Hi Stephen,

Below are a couple of papers that should be helpful to you. I read them last week and found them very insightful.

http://www.sciencedirect.com/science/article/pii/S0264410X02001809

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0060732

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0066485

I am sure, they address your specific interest, but at least it should provide you with a few tips and clues on how to go about your question.

Good luck:

Mathematical Models. Mathematics can be used to "model", or represent, how the real world works. Mathematical modelling can be used for a number of different reasons. It is used for tactical decisions by managers and for strategic decisions by planners. Deterministic models ignore random variation in vaccinated and unvaccinated population. Level of understanding in population about post vaccination output and success rates.

Attached one paper. Check out the references.

A text book explaining modelling approaches and with additional references: Keeling and Rohani, Modelling Infectious Diseases in humans and animals, Princeton Univ Press, Chapter 8.