## Léo Dort [1]

*First introduced and studied by Harris (1974), the Contact Process (CP) is a stochastic process usually used to model the spread of an epidemic in a population. We model population by a graph, where vertices represent the individuals and edges the possible pathways for infection to spread. Each individual can be "healthy" or "infected". The process evolves according to the **following dynamic. Each infected vertex become healthy at rate 1. Simultaneously each infected vertex infects all of its neighbours with rate λ.*

*In this talk, we will give some general and basic properties of the CP, and we will focus on the following interesting and natural question: does the infection become extinct or not ? We will show that for many graphs, we can exhibit a (at least one) phase transition. *