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Progression age enhanced backward bifurcation in an epidemic model with super-infection

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 We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one.

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Received: 11 October 2001 / Revised version: 17 September 2002 / Published online: 17 January 2003

Present address: Department of Biological Statistics and Computational Biology, 434 Warren Hall, Cornell University, Ithaca, NY 14853-7801

This author was visiting Arizona State University when most of the research was done.

Research partially supported by NSF grant DMS-0137687.

This author's research was partially supported by NSF grant DMS-9706787.

Key words or phrases: Backward bifurcation – Multiple endemic equilibria – Alternating stability – Break-point density – Super-infection – Dose-dependent latent period – Progressive and quiescent latent stages – Progression age structure – Threshold type disease activation – Operator semigroups – Hille-Yosida operators – Dynamical systems – Persistence – Global compact attractor

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Martcheva, M., Thieme, H. Progression age enhanced backward bifurcation in an epidemic model with super-infection. J. Math. Biol. 46, 385–424 (2003).

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