Abstract
In this chapter we model the spread of a disease through a population. Epidemics, such as the one modeled here, are of great concern to human societies. The complex interrelationships of biological, social, economic, and geographic relationships that drive or constrain an epidemic make dynamic models an invaluable tool for the analysis of particular diseases. The model developed here is fairly idealized but can be applied easily to real populations affected by a disease.1
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See Spain (1982). For some realism, see the data on the Black Death in the 1300s in Italy (Curtis and Barnes 1985). These data show a declining peak as people either became aware of the vector or those most likely exposed to the vector died off or the naturally immune were selected for and that immunity was inheritable. The four occurrences of the plague in that century had a period of about 11 years. For chaotic epidemics, see Schaffer (1985). Schaffer shows how a cyclic contact coefficient can produce chaos in this form of epidemic model.
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© 1994 Springer Science+Business Media New York
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Hannon, B., Ruth, M. (1994). Epidemic Modeling. In: Dynamic Modeling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25989-4_17
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DOI: https://doi.org/10.1007/978-3-662-25989-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-94309-9
Online ISBN: 978-3-662-25989-4
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