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Directly transmitted infectious diseases: control by vaccination. (English) Zbl 1225.37099
Summary: Mathematical models for the dynamics of directly transmitted viral and bacterial infections are guides to the understanding of observed patterns in the age-specific incidence of some common childhood diseases of humans, before and after the advent of vaccination programs. For those infections that show recurrent epidemic behavior, the interepidemic period can be related to parameters characterizing the infection (such as latent and infectious periods and the average age of first infection); this relation agrees with the data for a variety of childhood diseases. Criteria for the eradication of a disease are given, in terms of the proportion of the population to be vaccinated and the age-specific vaccination schedule. These criteria are compared with a detailed analysis of the vaccination programs against measles and whooping cough in Britain, and estimates are made of the levels of protection that would be needed to eradicate these diseases.

MSC:
37N25 Dynamical systems in biology
92D30 Epidemiology
34C25 Periodic solutions to ordinary differential equations
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