Related papers: A branching process with contact tracing
We investigate the contact process on scale-free networks evolving by a stationary dynamics whereby each vertex independently updates its connections with a rate depending on its power. This rate can be slowed down or speeded up by virtue…
We consider a two-type contact process on $\Z$ in which both types have equal finite range and supercritical infection rate. We show that a given type becomes extinct with probability 1 if and only if, in the initial configuration, it is…
We introduce a model for the evolution of species triggered by generation of novel features and exhaustive combination with other available traits. Under the assumption that innovations are rare, we obtain a bursty branching process of…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
Contact tracing is an effective method to control emerging diseases. Since the 1980's, mathematical modelers are developing a consistent theory for contact tracing, with the aim to find effective and efficient implementations of contact…
In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. The question of how many sequence sites are required to recover this evolutionary…
Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
In this paper we are concerned with the contact process with random recovery rates and edge weights on complete graph with $n$ vertices. We show that the model has a critical value which is inversely proportional to the product of the mean…
Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated L\'evy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using L\'evy snake techniques.…
Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…
We study the exploration (or height) process of a continuous time non-binary Galton-Watson random tree, in the subcritical, critical and supercritical cases. Thus we consider the branching process in continuous time (Z_{t})_{t\geq 0}, which…
An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other…
We consider a critical branching process $Y_{n}$ in an i.i.d. random environment, in which one immigrant arrives at each generation. Let $% \mathcal{A}_{i}(n)$ be the event that all individuals alive at time $n$ are offspring of the…
We consider Bernoulli bond percolation on a large scale-free tree in the supercritical regime, meaning informally that there exists a giant cluster with high probability. We obtain a weak limit theorem for the sizes of the next largest…
We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. We analyze the…
Our paper computationally explores the extinction dynamics of an animal species effected by a sudden spike in mortality due to an extreme event. In our study, the animal species has a 2-year life cycle and is endowed with a high survival…
We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344--353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344--353], the…
We consider a binary branching process structured by a stochastic trait that evolves according to a diffusion process that triggers the branching events, in the spirit of Kimmel's model of cell division with parasite infection. Based on the…
Dynamic extinction colonisation models (also called contact processes) are widely studied in epidemiology and in metapopulation theory. Contacts are usually assumed to be possible only through a network of connected patches. This network…