Abstract

PIP: The relationship between the number of people vaccinated for an infectious disease and the resulting decrease in incidence of the disease is not straightforward and linear because many independent variables determine the course of infection. However, these variables are quantifiable and can therefore by used to model the course of an infectious disease and impact of mass vaccination. Before one can construct a model, one must know for any specific infectious disease the number of individuals in the community protected by maternally derived antibodies, the number susceptible to infectious the number infected but not yet infectious (i.e., with latent infection), the number of infectious individuals, and the number of recovered (i.e., immune) individuals. Compartmental models are sets of differential equations which describe the rates of flow of individuals between these categories. Several major epidemiologic concepts comprise the ingredients of the model: the net rate of infection (i.e., incidence), the per capita rate of infection, the Force of Infection, and the basic reproductive rate of infection. When a community attains a high level of vaccination coverage, it is no longer necessary to vaccinate everyone because the herd immunity of the population protects the unvaccinated because it lowers the likelihood of their coming into contact with an infectious individual. Many infections that confer lasting immunity tend to have interepidemic periods when the number of susceptibles is too low to sustain an epidemic. Mass vacination programs reduce the net rate of transmission of the infective organism; they also increase the length of the interepidemic period. Many diseases primawrily associated with children have much more serious consequences in older people and the question arises as to at what point childhood immunization will successfully prevent the more dangerous incidence of the disease in older cohorts. Mathematical models of disease transmission enable one to predict the course of epidemics, design mass vaccination programs, and be guided as to what are the relevant data that should be collected.