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A simple SIS epidemic model with a backward bifurcation

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Abstract.

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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, B.C. V8W 3P4, Canada. e-mail: pvdd@math.uvic.ca; watmough@math.uvic.ca, , , , , , CA

    P. van den Driessche & James Watmough

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  1. P. van den Driessche
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  2. James Watmough
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Received: 7 May 1999 / Revised version: 24 November 1999 /¶Published online: 7 June 2000

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van den Driessche, P., Watmough, J. A simple SIS epidemic model with a backward bifurcation. J Math Biol 40, 525–540 (2000). https://doi.org/10.1007/s002850000032

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  • DOI: https://doi.org/10.1007/s002850000032

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