Mathematical Biosciences and Engineering (MBE)

A note on epidemic models with infective immigrants and vaccination

Pages: 557 - 566, Volume 3, Issue 3, July 2006      doi:10.3934/mbe.2006.3.557

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Eunha Shim - Department of Mathematics and Statistics, Arizona State University, P.O. Box 871804, Tempe, AZ 85287-1804, United States (email)

Abstract: The roles of immigration and vaccination on disease dynamics are explored in a simple setting that considers the possibility of conferred immunity. We focus on SIR and SIS models with a vaccinated class. Conditions for the existence of multiple endemic steady states and a fold bifurcation are discussed.

Keywords:  epidemic model; vaccination; immigration; SIS; SIR; fold bifurcation.
Mathematics Subject Classification:  34K18; 92D30.

Received: April 2005;      Accepted: February 2006;      Available Online: May 2006.