Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T16:19:33.123Z Has data issue: false hasContentIssue false
  • English
  • Français

A new look at the simple epidemic process

Published online by Cambridge University Press:  14 July 2016

L. Billard ,
H. Lacayo  and
N. A. Langberg
L. Billard*
Affiliation:
Florida State University
H. Lacayo*
Affiliation:
Florida State University
N. A. Langberg*
Affiliation:
Florida State University
*
∗ Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, Florida 32306, U.S.A.
∗ Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, Florida 32306, U.S.A.
∗ Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, Florida 32306, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Classical epidemic models have invariably proved to be mathematically intractable. By considering the distribution of the number of infectives in a simple epidemic process as a convolution of exponential waiting times, the solution to the classical model is obtained easily giving more insight into the underlying structure. The idea can be extended to other simple epidemic models.

Keywords

SIMPLE STOCHASTIC EPIDEMICINTERINFECTION TIMESDISTRIBUTION OF INFECTIVES
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 198 - 202
Copyright
Copyright © Applied Probability Trust 1979 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

Research supported by NSF Grant No. MCS76–10453.

References

Bailey, N. T. J. (1950) A simple stochastic epidemic. Biometrika 37, 193–202.Google Scholar
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications. Hafner, New York.Google Scholar
Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice Hall, Princeton, N.J.Google Scholar
Mcneil, D. R. (1972) On the simple stochastic epidemic. Biometrika 59, 494–497.Google Scholar
Renyi, A. (1970) Probability Theory. North Holland, Amsterdam.Google Scholar
Severo, N. C. (1969) Generalizations of some stochastic epidemic models. Math. Biosci. 4, 395–402.Google Scholar