*(English)*Zbl 1134.92026

Summary: The phenomenon of backward bifurcation in disease models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has important implications for disease control. In such a scenario, the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, condition for disease elimination.

This paper addresses the role of the choice of incidence functions in a vaccine-induced backward bifurcation in HIV models. Several examples are given where backward bifurcations occur using standard incidence, but not with their equivalents that employ mass action incidence. Furthermore, this result is independent of the type of vaccination program adopted. These results emphasize the need for further work on the incidence functions used in HIV models.

##### MSC:

92C60 | Medical epidemiology |

34D20 | Stability of ODE |

34C23 | Bifurcation (ODE) |

34D23 | Global stability of ODE |