A simple SIS epidemic model with a backward bifurcation.

@article{Driessche2000ASS,
  title={A simple SIS epidemic model with a backward bifurcation.},
  author={Pauline van den Driessche and James Watmough},
  journal={Journal of mathematical biology},
  year={2000},
  volume={40 6},
  pages={525-40}
}
It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria. 

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