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Site web personnel : https://sites.google.com/site/fekihsalemradhouane0/

Research activities

We focus 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 :

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

• The flocculation where the species who wins the competition inhibits its growth by the formation of flocs to be able to coexist with the other species.

•  The density-dependence which the model can be construct from the flocculation model by assuming that the dynamics of flocculation is faster than the growth of the species.

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.

Publications

1- R. Fekih-Salem, J. Harmand, C. Lobry, A. Rapaport and T. Sari, Extensions of the chemostat model with flocculation. Journal of Mathematical Analysis and Applications, Vol. 397, Issue 1, (2013), pages 292–306.2- R. Fekih-Salem, T. Sari and N. Abdellatif, Sur un modèle de compétition et de coexistence dans le chémostat. ARIMA, Vol. 14 (2011), pages 15-30.Actes de colloques:1- R. Fekih-Salem, N. Abdellatif, T. Sari, J. Harmand. Qualitative properties of 3-step model of anaerobic digestion including hydrolysis of particulate matter. Proceedings of the International Joint Conference CB-WR-MED Conference / 2nd AOP’ Tunisia Conference for Sustainable Water Management, Tunis, April, 24-27, (2013), pages 93-94.2- R. Fekih-Salem, N. Abdellatif, T. Sari, J. Harmand. Analyse mathématique d’un modèle de digestion anaérobie à trois étapes. CARI’2012, Proceedings of the 11th African Conference on Research in Computer Science and Applied Mathematics, Algeria, October 13-16, (2012), pages 459-466.3- R. Fekih-Salem, N. Abdellatif, T. Sari, J. Harmand. On a three step model of anaerobic digestion of solid waste. Mini-Symposium Bogaerts/Vanlmpe MATHMOD – 7th Vienna International Conference on Mathematical Modelling, F. Breitenecker, I. Troch (Eds), (2012), Volume 7, Part 1, pp. 671-676.

4- R. Fekih-Salem, T. Sari, A. Rapaport. La floculation et la coexistence dans le chémostat, TAMTAM’11, Proceedings of the 5th conference on Trends in Applied Mathematics in Tunisia, Algeria, Morocco, Sousse, 23-26 Avril 2011, Tunisia, M. Hassine and M. Moakher (Editors), Centre de Publication Universitaire (2011), pages 477-483.

5- R. Fekih-Salem, N. Abdellatif, T. Sari, J. Harmand. Sur un modèle de digestion anaérobie avec dégradation enzymatique du substrat sous forme solide, TAMTAM’11, pages 457-463.6- T. Sari, N. Abdellatif, B. Benyahia, M.L. Diagne, M. El Hajji, R. Fekih-Salem, Modélisation mathématique en biologie : compétition, coexistence et croissance, TAMTAM’11, pages 19-25.7- R. Fekih-Salem, T. Sari, N. Abdellatif. Sur un modèle de compétition et de coexistence dans le chémostat.CARI’10, Proceedings of the 10th African Conference on Research in Computer Science and Applied Mathematics, E. Badouel, A. Sbihi and I. Lokpo (Editors), INRIA (2010), pages 437-444.