Related papers: Characterization of the Endemic Equilibrium and Re…
Multicellular organisms comprise a diverse collection of stable tissues built from different cell types. It remains unclear how large numbers of interacting cells can precisely coordinate their gene expression during tissue…
Adaptive control in biological systems, such as intestinal immunity, remains poorly understood despite detailed knowledge of underlying regulatory networks. We propose an alternative framework based on stochastic martingale turnover, in…
We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the…
Consider an epidemic model with a constant flux of susceptibles, in a situation where the corresponding deterministic epidemic model has a unique stable endemic equilibrium. For the associated stochastic model, whose law of large numbers…
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…
In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by…
Microbial communities routinely have several alternative stable states observed for the same environmental parameters. Sudden and irreversible transitions between these states make external manipulation of these systems more complicated. To…
Ecosystems dynamics is often considered as driven by a coupling of species' resource consumption and its population size dynamics. Such resource-population dynamics is captured by MacArthur-type models. One biologically relevant feature…
Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context…
We formulate and analyse a robust mathematical model of the dynamics of gonorrhoea incorporating passive immunity and control. Our results show that the disease-free and endemic equilibria of the model are both locally and globally…
We present an SI epidemic model whereby a continuous variable captures variability in proliferative potential and resistance to infection among susceptibles. The occurrence of heritable, spontaneous changes in these phenotype and the…
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without…
Understanding which phenotypic traits are consistently correlated throughout evolution is a highly pertinent problem in modern evolutionary biology. Here, we propose a multivariate phylogenetic latent liability model for assessing the…
An interesting inference drawn by some Covid-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection -- even at the start of the current pandemic. This paper introduces a model of…
In this paper, we consider a resource-consumer model taking into account a mutation effect between species (with constant mutation rate). The corresponding mutation operator is a discretization of the Laplacian in such a way that the…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…
Epidemic models study the spread of an undesired agent through a population, be it infectious diseases through a country, misinformation in online social media, or pests infesting a region. In combating these epidemics, we rely neither on…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…