Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T04:32:39.370Z Has data issue: false hasContentIssue false
  • English
  • Français

The front velocity of the simple epidemic

Published online by Cambridge University Press:  14 July 2016

John C. Wierman
John C. Wierman*
Affiliation:
University of Minnesota
*
∗Postal address: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S. E. Minneapolis, Minnesota 55455, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The propagation rate of the one-dimensional stochastic simple epidemic converges almost surely to a front velocity for the epidemic. Percolation methods are used in the proof.

Keywords

SIMPLE EPIDEMICSSUBADDITIVE PROCESSFIRST-PASSAGE TIMEPERCOLATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 409 - 415
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 in part by University of Minnesota Graduate School Research Grant 494–0350–4909–02 and by National Science Foundation Grant MCS74-05786.

References

Hammersley, J. M. (1974) Postulates for subadditive processes. Ann. Prob. 2, 652–680.Google Scholar
Hammersley, J. M. and Welsh, D. J. A. (1965) First passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. In Bernoulli–Bayes–Laplace Anniversary Volume, Springer-Verlag, Berlin, 61–110.Google Scholar
Kingman, J. F. C. (1973) Subadditive ergodic theory. Ann. Prob. 1, 883–909.CrossRefGoogle Scholar
Kingman, J. F. C. (1976) Subadditive processes. In École d'Été de Probabilités de Saint-Flour, V. Lecture Notes in Mathematics 539, Springer-Verlag, Berlin.Google Scholar
Mollison, D. (1972) The rate of spatial propagation of simple epidemics. Proc. 6th Berkeley Symp. Math. Statist. Prob. 3, 579–614.Google Scholar
Mollison, D. (1974) Percolation processes and tumour growth (abstract). Adv. Appl. Prob. 6, 233–235.Google Scholar
Mollison, D. (1977) Spatial contact models for ecological and epidemic spread. J. R. Statist. Soc. B 39, 283–326.Google Scholar
Mollison, D. (1978) Markovian contact processes. Adv. Appl. Prob. 10, 85–108.CrossRefGoogle Scholar
Morgan, R. W. and Welsh, D. J. A. (1965) A two-dimensional Poisson growth process. J. R. Statist. Soc. B 27, 497–504.Google Scholar
Richardson, D. (1973) Random growth in a tesselation. Proc. Camb. Phil. Soc. 74, 515–528.Google Scholar
Smythe, R. T. and Wierman, J. C. (1978) First-Passage Percolation on the Square Lattice. Lecture Notes in Mathematics 671, Springer-Verlag, Berlin.Google Scholar