The vaccination of a range of age cohorts on a periodic basis – termed pulse vaccination – for the control of common childhood infections, may, under some circumstances, be an attractive alternative or addition to routine infant immunization schedules (Quadros et al. 1991, Agur et al. 1993). Following from the recent work of Agur et al. (1993), studies are in progress in an attempt to gain a better understanding of the mechanism by which pulse vaccination influences the infection dynamics of directly transmitted ‘close contact’ infections and to explore the merits of such immunization programmes when compared with routine continuous cohort immunization. The preliminary work presented here outlines a conceptual framework for understanding how pulse vaccination programmes effect control on infection transmission, and for establishing rough criteria for the necessary interval between pulses, Tv, for a defined age range vaccinated, and analyses some of the temporal changes induced by pulse strategies.

The basic criterion for control of an infection transmitted by close contact, such as measles, is to keep susceptible numbers, X, below that required to establish an epidemic, i.e. the equilibrium or threshold number of susceptibles, XT (or proportion x* = 1/R0). Assume a closed homogeneously mixing stationary population, exhibiting Type I survival (step function mortality), with an infection at stable endemic equilibrium. Further assume that all individuals are born susceptible, remaining so until of age A, the average age at infection, whence they become infected (for a negligible period of time), and rapidly move into the immune class in which they remain until death at age L (Anderson and May 1991).

Hepatitis B virus (HBV) is one of the most common viral infections in many parts of the world. There are an estimated 300 million carriers of the virus worldwide, each of whom has a high probability of suffering chronic liver disease. There is a safe and effective vaccine against HBV which does not interfere with other vaccines commonly given in childhood and would therefore appear to be ideally suited to mass cohort immunisation. However the vaccine is expensive compared to other Expanded Programme of Immunisation vaccines and there is evidence that vaccine induced immunity declines with time. As the epidemiology of HBV is complex (see below) the outcome of mass immunisation is difficult to predict. The aim of this work is to use a mathematical model of the transmission of HBV to aid the design of vaccination programmes in developing countries.

The epidemiology of HBV has a number of interesting features which complicate the dynamics of infection. Infection with HBV can lead to long-term carriage of the virus. Furthermore the propensity for individuals to develop this chronic carrier state is related to the age at infection in a highly nonlinear manner. The probability of developing the chronic carrier state is highest amongst infants (approximately 0.9), then rapidly declines, and levels off in late childhood so that older children and adults have approximately a 1 in 10 chance of becoming carriers if infected. The epidemiological study of HBV is further complicated by its modes of transmission.