The current spread of swine flu H1N1 raises serious concerns for public health worldwide. Mathematical modelling has proved to be an essential tool for both developing strategies in preparation for an outbreak and for predicting and evaluating the effectiveness of control policies during an outbreak. Given its growing importance, this article outlines some of the fundamental contributions of mathematical modelling in the study of infectious diseases. The authors review the classical SIR model which has become central to epidemiology, demonstrating basic concepts such as outbreak threshold, the reproductive number Ro and herd immunity. The authors show how the model can be expanded to include different intervention and mitigation strategies, and discuss other biological and social complexities that may be introduced. Finally, the paper illustrates different scenarios for the spread of swine flu in Israel and provides estimates for Reproductive rate (Ro).