Daily incidence for an influenza outbreak calculated using an SIR model. (a) With constant transmission rate. (b) With small seasonal variation in transmission rate. For a constant transmission rate, after an initial transient period, the system approaches an endemic level (that is, equilibrium) by damped oscillations. If a small amount of seasonal variation in transmission is introduced oscillations are sustained rather than damping out, and the system eventually tends to an annual cycle.
Coburn et al. BMC Medicine 2009 7:30 doi:10.1186/1741-7015-7-30