  We have performed individual-based lattice simulations of SIR and SEIR dynamics to investigate both the short and long-term dynamics of childhood epidemics. In our model, infection takes place through a combination of local and long-range contacts, in practice generating a dynamic small-world network. Sustained oscillations emerge with a period much larger than the duration of infection. We found that the network topology has a strong impact on the amplitude of oscillations and in the level of persistence. Diseases do not spread very effectively through local contacts. This can be seen by measuring an {\em effective} transmission rate $\beta_{\mbox {\scriptsize eff}}$ as well as the basic reproductive rate $R_0$. These quantities are lower in the small-world network than in an homogeneously mixed population, whereas the average age at infection is higher. 
Short and Long-Term Dynamics of Childhood Diseases on Dynamic   Small-World Networks