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Who is the infector? General multi-type epidemics and real-time susceptibility processes

Part of: Graph theory Special processes Markov processes

Published online by Cambridge University Press:  07 August 2019

Tom Britton ,
Ka Yin Leung  and
Pieter Trapman
Tom Britton*
Affiliation:
Stockholm University
Ka Yin Leung*
Affiliation:
Stockholm University
Pieter Trapman*
Affiliation:
Stockholm University
*
*Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
*Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
*Postal address: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden.
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Abstract

We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random weights (traversal times). This random graph representation is used to characterise the fractions of individuals infected by the different types of vertices among all infected individuals in the large population limit. For this characterisation, we rely on the theory of multi-type real-time branching processes. We identify a special case of the two-type model in which the fraction of individuals of a certain type infected by individuals of the same type is maximised among all two-type epidemics approximated by branching processes with the same mean offspring matrix.

Keywords

Epidemicsmulti-type branching process approximationsusceptibility processdirected random graph

MSC classification

Primary: 92D30: Epidemiology 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 05C80: Random graphs 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 51 , Issue 2 , June 2019 , pp. 606 - 631
Copyright
© Applied Probability Trust 2019 

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