A Theory of Epidemics

  • Frank C. Hoppensteadt
  • Charles S. Peskin
Part of the Texts in Applied Mathematics book series (TAM, volume 10)


The spread of a contagious disease involves interactions of two populations: the susceptibles and the infectives. In some diseases these two populations are from different species. For example, malaria is not passed directly between animals but by anopheline mosquitoes, and schistosomiasis is passed from animal to animal only through contact with water harboring snails that can incubate the disease-causing helminths. In other diseases, the infection can be passed directly from infectives to susceptibles: Viral diseases like chickenpox, measles, and influenza, and bacterial diseases like tuberculosis can pass through a population much as fire spreads through a forest.


Sampling Interval Sample Path Final Size Markov Chain Model Susceptible Population 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Annotated References

  1. Kermack, W.O., and McKendrick, A.G.: A contribution to the theory of epidemics, Proc. Roy. Soc.(A) 115 (1927), 700–721, 139 (1932), 55–83.CrossRefzbMATHGoogle Scholar
  2. McKendrick, A.G.: Mathematics applied to medical problems, Roy. Soc. Edinh., 1926.Google Scholar
  3. Bailey, N.T.J.: The Theory of Infectious Diseases and Its Applications, Charles Griffin, London, 1975.zbMATHGoogle Scholar
  4. May, R.M., and Anderson, R.M.: Transmission dynamics of HIV infections.Nature 326 (1987), 37–42.Google Scholar
  5. Hoppensteadt, F.C.: Mathematical Methods of Population Biology, Cambridge University Press, 1982.CrossRefzbMATHGoogle Scholar
  6. Hammersley, J.M., and Handscombe, D.C.: Monte Carlo Methods, Methuen, London, 1964.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  • Charles S. Peskin
    • 2
  1. 1.Center for Systems Science and EngineeringArizona State UniversityTempeUSA
  2. 2.Department of Mathematics Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations