Bifurcations of an SIRS epidemic model with a general saturated incidence rate

This paper is concerned with the bifurcations of a susceptible-infectious-recovered -susceptible (SIRS) epidemic model with a general saturated incidence rate kIp/(1 + alpha Ip). For general p > 1, it is shown that the model can undergo saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, and degenerate Hopf bifurcation of codimension two with the change of parameters. Combining with the results in [1] for 0 < p <= 1, this type of SIRS model has Hopf cyclicity 2 for any p > 0. These results also improve some previous ones in [2] and [3], which are dealt with the special case of p = 2.

Automated summary

This paper investigates the bifurcations of an SIRS epidemic model with a general saturated incidence rate. It shows that the model can undergo various bifurcations for p > 1. These results also improve upon previous findings for a specific case.