Vaccination campaigns for common childhood diseases.

Mathematical models exist for vaccination programs for common childhood diseases such as measles, chickenpox, polio, rubella, and mumps. In compartmental models, the population is divided into compartments containing susceptible, infected, and immune individuals, and the model also takes account of the age structure in the population. An equilibrium analysis is performed on the resulting partial differential equations to determine the vaccination program that just eliminates the disease. The stability of the resulting equilibrium solutions is also examined. Particular attention is paid to multistage vaccination strategies that vaccinate given proportions of susceptible individuals at various ages. Finally, some numerical results are analyzed to see what these vaccination coverages mean for certain common childhood diseases.