Related papers: A Structured-Population Model of Proteus mirabilis…
We present models and computational results which indicate that the spatial and temporal regularity seen in Proteus mirabilis swarm-colony development is largely an expression of a sharp age of dedifferentiation in the cell cycle from…
Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces. In this paper we investigate a mathematical model that has been shown to display these structures when solved numerically. The model…
We prove a global existence result for a model describing the swarming phenomenon of the bacterium Proteus mirabilis. The model consists of an ordinary differential equation coupled with an age-structured equation involving nonlinear…
In this paper we explain the biophysical principles which, according to us, govern the Proteus mirabilis swarm phenomenon. Then, we translate this explanation into a mathematical model, essentially based on partial differential equations.…
The periodic swarming of bacteria is one of the simplest examples for pattern formation produced by the self-organized collective behavior of a large number of organisms. In the spectacular colonies of Proteus mirabilis (the most common…
In this paper we present a modification of the usual Proteus mirabilis swarm model. For the obtained model (which is a two phase model with a non-linear diffusion term containing memory) we set up a collection of a priori estimates. Those…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
A general model of age-structured population dynamics is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition.…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
This chapter reviews some aspects of the theory of age-structured models of populations with finite maximum age. We formulate both the renewal equation for the birth rate and the partial differential equation for the age density, and show…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
Soil is a complex, dynamic material, with physical properties that depend on its biological content. We propose a cellular automaton model for self-organizing soil structure, where soil aggregates and serves as food for microbial species.…
We review some results on abstract linear and nonlinear population models with age and spatial structure. The results are mainly based on the assumption of maximal $L_p$-regularity of the spatial dispersion term. In particular, this…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We investigate epidemic models with spatial structure based on the cellular automata method. The construction of the cellular automata is from the study by Weimar and Boon about the reaction-diffusion equations [Phys. Rev. E 49, 1749…
The simplest model of a smart spatial redistribution of individuals is proposed. A single-species population is considered, to be composed of two discrete subpopulations inhabiting two stations; migration is a transfer between them. The…
Personalized models of the gut microbiome are valuable for disease prevention and treatment. For this, one requires a mathematical model that predicts microbial community composition and the emergent behavior of microbial communities. We…