Dynamics of an SIR epidemic model with limited medical resources, revisited and corrected

This paper generalizes and corrects a famous paper (more than 200 citations) concerning Hopf and Bogdanov-Takens bifurcations due to L. Zhou and M. Fan, "Dynamics of an SIR epidemic model with limited medical resources revisited", in which we discovered a significant numerical error. Importantly, unlike the paper of Zhou and Fan and several other papers that followed them, we offer a notebook where the reader may recover all the results and modify them for analyzing similar models. Our calculations lead to the introduction of some interesting symbolic objects, "Groebner eliminated traces and determinants" - see (4.5), (4.6), which seem to have appeared here for the first time and which might be of independent interest. We hope our paper might serve as yet another alarm bell regarding the importance of accompanying papers involving complicated hand computations by electronic notebooks.