Introduction

This paper is concerned with evaluation of vaccination programs for viral diseases such as measles, mumps, rubella and hepatitis A. For such diseases an individual starts off susceptible, at some stage catches the disease and after a short infectious period becomes permanently immune. Vaccines for measles, mumps and rubella are currently in use and vaccines for hepatitis A are not yet widely available but are currently undergoing testing. The aim of this paper is to look at the evaluation of vaccination programs and their sensitivity to different mixing assumptions.

Mathematical models which accurately describe the spread of a disease must take into account the age-structure of the population amongst whom the disease is spreading. Anderson and May (1985) describe an age-structured mathematical model using partial differential equations, which is the basis of the one which we shall use. Age-structured data for these diseases is available in the form of case reports, or more reliably age-serological profiles. Anderson and May divide the population into discrete age classes and use computer simulation methods to evaluate different vaccination programs for measles, mumps and rubella.

Method

The force of infection at time t, λ(a, t), is defined as the probability per unit time that a susceptible individual of age a will become infected. We follow Keiding's non-parametric maximum likelihood method to estimate the force of infection assuming that the disease has settled down to its longterm equilibrium value. We use age-structured serological profiles for hepatitis A in Bulgaria given by Keiding (1991).