Malcolm R. Adams, Samuel Obara
Abstract:
In this article, we analyze the behavior of solutions to
a variant of the SIR (susceptible, infected, recovered)
model from epidemiology. The model studied includes a secondary
route for susceptible individuals to be exposed to the infectious
agent. This secondary route provides a feedback mechanism that,
within certain parameter regimes, allows for a limit cycle; i.e.,
sustained periodic behavior in the solutions.
Submitted March 9, 2011. Published October 28, 2011.
Math Subject Classifications: 34C15, 34C23, 92D30.
Key Words: Epidemiology; recurrence; Hopf bifurcation; SIR model
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Malcolm R. Adams Department of Mathematics University of Georgia Athens, GA 30602, USA email: mradams@uga.edu, Fax 706-542-2573 |
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Samuel Obara Department of Mathematics Texas State University San Marcos, TX 78666, USA email: so16@txstate.edu |
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