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We revisit here a landmark five parameter SIR-type model of [DvdD93, Sec. 4],which is maybe the simplest example where a complete picture of all cases,including non-trivial bistability behavior, may be obtained using simple tools.We also generalize it by adding essential vaccination and vaccination-induceddeath parameters, with the aim of revealing the role of vaccination and itspossible failure. The main result is Theorem 5, which describes the stabilitybehavior of our model in all possible cases.

Stability analysis of an eight parameter SIR-type model including loss of immunity, and disease and vaccination fatalities