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
There are epidemics of opinion as well as of disease. —Sir B. Brodie, Psychological Inquiries
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References
See Spain, J.D. 1982. BASIC Microcomputer Models in Biology, Addison-Wesley, Reading, MA, p. 118. For some realism, see the data on the Black Death in the 1300s in Italy (Curtis H. and N. Barnes. 1985. Invitation to Biology, Worth Publishers, New York.) These data show a declining peak as either people 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, W. 1985. Can Nonlinear Dynamics Elucidate Mechanisms in Ecology and Epidemiology? IMA Journal of Mathematics Applied in Medicine and Biology, Vol. 2, pp. 221–252. Schaffer shows how a cyclic contact coefficient can produce chaos in this form of epidemic model.
Hannon, B. and M. Ruth (1997) Modeling Dynamic Biological Systems, Springer-Verlag, New York.
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Hannon, B., Ruth, M. (2001). Epidemic Modeling. In: Dynamic Modeling. Modeling Dynamic Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0211-7_19
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DOI: https://doi.org/10.1007/978-1-4613-0211-7_19
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