Fig. 12.

Periodicity of recurrent outbreaks of the same lineage under long-term time. Three curves in subplot (a) indicate the periodicity of recurrent outbreaks under short-term immunization ($T=15weeks,i.e.blueline,and48weeks,i.e.redline$.) and long-term immunization ($T=90weeks,i.e.greenline$.). subplot (b) shows the effect of the rate of loss of immunity (both protection $\psi$ and duration of immunization $T$) on the periodicity of recurrent outbreaks. Non-existent indicates that there will be an absence of recurrent outbreaks of the same lineage.