In this paper we establish the necessary and sufficient criterion for the contact process on
Galton–Watson trees (resp., random graphs) to exhibit the phase of extinction (resp., short …

We study the contact process on a class of geometric random graphs with scale-free degree
distribution, defined on a Poisson point process on R d. This class includes the age …

Given a weighted graph, we introduce a partition of its vertex set such that the distance
between any two clusters is bounded from below by a power of the minimum weight of both …

We consider the contact process on the model of hyperbolic random graph, in the regime
when the degree distribution obeys a power law with exponent χ∈(1, 2)(so that the degree …

We consider the contact process on finite and connected graphs and study the behavior of
the extinction time, that is, the amount of time that it takes for the infection to disappear in the …

We consider the contact process on the preferential attachment graph. The work of Berger,
Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process …

We study the contact process on random graphs with low infection rate $\lambda $. For
random $ d $-regular graphs, it is known that the survival time is $ O (\log n) $ below the …

In this paper we prove lower and upper bounds for the extinction time of the contact process
on random geometric graphs with connection radius tending to infinity. We obtain that for …

Researchers have been faced with the challenge of understanding the dynamics
surrounding the spread of an epidemic in complex networks, a key topic in network science …

We are interested in the spread of an epidemic between two communities that have higher
connectivity within than between them. We model the two communities as independent …