Analysis of a fractional-order discrete SIS epidemic model: stability, bifurcation, and $0-1$ test for chaos

Abstract

In this paper, we present a new conformable fractional-order discrete SIS-epidemic model to analyze the dynamics of infectious diseases. The model incorporates the effects of interspecific competition and memory, providing a novel approach to understanding disease spread. We analyze the stability of the model’s fixed points and calculate the basic reproduction number ( \(R_{0}\) ), which is critical for understanding the potential for epidemic outbreaks. We explore the chaos and bifurcations of the model through both theoretical analysis and numerical simulations. Our findings reveal complex dynamic behaviors, including stable equilibria, attracting invariant circles, periodic orbits, and chaotic attractors, which are affected by the discretization parameter and the fractional-order parameter.