## Mathematical Models for Competition and Coexistence of Microbial

20th January 2015 AM

Automatique, Boulevard Dolez 31 - 7000 Mons

Radhouane FEKIH SALEM

"Mathematical Models for Competition and Coexistence of Microbial - Species in a chemostat"

This thesis focuses on the mathematical analysis of models of several species in competition on a single resource in a chemostat. The objective is to model and show the coexistence of microbial species by different mechanisms to better realize biodiversity found in nature like in the bioreactors. We are interested mainly in three mechanisms of coexistence :

1. The inter-specific competition between populations of micro-organisms and intra-specific between individuals of the same species.

2. The flocculation where the species who wins the competition inhibits its growth by the formation of flocs, which allows the coexistence with the other species. In fact, these flocs consume less substrate than isolated bacteria since they have less access to the substrate, given that this access to the substrate is proportional to the outside surface of the floc.

3. The density-dependence, whose model can be built from the flocculation model, assuming that the dynamics of flocculation is faster than the growth dynamics of the species. In this density-dependent model, the growth rate depends not only on the density of substrate but also on the density of biomass, and the removal rate of biomass is not constant but depends also on the density of biomass. Finally, we studied a 3-step model of anaerobic digestion with enzymatic degradation of the substrate (organic matter) that can partly be under a solid form. The mathematical analysis shows that this model may exhibit the quadri-stability with washout of none, one or two species according to the initial condition. The mathematical study of the qualitative behavior of different models of the chemostat, allowed us to better understand the competition and the coexistence of microbial species.

## Basic statistical analysis and experiment design (part 1)

7th November 2014 AM

Automatique, Boulevard Dolez 31 - 7000 Mons

Alejandro Vargas

"Basic statistical analysis and experiment design (part 1)"

The first part of this short course will focus on reviewing basic statistical analysis tools, which are often needed in the experimental sciences. We will review the concepts of random variables and their distributions, the central limit theorem, tests for normality, confidence intervals for statistical parameters and hypothesis testing, with an emphasis on t-tests, chi-squared tests and the one-way analysis of variance (ANOVA). Examples will be worked out with the open-source statistical software package R.

## Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB

A. Vande Wouwer, P. Saucez, C. Vilas

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB

Scientific and Engineering Applications

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration.

## Basic statistical analysis and experiment design (part 2)

13th November 2014 AM

Automatique, Boulevard Dolez 31 - 7000 Mons

Alejandro Vargas

"Basic statistical analysis and experiment design (part 2)"

The second part of this short course will focus on expanding analysis of variance (ANOVA) techniques and presenting 2-level factorial experiment designs, including blocking and fractional designs. Other useful factorial experiment design techniques will be reviewed (e.g. central composite designs). Examples will again be worked out with the open-source statistical software package R.

## Networking event on biotechnologies

Alain Vande Wouwer and Laurent Dewasme were invited to a networking event on biotechnologies organized by the “Association des Ingénieurs de Mons” and GlaxoSmithKline Vaccines in Wavre on the 13th of March 2014.

Laurent Dewasme had the pleasure to present the BioSys Center activities in biotechnologies through a talk entitled “Bioprocesses: from modeling to control”

Slides are available here.