Related papers: Extensions of the chemostat model with flocculatio…
We revisit the well-known chemostat model, considering that bacteria can be attached together in aggregates or flocs. We distinguish explicitly free and attached compartments in the model and give sufficient conditions for coexistence of…
In this paper, we consider a flocculation model in a chemostat where one species is present in two forms: planktonic and aggregated bacteria with the presence of a single resource. The removal rates of isolated and attached bacteria are…
We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional…
We present a model for a biological reactor in which bacteria tend to aggregate in flocs, as encountered in wastewater treatment plants. The influence of this flocculation on the growth dynamics of the bacteria is studied. We argue that a…
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…
In many real life applications, a continuous culture bioreactor may cease to function properly due to bioclogging which is typically caused by the microbial overgrowth. This is a problem that has been largely overlooked in the chemostat…
We study the existence and uniqueness of the solution of a non-linear coupled system constituted of a degenerate diffusion-growth-fragmentation equation and a differential equation, resulting from the modeling of bacterial growth in a…
The purpose of this paper is to show that it is possible to replace Monod's type model of a chemostat by a constraint based model of bacteria at the genome scale. This new model is an extension of the RBA model of bacteria developed in a…
We investigate some chemostat models incorporating wall growth, competition, random fluctuations on the dilution rate, and different consumption functions (Monod and Haldane). We analyze the asymptotic behavior of the solutions of the…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during…
We investigate the propagating profiles of a degenerate chemotaxis model describing the bacteria chemotaxis and consumption of oxygen by aerobic bacteria, in particular, the effect of the initial attractant distribution on bacterial…
Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial…
In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out. The local and global stability analysis of the equilibria are…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separation and a limit cycle, in which a rising global population…
Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and \textit{in vitro} drug testing. In the present paper, a…