Abstract
Vaccination is an effective method to prevent individuals from contracting diseases like measles and the flu. Its success is clearly demonstrated by the large declines in the incidence of many diseases (e.g., childhood diseases like measles) after the start of mass vaccination programs. However, what happens after this drop in incidence can be complicated. It is known that some diseases exhibit "honeymoon periods" (long periods of temporary low disease incidence after start of mass vaccination). These periods end with a natural resurgence of the disease, which is not due to any change in the system. To study honeymoon periods, we used the compartmental model analyzed in [1] that can exhibit different types of vaccine failures: failure in degree (leakiness), in take (all-or-nothing) and in duration (waning of vaccine-derived immunity). We showed that traditional measures of transient dynamics in ecology may not distinguish between models with different honeymoon periods. We also provide a proof of global stability of the endemic equilibrium when the reproduction number (accounting for vaccination) is greater than one, and introduce a technical definition of the honeymoon period.
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