Introduction

If a fraction of a population is vaccinated, the spread of the infective agent is slowed down and consequently the incidence of infection for non-vaccinated persons is reduced. If the vaccine itself carries some risk then the risk of illness for a non-vaccinated person can drop below that for a vaccinated one. This occurs when the spread of infection has been greatly reduced by vaccination. It then becomes questionable whether people will agree to be vaccinated and whether, therefore, an infectious disease can be eliminated by vaccination on a voluntary basis. With smallpox vaccination it was shown that in the final years of the campaign more cases of illness were caused in the US by vaccination than by infections (CDC 1971) and nowadays there is a lively discussion about the oral poliomyelitis vaccines which have been incriminated in causing more paralytic cases in the US than the rare wild viruses do (Beale 1990, Begg et al 1987, Cossart 1977, McBean and Modlin 1987). Fine and Clarkson (1986) were the first to compare the risk of illness of vaccinated persons with that of non-vaccinated ones from a theoretical point of view. To estimate the incidence of infection that results from a given vaccination coverage, they made arbitrary assumptions which imply that an infection can only be eliminated if 100 percent of the population are effectively immunized. Moreover, they did not take into consideration an age-specific conditional probability of illness or death upon infection. Many of the so-called ‘childhood diseases’ tend to be more serious in adults than in infants.