On the method of bounded differences and a natural infection process in a random geometric environment
Author
Diaz, J.
Type of activity
Presentation of work at congresses
Name of edition
Probabilistic Combinatorics
Date of publication
2016
Presentation's date
2016-04-08
Book of congress proceedings
Probabilistic Combinatorics: A celebration of the work of Colin McDiarmid. Programme
First page
4
Last page
4
Abstract
Consider the following geometric infection model: Individuals are randomly placed points according to a Poisson point process in some appropriate metric space. Each individual has two states, infected or healthy. Any infected individual passes the infection to any other at distance d according to a Poisson process, whose rate is a function f(d) of d that decays as d increases. Any infected individual heals at rate 1. An epidemic is said to occur when, starting from one infected individual placed...
Consider the following geometric infection model: Individuals are randomly placed points according to a Poisson point process in some appropriate metric space. Each individual has two states, infected or healthy. Any infected individual passes the infection to any other at distance d according to a Poisson process, whose rate is a function f(d) of d that decays as d increases. Any infected individual heals at rate 1. An epidemic is said to occur when, starting from one infected individual placed at some point, the infection has positive probability of lasting forever. Otherwise, we say extinction occurs. We investigate conditions on and under which the function f(d) = (d + 1)¿ is epidemic.
Joint work with Xavier Perez and Nick Wormald.