SOME BOUNDS ON ESTIMATES FOR REPRODUCTIVE RATIOS DERIVED FROM THE AGE-SPECIFIC FORCE OF INFECTION

In this paper we shall look at estimation of reproductive ratios for c ommon childhood infections such as chickenpox, measles, mumps, and hep atitis A with and without a vaccination program. The paper starts with a survey of previous work in this area. We suppose that we are given data in the form of an age-related serological profile with a given va ccination program. This is used to estimate the reproductive ratio and evaluate vaccination campaigns. The effect of different mixing patter ns, such as homogeneous mixing, assortative mixing, proportional mixin g, and symmetric mixing are discussed. R(phi) denotes the reproductive ratio when a steady-state vaccination campaign phi is used. Assortati ve mixing maximizes the reproductive ratio R(phi). A mixing pattern wh ich minimizes R(phi) and a lower bound for R(phi) for the important sy mmetric mixing case are found. The most usual situation is that we are given the age-serological profile with no vaccination so that we have bounds for the basic reproductive ratio R(0). These results are illus trated with an application to vaccination against hepatitis A in Bulga ria. Numerical evaluations of the effect of different elimination vacc ination strategies are examined.