Bifurcations analysis of a discrete time SIR epidemic model with nonlinear incidence function

Abstract

In this paper, we present a discrete-time SIR epidemic model and investigate the stability of its fixed points, as well as the bifurcations of the one and two parameters. The numerical normal form is used to analyze bifurcations. This model exhibits Neimark–Sacker transcritical, flip, and strong resonance bifurcations. Using the critical coefficients, a scenario is identified for each bifurcation. We verify analytical results using the MATLAB package MatContM, which employs the numerical continuation method.

Keywords

• Bifurcation
• Normal form
• Numerical continuation method
• One parameter bifurcation
• SIR epidemic model
• Stability