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Epidemic processes on digraphs of random mappings

Part of: Combinatorics Graph theory

Published online by Cambridge University Press:  14 July 2016

Jerzy Jaworski
Jerzy Jaworski*
Affiliation:
Adam Mickiewicz University
*
∗Postal address: Department of Discrete Mathematics, Adam Mickiewicz University, Matejki 48/49, 60–769 Poznań, Poland. Email address: jaworski@main.amu.edu.pl
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Abstract

A random mapping (Tn;q) of a finite set V, V = {1,2,…,n}, into itself assigns independently to each i ∊ V its unique image j ∊ V with probability q if i = j and with probability P = (1-q)/(n−1) if i ≠ j. Three versions of epidemic processes on a random digraph GT representing (Tn;q) are studied. The exact probability distributions of the total number of infected elements as well as the threshold functions for these epidemic processes are determined.

Keywords

Random mappingsepidemic processesthreshold functionsAbel sumsgeneralized Stirling numbers

MSC classification

Primary: 05C80: Random graphs 05A19: Combinatorial identities, bijective combinatorics
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 780 - 798
Copyright
Copyright © Applied Probability Trust 1999 

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