Electron. J. Diff. Equ., Vol. 2011 (2011), No. 142, pp. 1-12.

Recurrent epidemics resulting from secondary transmission routes in SIR models

Malcolm R. Adams, Samuel Obara

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
Samuel Obara
Department of Mathematics
Texas State University
San Marcos, TX 78666, USA
email: so16@txstate.edu

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