Multiple dose vaccination against childhood diseases: high coverage with the first dose remains crucial for eradication.

The high vaccination coverage required to eradicate communicable diseases like measles, mumps and rubella, with a single dose of vaccine, has prompted many countries to introduce a second dose. In this paper we investigate the conditions to eradicate childhood diseases with multiple doses of vaccine by obtaining explicit analytical solutions to the classical compartment model that assumes an age-independent force of infection and conceptualizes the host population as divided into maternally protected (P), susceptibles (S), latents (E), infectious (I), and removed (R). The solutions allow a quantitative discussion of the long-term impact of vaccination schedules with an arbitrary number of doses of vaccine. It becomes possible to determine the effect of the number of doses, ages at vaccination, and coverage rates of vaccines against childhood diseases. In an example with a two-dose vaccination schedule against measles, we show that, in spite of a second dose, a high (> 90%) immunization coverage in the first dose is still crucial to achieve eradication. With a high first-dose coverage, however, eradication is relatively insensitive to the age of the second dose and requires only moderate coverage rates in the latter.