Related papers: Stochastic Modeling and Simulation of Viral Evolut…
We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into…
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
Stochastic epidemic models, generally more realistic than deterministic counterparts, have often been seen too complex for rigorous mathematical analysis because of level of details it requires to comprehensively capture the dynamics of…
Antigenic escape constitutes the main mechanism allowing rapidly evolving viruses to achieve endemicity. Beyond granting immune escape, empirical evidence also suggests that mutations of viruses might increase their inter-host…
Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to…
The packaging of genetic material within a protein shell, called the capsid, marks a pivotal step in the life cycle of numerous single-stranded RNA viruses. Understanding how hundreds, or even thousands, of proteins assemble around the…
We introduce two stochastic chemostat models consisting in a coupled population-nutrient process reflecting the interaction between the nutrient and the bacterias in the chemostat with finite volume. The nutrient concentration evolves…
A complete parametric analysis of dynamic regimes of a conceptual model of anti-tumor virus therapy is presented. The role and limitations of mass-action kinetics are discussed. A functional response, which is a function of the ratio of…
A bit-string model for the evolution of a population of haploid organisms, subject to competition, reproduction with mutation and selection is studied, using mean field theory and Monte Carlo simulations. We show that, depending on…
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
A theory of relative species abundance on sparsely-connected networks is presented by investigating the replicator dynamics with symmetric interactions. Sparseness of a network involves difficulty in analyzing the fixed points of the…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
Mathematical modelling of epidemiological and coevolutionary dynamics is widely being used to improve disease management strategies of infectious diseases. Many diseases present some form of intra-host quiescent stage, also known as covert…
We consider the classical Wright-Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak landscape. In the asymptotic regime studied in [3], a…
How multicellular life forms evolved out from unicellular ones constitutes a major problem in our understanding of the evolution of our biosphere. A recent set of experiments involving yeast cell populations has shown that selection for…
We consider general discrete-time multitype branching processes on a countable set $X$. According to these processes, a particle of type $x\in X$ generates a random number of children and chooses their type in $X$, not necessarily…
Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the…
How self-organized networks develop, mature and degenerate is a key question for sociotechnical, cyberphysical and biological systems with potential applications from tackling violent extremism through to neurological diseases. So far, it…