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One of the cornerstones in combating the HIV pandemic is being able to assess the current state and evolution of local HIV epidemics. This remains a complex problem, as many HIV infected individuals remain unaware of their infection status,…
We consider a birth-death process with the birth rates $i\lambda$ and death rates $i\mu +i(i-1)\theta$, where $i$ is the current state of the process. A positive competition rate $\theta$ is assumed to be small. In the supercritical case…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of…
This paper is not (or at least not only) about human infant mortality. In line with reliability theory, "infant" will refer here to the time interval following birth during which the mortality (or failure) rate decreases. This definition…
We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$.…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements -…
Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (noncompact) type space. Conditions are…
Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…
We generalize the evolution model introduced by Guiol, Machado and Schinazi (2010). In our model at odd times a random number X of species is created. Each species is endowed with a random fitness with arbitrary distribution on $[0, 1]$. At…
An epidemic model with births and deaths is considered on a two dimensional LxL lattice. Each individual can have global infective contacts according to the standard SIR model rules or local infective contacts with its nearest neighbors. We…
In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on $n$ contemporary tips. We show that this normalized phylogenetic balance index is a submartingale that…
The statistical estimation of phylogenies is always associated with uncertainty, and accommodating this uncertainty is an important component of modern phylogenetic comparative analysis. The birth-death polytomy resolver is a method of…
We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e. proliferation or differentiation)…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…
Index-based hedging solutions are used to transfer the longevity risk to the capital markets. However, mismatches between the liability of the hedger and the hedging instrument cause longevity basis risk. Therefore, an appropriate…
The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death…