Recurrent epidemics resulting from secondary transmission routes in SIR models

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.

Keywords

• Epidemiology
• recurrence
• Hopf bifurcation
• SIR model