Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 142, pp. 1-12.

Title: Recurrent epidemics resulting from secondary transmission
       routes in SIR models

Authors: Malcolm R. Adams (Univ. of Georgia, Athens, GA, USA}
         Samuel Obara (Texas State Univ., San Marcos, TX, USA)

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.