Abstract
In this model we consider the spread of an infectious disease within a population. We assume that there is some initial number of individuals already infected with the disease. These individuals can pass on the disease to a group of susceptibles S. We do not model explicitly the agents that cause the disease, such as viruses or bacteria. Doing that would be rather impractical if we would want to apply our model to real-world diseases. Tracing the billions of agents that can cause the outbreak with a particular disease is virtually impossible. Therefore, we do not explicitly model the dynamics of individuals in a population of disease-causing agents but deal with their effects in an aggregate way.
The endemic and epidemic diseases in Scotland fall chiefly, as is usual, on the poor. Thomas Malthus, 1798
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
For a powerful description of the dynamics of these viruses see R. Preston, The Hot Zone, New York: Anchor Books, 1995.
To achieve some realism with your model, consult the following literature for parameter values: L. Edelstein-Keshet, Mathematical Models in Biology. New York: Random House, 1988. R. Finger, J. Hughes, B.J. Meade, A.R. Pelletier, and C.T. Palmer. Age-Specific Incidence of Chickenpox. Public Health Reports Nov/Dec:750-755, 1994. H.W. Hethcote, Qualitative Analyses of Communicable Disease Models. Mathematical Biosciences 28:335-356, 1976. R.M. May, Parasitic Infections as Regulator of Animal Populations. American Scientist 71:36-45, 1983. Reader’s Digest Association, The American Medical Association Family Medical Guide. New York: Random House, 1982.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ruth, M., Hannon, B. (1997). Infectious Diseases. In: Modeling Dynamic Biological Systems. Modeling Dynamic Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0651-4_20
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0651-4_20
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6856-7
Online ISBN: 978-1-4612-0651-4
eBook Packages: Springer Book Archive