Related papers: Semigroup analysis of structured parasite populati…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird…
We describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in $\mathbb{R}^d$. We present conditions on the birth-and-death intensities which are…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed…
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the…
Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical…
We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a…
We construct a semiparametric estimator in case-control studies where the gene and the environment are assumed to be independent. A discrete or continuous parametric distribution of the genes is assumed in the model. A discrete distribution…
We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, and others). The formulation…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
This paper is to study some conditions on semigroups, generated by some class of non-densely defined operators in the closure of its domain, in order that certain bounded perturbations preserve some regularity properties of the semigroup…
The dynamics of a general structured population is modelled using a general stochastic differential equation (SDE) with an infinite decomposability property. This property allows the population to be divided into an arbitrary number of…
Spatial patterning can be crucially important for understanding the behavior of interacting populations. Here we investigate a simple model of parasite and host populations in which parasites are random walkers that must come into contact…
In the present work, we develop a delayed Logistic growth model to study the effects of decontamination on the bacterial population in the ambient environment. Using the linear stability analysis, we study different case scenarios, where…
We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor and is ruled by the interplay of hyperelastic energy…
In order to accommodate the empirical fact that population structures are rarely simple, modern studies of evolutionary dynamics allow for complicated and highly-heterogeneous spatial structures. As a result, one of the most difficult…
Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
The aim of this paper is twofold: (1) On the one hand, the paper revisits the spectral analysis of semigroups in a general Banach space setting. It presents some new and more general versions, and provides comprehensible proofs, of…
We consider an abstract first order evolution equation in a Hilbert space in which the linear part is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the…