Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T23:57:26.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Epidemic process on a random graph: some preliminary results

Published online by Cambridge University Press:  14 July 2016

I. B. Gertsbakh
I. B. Gertsbakh*
Affiliation:
Ben Gurion University of the Negev, Beersheva, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

A random graph is a collection of n points and n directed arcs: a directed arc goes equiprobably from each point to one of (n – 1) other points. m points are initially ‘infected'. We consider several schemes of epidemic process, e.g. when the infection is delivered according to arc direction. We prove that the probability of infecting all the n points with m = 1 is ∼ e/n, when n → ∞; another result is that m = o(√ n) cannot infect an essential part of the graph (having the size of O(n)). Possible applications of the models to real world phenomena are briefly discussed.

Keywords

RANDOM GRAPHRANDOM MAPPINGEPIDEMIC PROCESSTHRESHOLD FUNCTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 427 - 438
Copyright
Copyright © Applied Probability Trust 1977 

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.)

References

De Bruijn, N. G. (1958) Asymptotic Methods in Analysis. North-Holland, Amsterdam.Google Scholar
Harris, B. (1960) Probability distributions related to random mappings. Ann. Math. Statist. 31, 1045–1062.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Katz, L. (1955) Probability of indecomposability of a random mapping function. Ann. Math. Statist. 26, 512–517.Google Scholar
Riordan, J. (1958) An Introduction to Combinatorial Analysis. Wiley, New York.Google Scholar
Shante, V. and Kirkpatrick, S. (1971) An introduction to percolation theory. Adv. Phys. 20, 325–357.CrossRefGoogle Scholar
Stepanov, V. E. (1969) Limit distributions of certain characteristics of random mappings. Theory Prob. Appl. 14, 612–626.CrossRefGoogle Scholar