Bifurcations analysis of a discrete time S I R epidemic model with nonlinear incidence function

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.

Automated summary

This paper presents a discrete-time SIR epidemic model and investigates the stability of its fixed points, as well as the bifurcations of the one and two parameters. Bifurcations such as Neimark-Sacker transcritical, flip, and strong resonance are observed in this model. The MATLAB package MatContM is used to verify the analytical results.