infection will spread in society. The stability analysis is performed with phase portraits, which show that the infection-free and infection-present steady states of the considered model are locally and globally asymptotically stable. The sensitivity of the basic reproduction number is carried out through 3D graphs, which indicate the most sensitive and impactful parameters. Finally, for the numerical solution of the underlying model, a numerical technique is applied and these solutions evaluate the theoretical results through numerical simulations. Numerical simulations that aim to decrease the fractional parameter and convex incidence rate can bring about a significant change in infected individuals.