We've seen that a periodic contact rate can lead to periodic behavior for epidemic models, thereby providing an explanation for seasonal variation of the number of infected individuals for a disease. Other ways to get periodic behavior are given in the article ``Periodicity in Epidemiological Models'' by H.W. Hethcote and S.A. Levin, in Applied Mathematical Ecology, ed. S.A. Levin, T.G. Hallam, and L.J. Gross, Springer, New York, 1989.