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A simple SIS epidemic model with a backward bifurcation. (English) Zbl 0961.92029
Summary: It is shown that an SIS epidemic model with a nonconstant 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.

MSC:
92D30 Epidemiology
45D05 Volterra integral equations
45M10 Stability theory for integral equations
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