A shiny app for the Susceptible Infected Recovered (SIR) Model - http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SIR_model
This uses the code from a blog post from EconometricsBySimulation.com at:
http://www.econometricsbysimulation.com/2013/05/sir-model-flue-season-dynamic.html
There is a copy of this running at https://jonmoore.shinyapps.io/SIR-shiny/